Daily Papers

Generative control policies (GCPs), such as diffusion- and flow-based control policies, have emerged as effective parameterizations for robot learning. This work introduces Off-policy Generative Policy Optimization (OGPO), a sample-efficient algorithm for finetuning GCPs that maintains off-policy critic networks to maximize data reuse and propagate policy gradients through the full generative process of the policy via a modified PPO objective, using critics as the terminal reward. OGPO achieves state-of-the-art performance on manipulation tasks spanning multi-task settings, high-precision insertion, and dexterous control. To our knowledge, it is also the only method that can fine-tune poorly-initialized behavior cloning policies to near full task-success with no expert data in the online replay buffer, and does so with few task-specific hyperparameter tuning. Through extensive empirical investigations, we demonstrate that OGPO drastically outperforms methods alternatives on policy steering and learning residual corrections, and identify the key mechanisms behind its performance. We further introduce practical stabilization tricks, including success-buffer regularization, two-sided conservative advantages, and Q-variance reduction, to mitigate critic over-exploitation across state- and pixel-based settings. Beyond proposing OGPO, we conduct a systematic empirical study of GCP finetuning, identifying the stabilizing mechanisms and failure modes that govern successful off-policy full-policy improvement.

Among on-policy reinforcement learning algorithms, Proximal Policy Optimization (PPO) demonstrates is widely favored for its simplicity, numerical stability, and strong empirical performance. Standard PPO relies on surrogate objectives defined via importance ratios, which require evaluating policy likelihood that is typically straightforward when the policy is modeled as a Gaussian distribution. However, extending PPO to more expressive, high-capacity policy models such as continuous normalizing flows (CNFs), also known as flow-matching models, is challenging because likelihood evaluation along the full flow trajectory is computationally expensive and often numerically unstable. To resolve this issue, we propose PolicyFlow, a novel on-policy CNF-based reinforcement learning algorithm that integrates expressive CNF policies with PPO-style objectives without requiring likelihood evaluation along the full flow path. PolicyFlow approximates importance ratios using velocity field variations along a simple interpolation path, reducing computational overhead without compromising training stability. To further prevent mode collapse and further encourage diverse behaviors, we propose the Brownian Regularizer, an implicit policy entropy regularizer inspired by Brownian motion, which is conceptually elegant and computationally lightweight. Experiments on diverse tasks across various environments including MultiGoal, PointMaze, IsaacLab and MuJoCo Playground show that PolicyFlow achieves competitive or superior performance compared to PPO using Gaussian policies and flow-based baselines including FPO and DPPO. Notably, results on MultiGoal highlight PolicyFlow's ability to capture richer multimodal action distributions.

Reinforcement learning (RL) has recently become the core paradigm for aligning and strengthening large language models (LLMs). Yet, applying RL in off-policy settings--where stale data from past policies are used for training--improves sample efficiency, but remains challenging: policy entropy declines sharply, optimization often becomes unstable and may even collapse. Through theoretical and empirical analysis, we identify two key insights: (i) an imbalance in optimization, where negative-advantage samples dominate the policy gradient, suppressing useful behaviors and risking gradient explosions; and (ii) the derived Entropy-Clip Rule, which reveals that the fixed clipping mechanism in PPO-like objectives systematically blocks entropy-increasing updates, thereby driving the policy toward over-exploitation at the expense of exploration. Building on these insights, we propose BAlanced Policy Optimization with Adaptive Clipping (BAPO), a simple yet effective method that dynamically adjusts clipping bounds to adaptively re-balance positive and negative contributions, preserve entropy, and stabilize RL optimization. Across diverse off-policy scenarios--including sample replay and partial rollout--BAPO achieves fast, stable, and data-efficient training. On AIME 2024 and AIME 2025 benchmarks, our 7B BAPO model surpasses open-source counterparts such as SkyWork-OR1-7B, while our 32B BAPO model not only achieves state-of-the-art results among models of the same scale but also outperforms leading proprietary systems like o3-mini and Gemini-2.5-Flash-Thinking.

Advantage Actor-critic (A2C) and Proximal Policy Optimization (PPO) are popular deep reinforcement learning algorithms used for game AI in recent years. A common understanding is that A2C and PPO are separate algorithms because PPO's clipped objective appears significantly different than A2C's objective. In this paper, however, we show A2C is a special case of PPO. We present theoretical justifications and pseudocode analysis to demonstrate why. To validate our claim, we conduct an empirical experiment using Stable-baselines3, showing A2C and PPO produce the exact same models when other settings are controlled.

On-policy Reinforcement Learning (RL) with PPO-like clip objectives has become the standard choice for reward-based fine-tuning of large language models (LLMs). Although recent work has explored improved estimators of advantages and normalization, the clipping mechanism itself has remained untouched. Originally introduced as a proxy for principled KL-based trust regions, clipping is a crude approximation that often causes unstable updates and suboptimal performance. We replace the clip objective with a novel discrete differentiable trust region projection, which provides principled token-level KL constraints. The projection operates on a sparse subset of the model's most important token logits to balance computational cost and projection effectiveness. Our approach, Trust Region Optimization for Large Language Models (TROLL), serves as a direct replacement for PPO-like clipping during training and does not alter the model's inference behavior. Across datasets, model families, and advantage-estimation methods, TROLL consistently outperforms PPO-like clipping in terms of training speed, stability, and final success rates.

Reinforcement learning fine-tuning (RLFT) is a dominant paradigm for improving pretrained policies for downstream tasks. These pretrained policies, trained on large datasets, produce generations with a broad range of promising but unrefined behaviors. Often, a critical failure mode of RLFT arises when policies lose this diversity and collapse into a handful of easily exploitable outputs. This convergence hinders exploration, which is essential for expanding the capabilities of the pretrained policy and for amplifying the benefits of test-time compute scaling. To address this, we introduce an objective for policy gradient methods that explicitly enforces the exploration and refinement of diverse generations, which we call a polychromic objective. We then show how proximal policy optimization (PPO) can be adapted to optimize this objective. Our method (1) employs vine sampling to collect on-policy rollouts and (2) modifies the advantage function to reflect the advantage under our new objective. Experiments on BabyAI, Minigrid, and Algorithmic Creativity show that our method improves success rates by reliably solving a larger set of environment configurations and generalizes better under large perturbations. Moreover, when given multiple attempts in pass@k experiments, the policy achieves substantially higher coverage, demonstrating its ability to maintain and exploit a diverse repertoire of strategies.

Large language models (LLMs) have formulated a blueprint for the advancement of artificial general intelligence. Its primary objective is to function as a human-centric (helpful, honest, and harmless) assistant. Alignment with humans assumes paramount significance, and reinforcement learning with human feedback (RLHF) emerges as the pivotal technological paradigm underpinning this pursuit. Current technical routes usually include reward models to measure human preferences, Proximal Policy Optimization (PPO) to optimize policy model outputs, and process supervision to improve step-by-step reasoning capabilities. However, due to the challenges of reward design, environment interaction, and agent training, coupled with huge trial and error cost of large language models, there is a significant barrier for AI researchers to motivate the development of technical alignment and safe landing of LLMs. The stable training of RLHF has still been a puzzle. In the first report, we dissect the framework of RLHF, re-evaluate the inner workings of PPO, and explore how the parts comprising PPO algorithms impact policy agent training. We identify policy constraints being the key factor for the effective implementation of the PPO algorithm. Therefore, we explore the PPO-max, an advanced version of PPO algorithm, to efficiently improve the training stability of the policy model. Based on our main results, we perform a comprehensive analysis of RLHF abilities compared with SFT models and ChatGPT. The absence of open-source implementations has posed significant challenges to the investigation of LLMs alignment. Therefore, we are eager to release technical reports, reward models and PPO codes

Aligning large language models (LLMs) with human values and safety constraints is challenging, especially when objectives like helpfulness, truthfulness, and avoidance of harm conflict. Reinforcement Learning from Human Feedback (RLHF) has achieved notable success in steering models, but is complex and can be unstable. Recent approaches such as Direct Preference Optimization (DPO) simplify preference-based fine-tuning but may introduce bias or trade-off certain objectives~dpo. In this work, we propose a Group Relative Policy Optimization (GRPO) framework with a multi-label reward regression model to achieve safe and aligned language generation. The GRPO algorithm optimizes a policy by comparing groups of sampled responses, eliminating the need for a separate value critic and improving training efficiency~grpo. We train a reward model to predict multiple alignment scores (e.g., safety, helpfulness, etc.), which are combined into a single reward signal. We provide a theoretical derivation for using this learned multi-aspect reward within GRPO and discuss its advantages and limitations. Empirically, our approach improves all the safety and quality metrics evaluated in language generation tasks on model scales (0.5B, 7B, and 14B parameters), demonstrating a robust balance of objectives. We compare GRPO to PPO-based RLHF and DPO, highlighting that GRPO achieves alignment with significantly lower computational cost and explicit multi-objective handling. \textbf{We will open-source all trained models at https://huggingface.co/hydroxai.

Multi-objective reinforcement learning (MORL) seeks to learn policies that balance multiple, often conflicting objectives. Although a single preference-conditioned policy is the most flexible and scalable solution, existing approaches remain brittle in practice, frequently failing to recover complete Pareto fronts. We show that this failure stems from two structural issues in current methods: destructive gradient interference caused by premature scalarization and representational collapse across the preference space. We introduce D^3PO, a PPO-based framework that reorganizes multi-objective policy optimization to address these issues directly. D^3PO preserves per-objective learning signals through a decomposed optimization pipeline and integrates preferences only after stabilization, enabling reliable credit assignment. In addition, a scaled diversity regularizer enforces sensitivity of policy behavior to preference changes, preventing collapse. Across standard MORL benchmarks, including high-dimensional and many-objective control tasks, D^3PO consistently discovers broader and higher-quality Pareto fronts than prior single- and multi-policy methods, matching or exceeding state-of-the-art hypervolume and expected utility while using a single deployable policy.

The Unrelated Parallel Machine Scheduling Problem (UPMSP) with release dates, setups, and eligibility constraints presents a significant multi-objective challenge. Traditional methods struggle to balance minimizing Total Weighted Tardiness (TWT) and Total Setup Time (TST). This paper proposes a Deep Reinforcement Learning framework using Proximal Policy Optimization (PPO) and a Graph Neural Network (GNN). The GNN effectively represents the complex state of jobs, machines, and setups, allowing the PPO agent to learn a direct scheduling policy. Guided by a multi-objective reward function, the agent simultaneously minimizes TWT and TST. Experimental results on benchmark instances demonstrate that our PPO-GNN agent significantly outperforms a standard dispatching rule and a metaheuristic, achieving a superior trade-off between both objectives. This provides a robust and scalable solution for complex manufacturing scheduling.

Temporal credit assignment in reinforcement learning is often approached by introducing value estimates at multiple discount factors. A natural next step is to let the actor dynamically route among these temporal heads, using either differentiable attention or heuristic uncertainty weights. This paper argues that such routing can create a numerical shortcut rather than a reliable temporal abstraction. We study this issue in a controlled PPO setting on LunarLander-v2, using the environment as a visual sandbox for diagnosing failure modes. First, we formalize Surrogate Objective Hacking: a differentiable softmax router exposed to the PPO surrogate receives a direct gradient toward advantage heads that are numerically favorable for the current update, even when this routing change does not correspond to improved physical control. Because unnormalized advantages at different discount factors have different effective scales, this creates a scale-discrepancy vulnerability. Second, we identify the Paradox of Temporal Uncertainty in gradient-free error-based routing: short-horizon heads can receive the largest routing share because their prediction targets are easier, even when they are less aligned with delayed task success. As a structural response, we study Target Decoupling: the critic may retain multi-timescale auxiliary heads, but the actor is updated only with the long-horizon advantage. Target Decoupling is not presented as a broad performance booster; in this run set it removes the exploitable actor-side routing pathway and improves the observed worst-seed return. Code is available at https://github.com/ben-dlwlrma/Representation-Over-Routing.

Policy-based reinforcement learning algorithms are widely used in various fields. Among them, mainstream policy optimization algorithms such as TRPO and PPO introduce importance sampling into policy iteration, which allows the reuse of historical data. However, this can also lead to a high variance of the surrogate objective and indirectly affects the stability and convergence of the algorithm. In this paper, we first derived an upper bound of the surrogate objective variance, which can grow quadratically with the increase of the surrogate objective. Next, we proposed the dropout technique to avoid the excessive increase of the surrogate objective variance caused by importance sampling. Then, we introduced a general reinforcement learning framework applicable to mainstream policy optimization methods, and applied the dropout technique to the PPO algorithm to obtain the D-PPO variant. Finally, we conduct comparative experiments between D-PPO and PPO algorithms in the Atari 2600 environment, and the results show that D-PPO achieved significant performance improvements compared to PPO, and effectively limited the excessive increase of the surrogate objective variance during training.

Plateaus, where an agent's performance stagnates at a suboptimal level, are a common problem in deep on-policy RL. Focusing on PPO due to its widespread adoption, we show that plateaus in certain regimes arise not because of known exploration, capacity, or optimization challenges, but because sample-based estimates of the loss eventually become poor proxies for the true objective over the course of training. As a recap, PPO switches between sampling rollouts from several parallel environments online using the current policy (which we call the outer loop) and performing repeated minibatch SGD steps against this offline dataset (the inner loop). In our work we consider only the outer loop, and conceptually model it as stochastic optimization. The step size is then controlled by the regularization strength towards the previous policy and the gradient noise by the number of samples collected between policy update steps. This model predicts that performance will plateau at a suboptimal level if the outer step size is too large relative to the noise. Recasting PPO in this light makes it clear that there are two ways to address this particular type of learning stagnation: either reduce the step size or increase the number of samples collected between updates. We first validate the predictions of our model and investigate how hyperparameter choices influence the step size and update noise, concluding that increasing the number of parallel environments is a simple and robust way to reduce both factors. Next, we propose a recipe for how to co-scale the other hyperparameters when increasing parallelization, and show that incorrectly doing so can lead to severe performance degradation. Finally, we vastly outperform prior baselines in a complex open-ended domain by scaling PPO to more than 1M parallel environments, thereby enabling monotonic performance improvement up to one trillion transitions.

While large language models demonstrate remarkable capabilities, they often present challenges in terms of safety, alignment with human values, and stability during training. Here, we focus on two prevalent methods used to align these models, Supervised Fine-Tuning (SFT) and Reinforcement Learning from Human Feedback (RLHF). SFT is simple and robust, powering a host of open-source models, while RLHF is a more sophisticated method used in top-tier models like ChatGPT but also suffers from instability and susceptibility to reward hacking. We propose a novel approach, Supervised Iterative Learning from Human Feedback (SuperHF), which seeks to leverage the strengths of both methods. Our hypothesis is two-fold: that the reward model used in RLHF is critical for efficient data use and model generalization and that the use of Proximal Policy Optimization (PPO) in RLHF may not be necessary and could contribute to instability issues. SuperHF replaces PPO with a simple supervised loss and a Kullback-Leibler (KL) divergence prior. It creates its own training data by repeatedly sampling a batch of model outputs and filtering them through the reward model in an online learning regime. We then break down the reward optimization problem into three components: robustly optimizing the training rewards themselves, preventing reward hacking-exploitation of the reward model that degrades model performance-as measured by a novel METEOR similarity metric, and maintaining good performance on downstream evaluations. Our experimental results show SuperHF exceeds PPO-based RLHF on the training objective, easily and favorably trades off high reward with low reward hacking, improves downstream calibration, and performs the same on our GPT-4 based qualitative evaluation scheme all the while being significantly simpler to implement, highlighting SuperHF's potential as a competitive language model alignment technique.

We propose a new family of policy gradient methods for reinforcement learning, which alternate between sampling data through interaction with the environment, and optimizing a "surrogate" objective function using stochastic gradient ascent. Whereas standard policy gradient methods perform one gradient update per data sample, we propose a novel objective function that enables multiple epochs of minibatch updates. The new methods, which we call proximal policy optimization (PPO), have some of the benefits of trust region policy optimization (TRPO), but they are much simpler to implement, more general, and have better sample complexity (empirically). Our experiments test PPO on a collection of benchmark tasks, including simulated robotic locomotion and Atari game playing, and we show that PPO outperforms other online policy gradient methods, and overall strikes a favorable balance between sample complexity, simplicity, and wall-time.

Reinforcement learning (RL)-based fine-tuning has emerged as a powerful approach for aligning diffusion models with black-box objectives. Proximal policy optimization (PPO) is the most popular choice of method for policy optimization. While effective in terms of performance, PPO is highly sensitive to hyper-parameters and involves substantial computational overhead. REINFORCE, on the other hand, mitigates some computational complexities such as high memory overhead and sensitive hyper-parameter tuning, but has suboptimal performance due to high-variance and sample inefficiency. While the variance of the REINFORCE can be reduced by sampling multiple actions per input prompt and using a baseline correction term, it still suffers from sample inefficiency. To address these challenges, we systematically analyze the efficiency-effectiveness trade-off between REINFORCE and PPO, and propose leave-one-out PPO (LOOP), a novel RL for diffusion fine-tuning method. LOOP combines variance reduction techniques from REINFORCE, such as sampling multiple actions per input prompt and a baseline correction term, with the robustness and sample efficiency of PPO via clipping and importance sampling. Our results demonstrate that LOOP effectively improves diffusion models on various black-box objectives, and achieves a better balance between computational efficiency and performance.

During the last stage of RLHF, a large language model is aligned to human intents via PPO training, a process that generally requires large-scale computational resources. In this technical report, we empirically investigate an efficient implementation of RLHF using low-rank adaptation (LoRA), which allows us to align the LLaMA 7B checkpoint on the Alpaca dataset using only two A100 GPUs instead of the eight required for full model fine-tuning. Despite tuning only 0.2% of LLaMA 7B's parameters, our implementation achieves better performance than the publicly-released AlpacaFarm checkpoint with full model fine-tuning. Next, we analyze several configurations of our LoRA-based PPO implementation, varying the form of the KL regularization term in the training objective. We find that (1) removing this penalty term does not harm performance on the AlpacaFarm evaluation set under our LoRA setup; (2) other regularizers, such as Jensen-Shannon divergence, lead to improved performance; and (3) while PPO training negatively impacts the factuality of model-generated responses, training with LoRA largely mitigates this effect. We release our code and pretrained checkpoints to facilitate future research on more efficient RLHF.

Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL -- guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher--old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

Speculative decoding accelerates large language model (LLM) inference by letting a lightweight draft model propose multiple tokens that the target model verifies in parallel. Yet existing training objectives optimize only a single greedy draft path, while decoding follows a tree policy that re-ranks and verifies multiple branches. This draft policy misalignment limits achievable speedups. We introduce Group Tree Optimization (GTO), which aligns training with the decoding-time tree policy through two components: (i) Draft Tree Reward, a sampling-free objective equal to the expected acceptance length of the draft tree under the target model, directly measuring decoding performance; (ii) Group-based Draft Policy Training, a stable optimization scheme that contrasts trees from the current and a frozen reference draft model, forming debiased group-standardized advantages and applying a PPO-style surrogate along the longest accepted sequence for robust updates. We further prove that increasing our Draft Tree Reward provably improves acceptance length and speedup. Across dialogue (MT-Bench), code (HumanEval), and math (GSM8K), and multiple LLMs (e.g., LLaMA-3.1-8B, LLaMA-3.3-70B, Vicuna-1.3-13B, DeepSeek-R1-Distill-LLaMA-8B, Qwen3-8B), GTO increases acceptance length by (7.4%) and yields an additional (7.7%) speedup over prior state-of-the-art EAGLE-3. By bridging draft policy misalignment, GTO offers a practical, general solution for efficient LLM inference. Code and draft models are available at https://github.com/hsj576/GTO.

Reinforcement learning from human feedback (RLHF) is a standard approach for fine-tuning large language models to follow instructions. As part of this process, learned reward models are used to approximately model human preferences. However, as imperfect representations of the "true" reward, these learned reward models are susceptible to overoptimization. Gao et al. (2023) studied this phenomenon in a synthetic human feedback setup with a significantly larger "gold" reward model acting as the true reward (instead of humans) and showed that overoptimization remains a persistent problem regardless of the size of the proxy reward model and training data used. Using a similar setup, we conduct a systematic study to evaluate the efficacy of using ensemble-based conservative optimization objectives, specifically worst-case optimization (WCO) and uncertainty-weighted optimization (UWO), for mitigating reward model overoptimization when using two optimization methods: (a) best-of-n sampling (BoN) (b) proximal policy optimization (PPO). We additionally extend the setup of Gao et al. (2023) to include 25% label noise to better mirror real-world conditions. Both with and without label noise, we find that conservative optimization practically eliminates overoptimization and improves performance by up to 70% for BoN sampling. For PPO, ensemble-based conservative optimization always reduces overoptimization and outperforms single reward model optimization. Moreover, combining it with a small KL penalty successfully prevents overoptimization at no performance cost. Overall, our results demonstrate that ensemble-based conservative optimization can effectively counter overoptimization.

Reinforcement learning (RL) is pivotal for enabling large language models (LLMs) to generate long chains of thought (CoT) for complex tasks like math and reasoning. However, Proximal Policy Optimization (PPO), effective in many RL scenarios, fails in long CoT tasks. This paper identifies that value initialization bias and reward signal decay are the root causes of PPO's failure. We propose Value-Calibrated PPO (VC-PPO) to address these issues. In VC-PPO, the value model is pretrained to tackle initialization bias, and the Generalized Advantage Estimation (GAE) computation is decoupled between the actor and critic to mitigate reward signal decay. Experiments on the American Invitational Mathematics Examination (AIME) show that VC-PPO significantly boosts PPO performance. Ablation studies show that techniques in VC-PPO are essential in enhancing PPO for long CoT tasks.

Proximal Policy Optimization (PPO) is a ubiquitous on-policy reinforcement learning algorithm but is significantly less utilized than off-policy learning algorithms in multi-agent settings. This is often due to the belief that PPO is significantly less sample efficient than off-policy methods in multi-agent systems. In this work, we carefully study the performance of PPO in cooperative multi-agent settings. We show that PPO-based multi-agent algorithms achieve surprisingly strong performance in four popular multi-agent testbeds: the particle-world environments, the StarCraft multi-agent challenge, Google Research Football, and the Hanabi challenge, with minimal hyperparameter tuning and without any domain-specific algorithmic modifications or architectures. Importantly, compared to competitive off-policy methods, PPO often achieves competitive or superior results in both final returns and sample efficiency. Finally, through ablation studies, we analyze implementation and hyperparameter factors that are critical to PPO's empirical performance, and give concrete practical suggestions regarding these factors. Our results show that when using these practices, simple PPO-based methods can be a strong baseline in cooperative multi-agent reinforcement learning. Source code is released at https://github.com/marlbenchmark/on-policy.

Following the success of Proximal Policy Optimization (PPO) for Reinforcement Learning from Human Feedback (RLHF), new techniques such as Sequence Likelihood Calibration (SLiC) and Direct Policy Optimization (DPO) have been proposed that are offline in nature and use rewards in an indirect manner. These techniques, in particular DPO, have recently become the tools of choice for LLM alignment due to their scalability and performance. However, they leave behind important features of the PPO approach. Methods such as SLiC or RRHF make use of the Reward Model (RM) only for ranking/preference, losing fine-grained information and ignoring the parametric form of the RM (eg., Bradley-Terry, Plackett-Luce), while methods such as DPO do not use even a separate reward model. In this work, we propose a novel approach, named BRAIn, that re-introduces the RM as part of a distribution matching approach.BRAIn considers the LLM distribution conditioned on the assumption of output goodness and applies Bayes theorem to derive an intractable posterior distribution where the RM is explicitly represented. BRAIn then distills this posterior into an amortized inference network through self-normalized importance sampling, leading to a scalable offline algorithm that significantly outperforms prior art in summarization and AntropicHH tasks. BRAIn also has interesting connections to PPO and DPO for specific RM choices.

We seek to identify the most relevant benefits offered by Medicare Advantage Health Plans that drive membership and market share. As an example, we explore plans operating in a single county in New Jersey between 2018 and 2023. A dataset of benefits from publicly available data sources was created and the variance inflation factor was applied to identify the correlation between the extracted features, to avoid multicollinearity and overparameterization problems. We categorized the variable Market Share and used it as a multinomial response variable with three categories: less than 0.3\%, 0.3\% to 1.5\%, and over 1.5\%. Categories were chosen to achieve approximately uniform distribution of plans (47, 60, and 65 respectively). We built a multinomial Lasso model using 5-fold cross-validation to tune the penalty parameter. Lasso forced some features to be dropped from the model, which reduces the risk of overfitting and increases the interpretability of the results. For each category, important variables are different. Certain brands drive market share, as do PPO plans and prescription drug coverage. Benefits, particularly ancillary benefits that are not part of CMS's required benefits, appear to have little influence, while financial terms such as deductibles, copays, and out-of-pocket limits are associated with higher market share. Finally, we evaluated the predictive accuracy of the Lasso model with the test set. The accuracy is 0.76.

This paper presents Post-Decision Proximal Policy Optimization (PDPPO), a novel variation of the leading deep reinforcement learning method, Proximal Policy Optimization (PPO). The PDPPO state transition process is divided into two steps: a deterministic step resulting in the post-decision state and a stochastic step leading to the next state. Our approach incorporates post-decision states and dual critics to reduce the problem's dimensionality and enhance the accuracy of value function estimation. Lot-sizing is a mixed integer programming problem for which we exemplify such dynamics. The objective of lot-sizing is to optimize production, delivery fulfillment, and inventory levels in uncertain demand and cost parameters. This paper evaluates the performance of PDPPO across various environments and configurations. Notably, PDPPO with a dual critic architecture achieves nearly double the maximum reward of vanilla PPO in specific scenarios, requiring fewer episode iterations and demonstrating faster and more consistent learning across different initializations. On average, PDPPO outperforms PPO in environments with a stochastic component in the state transition. These results support the benefits of using a post-decision state. Integrating this post-decision state in the value function approximation leads to more informed and efficient learning in high-dimensional and stochastic environments.

Large Language Models (LLMs) can acquire extensive world knowledge through pre-training on large corpora. However, due to exposure to low-quality data, LLMs may exhibit harmful behavior without aligning with human values. The dominant approach for steering LLMs towards beneficial behavior involves Reinforcement Learning with Human Feedback (RLHF), with Proximal Policy Optimization (PPO) serving as the default RL optimizer. Despite its effectiveness, PPO has limitations when optimizing rewards trained from comparison-based loss. Primarily, PPO is not invariant to equivalent reward functions containing identical preference information due to the need to calibrate the reward scale. Additionally, PPO's necessity for token-wise updates introduces complexity in both function approximation and algorithm design compared to trajectory-wise optimization. This paper proposes a new framework, reinforcement learning with relative feedback, and a novel trajectory-wise policy gradient algorithm, Pairwise Proximal Policy Optimization (P3O) that operates directly on comparative rewards. We show theoretically that P3O is invariant to equivalent rewards and avoids the complexity of PPO. Empirical evaluations demonstrate that P3O outperforms PPO in the KL-Reward trade-off and can align with human preferences as well as or better than prior methods. In summary, this work introduces a simpler yet effective approach for aligning LLMs to human preferences through relative feedback.

Reinforcement learning (RL) agents need to explore their environments in order to learn optimal policies. In many environments and tasks, safety is of critical importance. The widespread use of simulators offers a number of advantages, including safe exploration which will be inevitable in cases when RL systems need to be trained directly in the physical environment (e.g. in human-robot interaction). The popular Safety Gym library offers three mobile agent types that can learn goal-directed tasks while considering various safety constraints. In this paper, we extend the applicability of safe RL algorithms by creating a customized environment with Panda robotic arm where Safety Gym algorithms can be tested. We performed pilot experiments with the popular PPO algorithm comparing the baseline with the constrained version and show that the constrained version is able to learn the equally good policy while better complying with safety constraints and taking longer training time as expected.

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning LLMs.

Reinforcement Learning from Human Feedback (RLHF) is currently the most widely used method to align large language models (LLMs) with human preferences. Existing RLHF methods can be roughly categorized as either reward-based or reward-free. Novel applications such as ChatGPT and Claude leverage reward-based methods that first learn a reward model and apply actor-critic algorithms, such as Proximal Policy Optimization (PPO). However, in academic benchmarks, state-of-the-art results are often achieved via reward-free methods, such as Direct Preference Optimization (DPO). Is DPO truly superior to PPO? Why does PPO perform poorly on these benchmarks? In this paper, we first conduct both theoretical and empirical studies on the algorithmic properties of DPO and show that DPO may have fundamental limitations. Moreover, we also comprehensively examine PPO and reveal the key factors for the best performances of PPO in fine-tuning LLMs. Finally, we benchmark DPO and PPO across various a collection of RLHF testbeds, ranging from dialogue to code generation. Experiment results demonstrate that PPO is able to surpass other alignment methods in all cases and achieve state-of-the-art results in challenging code competitions.

Health economic evaluations are sensitive to the choice of analytical perspective (e.g., health system vs. societal). While guidelines often recommend specific perspectives, the uncertainty associated with this choice - and the potential decision discordance it creates - is rarely quantified. We present vop_poc_nz, a Python package that implements a framework for Distributional Cost-Effectiveness Analysis (DCEA) and operationalizes the quantification of perspective uncertainty through the Value of Perspective (VoP) metric. The package provides tools for Markov modeling, probabilistic sensitivity analysis, value of information analysis, and equity impact assessment. Unlike existing tools that treat perspective as a fixed input, vop_poc_nz allows for the simultaneous evaluation of multiple perspectives. This enables decision-makers to estimate the opportunity cost of perspective misalignment. We demonstrate the package's capabilities using case studies from Aotearoa New Zealand.

We introduce Diffusion Policy Policy Optimization, DPPO, an algorithmic framework including best practices for fine-tuning diffusion-based policies (e.g. Diffusion Policy) in continuous control and robot learning tasks using the policy gradient (PG) method from reinforcement learning (RL). PG methods are ubiquitous in training RL policies with other policy parameterizations; nevertheless, they had been conjectured to be less efficient for diffusion-based policies. Surprisingly, we show that DPPO achieves the strongest overall performance and efficiency for fine-tuning in common benchmarks compared to other RL methods for diffusion-based policies and also compared to PG fine-tuning of other policy parameterizations. Through experimental investigation, we find that DPPO takes advantage of unique synergies between RL fine-tuning and the diffusion parameterization, leading to structured and on-manifold exploration, stable training, and strong policy robustness. We further demonstrate the strengths of DPPO in a range of realistic settings, including simulated robotic tasks with pixel observations, and via zero-shot deployment of simulation-trained policies on robot hardware in a long-horizon, multi-stage manipulation task. Website with code: diffusion-ppo.github.io

Inference-time search algorithms such as Monte-Carlo Tree Search (MCTS) may seem unnecessary when generating natural language text based on state-of-the-art reinforcement learning such as Proximal Policy Optimization (PPO). In this paper, we demonstrate that it is possible to get extra mileage out of PPO by integrating MCTS on top. The key idea is not to throw out the value network, a byproduct of PPO training for evaluating partial output sequences, when decoding text out of the policy network. More concretely, we present a novel value-guided decoding algorithm called PPO-MCTS, which can integrate the value network from PPO to work closely with the policy network during inference-time generation. Compared to prior approaches based on MCTS for controlled text generation, the key strength of our approach is to reduce the fundamental mismatch of the scoring mechanisms of the partial outputs between training and test. Evaluation on four text generation tasks demonstrate that PPO-MCTS greatly improves the preferability of generated text compared to the standard practice of using only the PPO policy. Our results demonstrate the promise of search algorithms even on top of the aligned language models from PPO, and the under-explored benefit of the value network.

Learning from preference feedback has emerged as an essential step for improving the generation quality and performance of modern language models (LMs). Despite its widespread use, the way preference-based learning is applied varies wildly, with differing data, learning algorithms, and evaluations used, making disentangling the impact of each aspect difficult. In this work, we identify four core aspects of preference-based learning: preference data, learning algorithm, reward model, and policy training prompts, systematically investigate the impact of these components on downstream model performance, and suggest a recipe for strong learning for preference feedback. Our findings indicate that all aspects are important for performance, with better preference data leading to the largest improvements, followed by the choice of learning algorithm, the use of improved reward models, and finally the use of additional unlabeled prompts for policy training. Notably, PPO outperforms DPO by up to 2.5% in math and 1.2% in general domains. High-quality preference data leads to improvements of up to 8% in instruction following and truthfulness. Despite significant gains of up to 5% in mathematical evaluation when scaling up reward models, we surprisingly observe marginal improvements in other categories. We publicly release the code used for training (https://github.com/hamishivi/EasyLM) and evaluating (https://github.com/allenai/open-instruct) our models, along with the models and datasets themselves (https://huggingface.co/collections/allenai/tulu-v25-suite-66676520fd578080e126f618).

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.

The reward hypothesis posits that, "all of what we mean by goals and purposes can be well thought of as maximization of the expected value of the cumulative sum of a received scalar signal (reward)." We aim to fully settle this hypothesis. This will not conclude with a simple affirmation or refutation, but rather specify completely the implicit requirements on goals and purposes under which the hypothesis holds.

Recent advances in large language models (LLMs) have shown strong reasoning capabilities through large-scale pretraining and post-training reinforcement learning, demonstrated by DeepSeek-R1. However, current post-training methods, such as Grouped Relative Policy Optimization (GRPO), mainly reward correctness, which is not aligned with the multi-dimensional objectives required in high-stakes fields such as medicine, where reasoning must also be faithful and comprehensive. We introduce Clinical-Objective Relative Policy Optimization (CRPO), a scalable, multi-objective, verifiable reinforcement learning method designed to align LLM post-training with clinical reasoning principles. CRPO integrates rule-based and verifiable reward signals that jointly optimize accuracy, faithfulness, and comprehensiveness without relying on human annotation. To demonstrate its effectiveness, we train Clinical-R1-3B, a 3B-parameter model for clinical reasoning. The experiments on three benchmarks demonstrate that our CRPO substantially improves reasoning on truthfulness and completeness over standard GRPO while maintaining comfortable accuracy enhancements. This framework provides a scalable pathway to align LLM reasoning with clinical objectives, enabling safer and more collaborative AI systems for healthcare while also highlighting the potential of multi-objective, verifiable RL methods in post-training scaling of LLMs for medical domains.

We investigate reinforcement learning (RL) for privileged planning in autonomous driving. State-of-the-art approaches for this task are rule-based, but these methods do not scale to the long tail. RL, on the other hand, is scalable and does not suffer from compounding errors like imitation learning. Contemporary RL approaches for driving use complex shaped rewards that sum multiple individual rewards, \eg~progress, position, or orientation rewards. We show that PPO fails to optimize a popular version of these rewards when the mini-batch size is increased, which limits the scalability of these approaches. Instead, we propose a new reward design based primarily on optimizing a single intuitive reward term: route completion. Infractions are penalized by terminating the episode or multiplicatively reducing route completion. We find that PPO scales well with higher mini-batch sizes when trained with our simple reward, even improving performance. Training with large mini-batch sizes enables efficient scaling via distributed data parallelism. We scale PPO to 300M samples in CARLA and 500M samples in nuPlan with a single 8-GPU node. The resulting model achieves 64 DS on the CARLA longest6 v2 benchmark, outperforming other RL methods with more complex rewards by a large margin. Requiring only minimal adaptations from its use in CARLA, the same method is the best learning-based approach on nuPlan. It scores 91.3 in non-reactive and 90.6 in reactive traffic on the Val14 benchmark while being an order of magnitude faster than prior work.

Recent advancements in reinforcement learning from human feedback have shown that utilizing fine-grained token-level reward models can substantially enhance the performance of Proximal Policy Optimization (PPO) in aligning large language models. However, it is challenging to leverage such token-level reward as guidance for Direct Preference Optimization (DPO), since DPO is formulated as a sequence-level bandit problem. To address this challenge, this work decomposes the sequence-level PPO into a sequence of token-level proximal policy optimization problems and then frames the problem of token-level PPO with token-level reward guidance, from which closed-form optimal token-level policy and the corresponding token-level reward can be derived. Using the obtained reward and Bradley-Terry model, this work establishes a framework of computable loss functions with token-level reward guidance for DPO, and proposes a practical reward guidance based on the induced DPO reward. This formulation enables different tokens to exhibit varying degrees of deviation from reference policy based on their respective rewards. Experiment results demonstrate that our method achieves substantial performance improvements over DPO, with win rate gains of up to 7.5 points on MT-Bench, 6.2 points on AlpacaEval 2, and 4.3 points on Arena-Hard. Code is available at https://github.com/dvlab-research/TGDPO.

Proximal Policy Optimization (PPO)-based Reinforcement Learning from Human Feedback (RLHF) is essential for aligning large language models (LLMs) with human preferences. It requires joint training of an actor and critic with a pretrained, fixed reward model for guidance. This approach increases computational complexity and instability due to actor-critic interdependence. Additionally, PPO lacks access to true environment rewards in LLM tasks, limiting its adaptability. Under such conditions, pretraining a value model or a reward model becomes equivalent, as both provide fixed supervisory signals without new ground-truth feedback. To address these issues, we propose Decoupled Value Policy Optimization (DVPO), a lean framework that replaces traditional reward modeling with a pretrained global value model (GVM). The GVM is conditioned on policy trajectories and predicts token-level return-to-go estimates. By decoupling value model from policy training (via frozen GVM-driven RL objectives), DVPO eliminates actor-critic interdependence, reducing GPU memory usage by 40\% and training time by 35\% compared to conventional RLHF. Experiments across benchmarks show DVPO outperforms efficient RLHF methods (e.g., DPO) while matching state-of-the-art PPO in performance.

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by {\it general utilities}, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and κ-hop neighbor truncation under a form of correlation decay property, where κ is the communication radius. In the exact setting, our algorithm converges to a first-order stationary point (FOSP) at the rate of Oleft(T^{-2/3}right). In the sample-based setting, we demonstrate that, with high probability, our algorithm requires mathcal{O}left(ε^{-3.5}right) samples to achieve an ε-FOSP with an approximation error of O(φ_0^{2κ}), where φ_0in (0,1). Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.

Reinforcement learning from human feedback (RLHF) has emerged as a reliable approach to aligning large language models (LLMs) to human preferences. Among the plethora of RLHF techniques, proximal policy optimization (PPO) is of the most widely used methods. Despite its popularity, however, PPO may suffer from mode collapse, instability, and poor sample efficiency. We show that these issues can be alleviated by a novel algorithm that we refer to as Advantage-Induced Policy Alignment (APA), which leverages a squared error loss function based on the estimated advantages. We demonstrate empirically that APA consistently outperforms PPO in language tasks by a large margin, when a separate reward model is employed as the evaluator. In addition, compared with PPO, APA offers a more stable form of control over the deviation from the model's initial policy, ensuring that the model improves its performance without collapsing to deterministic output. In addition to empirical results, we also provide a theoretical justification supporting the design of our loss function.

Given a set of trajectories demonstrating the execution of a task safely in a constrained MDP with observable rewards but with unknown constraints and non-observable costs, we aim to find a policy that maximizes the likelihood of demonstrated trajectories trading the balance between being conservative and increasing significantly the likelihood of high-rewarding trajectories but with potentially unsafe steps. Having these objectives, we aim towards learning a policy that maximizes the probability of the most promising trajectories with respect to the demonstrations. In so doing, we formulate the ``promise" of individual state-action pairs in terms of Q values, which depend on task-specific rewards as well as on the assessment of states' safety, mixing expectations in terms of rewards and safety. This entails a safe Q-learning perspective of the inverse learning problem under constraints: The devised Safe Q Inverse Constrained Reinforcement Learning (SafeQIL) algorithm is compared to state-of-the art inverse constraint reinforcement learning algorithms to a set of challenging benchmark tasks, showing its merits.

In the classical Reinforcement Learning from Human Feedback (RLHF) framework, Proximal Policy Optimization (PPO) is employed to learn from sparse, sentence-level rewards -- a challenging scenario in traditional deep reinforcement learning. Despite the great successes of PPO in the alignment of state-of-the-art closed-source large language models (LLMs), its open-source implementation is still largely sub-optimal, as widely reported by numerous research studies. To address these issues, we introduce a framework that models RLHF problems as a Markov decision process (MDP), enabling the capture of fine-grained token-wise information. Furthermore, we provide theoretical insights that demonstrate the superiority of our MDP framework over the previous sentence-level bandit formulation. Under this framework, we introduce an algorithm, dubbed as Reinforced Token Optimization (RTO), which learns the token-wise reward function from preference data and performs policy optimization based on this learned token-wise reward signal. Theoretically, RTO is proven to have the capability of finding the near-optimal policy sample-efficiently. For its practical implementation, RTO innovatively integrates Direct Preference Optimization (DPO) and PPO. DPO, originally derived from sparse sentence rewards, surprisingly provides us with a token-wise characterization of response quality, which is seamlessly incorporated into our subsequent PPO training stage. Extensive real-world alignment experiments verify the effectiveness of the proposed approach.

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO's approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

Reinforcement learning (RL) has re-emerged as a natural approach for training interactive LLM agents in real-world environments. However, directly applying the widely used Group Relative Policy Optimization (GRPO) algorithm to multi-turn tasks exposes notable limitations, particularly in scenarios requiring long-horizon reasoning. To address these challenges, we investigate more stable and effective advantage estimation strategies, especially for multi-turn settings. We first explore Proximal Policy Optimization (PPO) as an alternative and find it to be more robust than GRPO. To further enhance PPO in multi-turn scenarios, we introduce turn-PPO, a variant that operates on a turn-level MDP formulation, as opposed to the commonly used token-level MDP. Our results on the WebShop and Sokoban datasets demonstrate the effectiveness of turn-PPO, both with and without long reasoning components.

We consider the problem of locating a facility to serve a set of agents located along a line. The Nash welfare objective function, defined as the product of the agents' utilities, is known to provide a compromise between fairness and efficiency in resource allocation problems. We apply this welfare notion to the facility location problem, converting individual costs to utilities and analyzing the facility placement that maximizes the Nash welfare. We give a polynomial-time approximation algorithm to compute this facility location, and prove results suggesting that it achieves a good balance of fairness and efficiency. Finally, we take a mechanism design perspective and propose a strategy-proof mechanism with a bounded approximation ratio for Nash welfare.

To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that typically look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO. Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose LamPO, a Lambda-Style Policy Optimization method that replaces scalar group advantages with a Pairwise Decomposed Advantage. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.

Reinforcement learning from human feedback (RLHF) has become the leading approach for fine-tuning large language models (LLM). However, RLHF has limitations in multi-task learning (MTL) due to challenges of reward hacking and extreme multi-objective optimization (i.e., trade-off of multiple and/or sometimes conflicting objectives). Applying RLHF for MTL currently requires careful tuning of the weights for reward model and data combinations. This is often done via human intuition and does not generalize. In this work, we introduce a novel post-training paradigm which we called Constrained Generative Policy Optimization (CGPO). The core of CGPO is Mixture of Judges (MoJ) with cost-efficient constrained policy optimization with stratification, which can identify the perfect blend in RLHF in a principled manner. It shows strong empirical results with theoretical guarantees, does not require extensive hyper-parameter tuning, and is plug-and-play in common post-training pipelines. Together, this can detect and mitigate reward hacking behaviors while reaching a pareto-optimal point across an extremely large number of objectives. Our empirical evaluations demonstrate that CGPO significantly outperforms standard RLHF algorithms like PPO and DPO across various tasks including general chat, STEM questions, instruction following, and coding. Specifically, CGPO shows improvements of 7.4% in AlpacaEval-2 (general chat), 12.5% in Arena-Hard (STEM & reasoning), and consistent gains in other domains like math and coding. Notably, PPO, while commonly used, is prone to severe reward hacking in popular coding benchmarks, which CGPO successfully addresses. This breakthrough in RLHF not only tackles reward hacking and extreme multi-objective optimization challenges but also advances the state-of-the-art in aligning general-purpose LLMs for diverse applications.

This paper introduces Personalized Path Recourse, a novel method that generates recourse paths for an agent. The objective is to achieve desired goals (e.g., better outcomes compared to the agent's original paths of action), while ensuring a high similarity to the agent's original paths and being personalized to the agent. Personalization refers to the extent to which the new path is tailored to the agent's observed behavior patterns from their policy function. We train a personalized recourse agent to generate such personalized paths, which are obtained using reward functions that consider the goal, similarity, and personalization. The proposed method is applicable to both reinforcement learning and supervised learning settings for correcting or improving sequences of actions or sequences of data to achieve a pre-determined goal. The method is evaluated in various settings and demonstrates promising results.

Alignment is crucial for training large language models. The predominant strategy is Reinforcement Learning from Human Feedback (RLHF), with Proximal Policy Optimization (PPO) as the de-facto algorithm. Yet, PPO is known to struggle with computational inefficiency, a challenge that this paper aims to address. We identify three important properties of RLHF tasks: fast simulation, deterministic transitions, and trajectory-level rewards, which are not leveraged in PPO. Based on these properties, we develop ReMax, a new algorithm tailored for RLHF. The design of ReMax builds on the celebrated algorithm REINFORCE but is enhanced with a new variance-reduction technique. ReMax offers threefold advantages over PPO: first, it is simple to implement with just 6 lines of code. It further eliminates more than 4 hyper-parameters in PPO, which are laborious to tune. Second, ReMax reduces memory usage by about 50%. To illustrate, PPO runs out of memory when fine-tuning a Llama2-7B model on A100-80GB GPUs, whereas ReMax can support the training. Even though memory-efficient techniques (e.g., ZeRO and offload) are employed for PPO to afford training, ReMax can utilize a larger batch size to increase throughput. Third, in terms of wall-clock time, PPO is about twice as slow as ReMax per iteration. Importantly, these improvements do not sacrifice task performance. We hypothesize that these advantages can be maintained in larger-scale models.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".

Reward finetuning has emerged as a promising approach to aligning foundation models with downstream objectives. Remarkable success has been achieved in the language domain by using reinforcement learning (RL) to maximize rewards that reflect human preference. However, in the vision domain, existing RL-based reward finetuning methods are limited by their instability in large-scale training, rendering them incapable of generalizing to complex, unseen prompts. In this paper, we propose Proximal Reward Difference Prediction (PRDP), enabling stable black-box reward finetuning for diffusion models for the first time on large-scale prompt datasets with over 100K prompts. Our key innovation is the Reward Difference Prediction (RDP) objective that has the same optimal solution as the RL objective while enjoying better training stability. Specifically, the RDP objective is a supervised regression objective that tasks the diffusion model with predicting the reward difference of generated image pairs from their denoising trajectories. We theoretically prove that the diffusion model that obtains perfect reward difference prediction is exactly the maximizer of the RL objective. We further develop an online algorithm with proximal updates to stably optimize the RDP objective. In experiments, we demonstrate that PRDP can match the reward maximization ability of well-established RL-based methods in small-scale training. Furthermore, through large-scale training on text prompts from the Human Preference Dataset v2 and the Pick-a-Pic v1 dataset, PRDP achieves superior generation quality on a diverse set of complex, unseen prompts whereas RL-based methods completely fail.

The goal of this article is to provide an introduction to the desirability function approach to multi-objective optimization (direct and surrogate model-based), and multi-objective hyperparameter tuning. This work is based on the paper by Kuhn (2016). It presents a `Python` implementation of Kuhn's `R` package `desirability`. The `Python` package `spotdesirability` is available as part of the `sequential parameter optimization` framework. After a brief introduction to the desirability function approach is presented, three examples are given that demonstrate how to use the desirability functions for classical optimization, surrogate-model based optimization, and hyperparameter tuning.

Language model calibration refers to the alignment between the confidence of the model and the actual performance of its responses. While previous studies point out the overconfidence phenomenon in Large Language Models (LLMs) and show that LLMs trained with Reinforcement Learning from Human Feedback (RLHF) are overconfident with a more sharpened output probability, in this study, we reveal that RLHF tends to lead models to express verbalized overconfidence in their own responses. We investigate the underlying cause of this overconfidence and demonstrate that reward models used for Proximal Policy Optimization (PPO) exhibit inherent biases towards high-confidence scores regardless of the actual quality of responses. Building upon this insight, we propose two PPO variants: PPO-M: PPO with Calibrated Reward Modeling and PPO-C: PPO with Calibrated Reward Calculation. PPO-M integrates explicit confidence scores in reward model training, which calibrates reward models to better capture the alignment between response quality and verbalized confidence. PPO-C adjusts the reward score during PPO based on the difference between the current reward and the moving average of past rewards. Both PPO-M and PPO-C can be seamlessly integrated into the current PPO pipeline and do not require additional golden labels. We evaluate our methods on both Llama3-8B and Mistral-7B across six diverse datasets including multiple-choice and open-ended generation. Experiment results demonstrate that both of our methods can reduce calibration error and maintain performance comparable to standard PPO. We further show that they do not compromise model capabilities in open-ended conversation settings.

Large language models (LLMs) have shown impressive success in various applications. However, these models are often not well aligned with human intents, which calls for additional treatments on them, that is, the alignment problem. To make LLMs better follow user instructions, existing alignment methods mostly focus on further training them. However, the extra training of LLMs are usually expensive in terms of GPU compute; worse still, LLMs of interest are oftentimes not accessible for user-demanded training, such as GPTs. In this work, we take a different perspective -- Black-Box Prompt Optimization (BPO) -- to perform alignments. The idea is to optimize user prompts to suit LLMs' input understanding, so as to best realize users' intents without updating LLMs' parameters. BPO is model-agnostic and the empirical results demonstrate that the BPO-aligned ChatGPT yields a 22% increase in the win rate against its original version, and 10% for GPT-4. Importantly, the BPO-aligned LLMs can outperform the same models aligned by PPO and DPO, and it also brings additional performance gains when combining BPO with PPO or DPO. Code and datasets are released at https://github.com/thu-coai/BPO.

Generating high-quality code that solves complex programming tasks is challenging, especially with current decoder-based models that produce highly stochastic outputs. In code generation, even minor errors can easily break the entire solution. Leveraging multiple sampled solutions can significantly improve the overall output quality. One effective way to enhance code generation is by pairing a code generation model with a reranker model, which selects the best solution from the generated samples. We propose a novel iterative self-training approach for self-training reranker models using Proximal Policy Optimization (PPO), aimed at improving both reranking accuracy and the overall code generation process. Unlike traditional PPO approaches, where the focus is on optimizing a generative model with a reward model, our approach emphasizes the development of a robust reward/reranking model. This model improves the quality of generated code through reranking and addresses problems and errors that the reward model might overlook during PPO alignment with the reranker. Our method iteratively refines the training dataset by re-evaluating outputs, identifying high-scoring negative examples, and incorporating them into the training loop, that boosting model performance. Our evaluation on the MultiPL-E dataset demonstrates that our 13.4B parameter model outperforms a 33B model in code generation quality while being three times faster. Moreover, it achieves performance comparable to GPT-4 and surpasses it in one programming language.

We introduce Open-Reasoner-Zero, the first open source implementation of large-scale reasoning-oriented RL training focusing on scalability, simplicity and accessibility. Through extensive experiments, we demonstrate that a minimalist approach, vanilla PPO with GAE (lambda=1, gamma=1) and straightforward rule-based rewards, without any KL regularization, is sufficient to scale up both response length and benchmark performance, similar to the phenomenon observed in DeepSeek-R1-Zero. Using the same base model as DeepSeek-R1-Zero-Qwen-32B, our implementation achieves superior performance on AIME2024, MATH500, and the GPQA Diamond benchmark while demonstrating remarkable efficiency -- requiring only a tenth of the training steps, compared to DeepSeek-R1-Zero pipeline. In the spirit of open source, we release our source code, parameter settings, training data, and model weights across various sizes.

Diffusion models are a class of flexible generative models trained with an approximation to the log-likelihood objective. However, most use cases of diffusion models are not concerned with likelihoods, but instead with downstream objectives such as human-perceived image quality or drug effectiveness. In this paper, we investigate reinforcement learning methods for directly optimizing diffusion models for such objectives. We describe how posing denoising as a multi-step decision-making problem enables a class of policy gradient algorithms, which we refer to as denoising diffusion policy optimization (DDPO), that are more effective than alternative reward-weighted likelihood approaches. Empirically, DDPO is able to adapt text-to-image diffusion models to objectives that are difficult to express via prompting, such as image compressibility, and those derived from human feedback, such as aesthetic quality. Finally, we show that DDPO can improve prompt-image alignment using feedback from a vision-language model without the need for additional data collection or human annotation.

Supervised fine-tuning (SFT) has emerged as a crucial method for aligning large language models (LLMs) with human-annotated demonstrations. However, SFT, being an off-policy approach similar to behavior cloning, often struggles with overfitting and poor out-of-domain generalization, especially in limited-data scenarios. To address these limitations, we propose Self-Rewarding PPO, a novel fine-tuning method that leverages on-policy techniques to enhance generalization performance. Our approach combines the strengths of SFT and proximal policy optimization (PPO) to achieve more effective alignment from demonstration data. At its core is a reward function designed as the log policy ratio between the SFT model and the pretrained base model. This function serves as an implicit reward signal, using the pretrained policy as a baseline and the SFT policy as a target. By doing so, it enables on-policy fine-tuning without relying on human preference annotations. The integration of this self-rewarding mechanism with PPO addresses key limitations of SFT, improving generalization, data efficiency, and robustness. Our empirical evaluation across a range of natural language processing tasks demonstrates that Self-Rewarding PPO consistently outperforms traditional SFT methods. The results highlight the effectiveness of our approach in aligning LLMs using demonstration data, particularly in scenarios where high-quality annotated data is scarce.

Optimization (PPO) has been positioned by recent literature as the canonical method for the RL part of RLHF. PPO performs well empirically but has a heuristic motivation and handles the KL-divergence constraint used in LM-RLHF in an ad-hoc manner and suffers form reward oscillations, entropy collapse, value function drift, and sudden policy divergence that require frequent restarts and extensive hyperparameter tuning. In this paper, we develop a new pure on policy actor-critic RL method for the LM-RLHF setting. We present SAFE (Stable Alignment Finetuning with Entropy-aware control),a novel RLHF algorithm that combines a Double Soft-Min Critic for pessimistic value estimation with a new multi-layer stabilization framework combining entropy-gated KL regulation, and PID-controlled adaptive thresholds. Unlike standard PPO's symmetric KL penalties, SAFE distinguishes high-entropy exploration from low-entropy mode collapse and adjusts penalties dynamically based on reward velocity. Experiments on a 3B parameter model show SAFE achieves +5.15\% training-average reward than PPO (0.725 vs 0.689), negligible reward crashes, and superior KL control than ppo . Our method adds minimal computational overhead and provides an interpretable, crash-resistant RLHF framework that maintains aggressive learning speed while ensuring stable long-horizon optimization suitable for production deployment. Code is available at https://github.com/ryyzn9/SAFE

The study of decentralized learning or independent learning in cooperative multi-agent reinforcement learning has a history of decades. Recently empirical studies show that independent PPO (IPPO) can obtain good performance, close to or even better than the methods of centralized training with decentralized execution, in several benchmarks. However, decentralized actor-critic with convergence guarantee is still open. In this paper, we propose decentralized policy optimization (DPO), a decentralized actor-critic algorithm with monotonic improvement and convergence guarantee. We derive a novel decentralized surrogate for policy optimization such that the monotonic improvement of joint policy can be guaranteed by each agent independently optimizing the surrogate. In practice, this decentralized surrogate can be realized by two adaptive coefficients for policy optimization at each agent. Empirically, we compare DPO with IPPO in a variety of cooperative multi-agent tasks, covering discrete and continuous action spaces, and fully and partially observable environments. The results show DPO outperforms IPPO in most tasks, which can be the evidence for our theoretical results.

Recent large reasoning models (LRMs) driven by reinforcement learning algorithms (e.g., GRPO) have achieved remarkable performance on challenging reasoning tasks. However, these models suffer from overthinking, generating unnecessarily long and redundant reasoning even for simple questions, which substantially increases computational cost and response latency. While existing methods incorporate length rewards to GRPO to promote concise reasoning, they incur significant performance degradation. We identify the root cause: when rewards for correct but long rollouts are penalized, GRPO's group-relative advantage function can assign them negative advantages, actively discouraging valid reasoning. To overcome this, we propose Decoupled Reward Policy Optimization (DRPO), a novel framework that decouples the length-based learning signal of correct rollouts from incorrect ones. DRPO ensures that reward signals for correct rollouts are normalized solely within the positive group, shielding them from interference by negative samples. The DRPO's objective is grounded in integrating an optimized positive data distribution, which maximizes length-based rewards under a KL regularization, into a discriminative objective. We derive a closed-form solution for this distribution, enabling efficient computation of the objective and its gradients using only on-policy data and importance weighting. Of independent interest, this formulation is general and can incorporate other preference rewards of positive data beyond length. Experiments on mathematical reasoning tasks demonstrate DRPO's significant superiority over six efficient reasoning baselines. Notably, with a 1.5B model, our method achieves 77\% length reduction with only 1.1\% performance loss on simple questions like GSM8k dataset, while the follow-up baseline sacrifices 4.3\% for 68\% length reduction.

AI alignment in the shape of Reinforcement Learning from Human Feedback (RLHF) is increasingly treated as a crucial ingredient for high performance large language models. Proximal Policy Optimization (PPO) has been positioned by recent literature as the canonical method for the RL part of RLHF. However, it involves both high computational cost and sensitive hyperparameter tuning. We posit that most of the motivational principles that led to the development of PPO are less of a practical concern in RLHF and advocate for a less computationally expensive method that preserves and even increases performance. We revisit the formulation of alignment from human preferences in the context of RL. Keeping simplicity as a guiding principle, we show that many components of PPO are unnecessary in an RLHF context and that far simpler REINFORCE-style optimization variants outperform both PPO and newly proposed "RL-free" methods such as DPO and RAFT. Our work suggests that careful adaptation to LLMs alignment characteristics enables benefiting from online RL optimization at low cost.

We say an algorithm is batch size-invariant if changes to the batch size can largely be compensated for by changes to other hyperparameters. Stochastic gradient descent is well-known to have this property at small batch sizes, via the learning rate. However, some policy optimization algorithms (such as PPO) do not have this property, because of how they control the size of policy updates. In this work we show how to make these algorithms batch size-invariant. Our key insight is to decouple the proximal policy (used for controlling policy updates) from the behavior policy (used for off-policy corrections). Our experiments help explain why these algorithms work, and additionally show how they can make more efficient use of stale data.

The Natural Language for Optimization (NL4Opt) Competition was created to investigate methods of extracting the meaning and formulation of an optimization problem based on its text description. Specifically, the goal of the competition is to increase the accessibility and usability of optimization solvers by allowing non-experts to interface with them using natural language. We separate this challenging goal into two sub-tasks: (1) recognize and label the semantic entities that correspond to the components of the optimization problem; (2) generate a meaning representation (i.e., a logical form) of the problem from its detected problem entities. The first task aims to reduce ambiguity by detecting and tagging the entities of the optimization problems. The second task creates an intermediate representation of the linear programming (LP) problem that is converted into a format that can be used by commercial solvers. In this report, we present the LP word problem dataset and shared tasks for the NeurIPS 2022 competition. Furthermore, we investigate and compare the performance of the ChatGPT large language model against the winning solutions. Through this competition, we hope to bring interest towards the development of novel machine learning applications and datasets for optimization modeling.

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, including mixed-precision quantization, non-uniform pruning, and expert selection. The objective, typically model loss, depends jointly on all assignments and does not decompose across groups, preventing combinatorial solvers from directly optimizing the true objective and forcing reliance on proxy formulations. Methods such as evolutionary search evaluate the actual loss but lack gradient information, while penalty-based approaches enforce the budget only approximately and often require extensive hyperparameter tuning. We present a new approach by showing that, under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with unusually simple geometry. The normal vector admits a closed-form expression, shifting logits along the cost vector changes expected cost monotonically, and vector transport reduces to a single inner product. Building on these properties, we propose Riemannian Constrained Optimization (RCO), which augments a standard Adam step with tangent projection, binary-search retraction, and momentum transport. Combined with Gumbel straight-through estimation and budget-constrained dynamic programming for discrete feasibility, RCO enables first-order optimization of the actual loss under exact budget enforcement without introducing constraint-specific hyperparameters. Across both synthetic benchmarks and realistic LLM compression settings, RCO matches or exceeds state-of-the-art methods while often requiring substantially less wall-clock time. Source code is available at https://github.com/IST-DASLab/RCO.

Direct Preference Optimization (DPO) aligns text-to-image (T2I) generation models with human preferences using pairwise preference data. Although substantial resources are expended in collecting and labeling datasets, a critical aspect is often neglected: preferences vary across individuals and should be represented with more granularity. To address this, we propose SmPO-Diffusion, a novel method for modeling preference distributions to improve the DPO objective, along with a numerical upper bound estimation for the diffusion optimization objective. First, we introduce a smoothed preference distribution to replace the original binary distribution. We employ a reward model to simulate human preferences and apply preference likelihood averaging to improve the DPO loss, such that the loss function approaches zero when preferences are similar. Furthermore, we utilize an inversion technique to simulate the trajectory preference distribution of the diffusion model, enabling more accurate alignment with the optimization objective. Our approach effectively mitigates issues of excessive optimization and objective misalignment present in existing methods through straightforward modifications. Our SmPO-Diffusion achieves state-of-the-art performance in preference evaluation, outperforming baselines across metrics with lower training costs. The project page is https://jaydenlyh.github.io/SmPO-project-page/.

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings.

Reinforcement learning from human feedback (RLHF) is one of the key techniques that helps large language models (LLMs) to follow instructions and provide helpful and harmless responses. While direct policy optimization methods exist, state-of-the-art LLMs adopt RL-based methods (usually PPO) in RLHF to train the policy to generate good responses guided by a reward model learned from preference data. The main challenge of these methods is the inaccuracy of the intermediate reward model, especially in code generation tasks that require long and complex reasoning to score a response. We find that the reliability of the reward model varies across responses assigned with different rewards. This motivates us to filter the samples whose rewards may be unreliable to improve signal-to-noise ratio during policy learning, resulting in Policy Filtration for Proximal Policy Optimization (PF-PPO). To choose a proper policy filtration strategy for a given reward model, the coefficient of determination (R^2) between rewards and actual scores on filtered samples serves as a good metrics and helps us find several promising strategies. We provide extensive experiments to validate the effectiveness of PF-PPO in code generation tasks, and find that some variants of PF-PPO are highly effective and achieve new state-of-the-art performance across 7-billion-parameter models on HumanEval, MBPP, and a new and more challenging LeetCode Contest benchmark.

The prevalent deployment of learning from human preferences through reinforcement learning (RLHF) relies on two important approximations: the first assumes that pairwise preferences can be substituted with pointwise rewards. The second assumes that a reward model trained on these pointwise rewards can generalize from collected data to out-of-distribution data sampled by the policy. Recently, Direct Preference Optimisation (DPO) has been proposed as an approach that bypasses the second approximation and learn directly a policy from collected data without the reward modelling stage. However, this method still heavily relies on the first approximation. In this paper we try to gain a deeper theoretical understanding of these practical algorithms. In particular we derive a new general objective called PsiPO for learning from human preferences that is expressed in terms of pairwise preferences and therefore bypasses both approximations. This new general objective allows us to perform an in-depth analysis of the behavior of RLHF and DPO (as special cases of PsiPO) and to identify their potential pitfalls. We then consider another special case for PsiPO by setting Psi simply to Identity, for which we can derive an efficient optimisation procedure, prove performance guarantees and demonstrate its empirical superiority to DPO on some illustrative examples.

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

While existing work focuses primarily on task success, we argue that effective real-world agents require optimizing three dimensions: productivity (task completion), proactivity (asking essential questions), and personalization (adapting to diverse user preferences). We introduce UserVille, an interactive environment with LLM-based user simulators enabling diverse, configurable user preferences. Leveraging UserVille, we introduce PPP, a multi-objective reinforcement learning approach that jointly optimizes all three dimensions: Productivity, Proactivity, and Personalization. Experiments on software engineering and deep research tasks show that agents trained with PPP achieve substantial improvements over strong baselines such as GPT-5 (+21.6 on average), demonstrating the ability to ask strategic clarifying questions, adapt to unseen user preferences, and improve task success through better interaction. This work demonstrates that explicitly optimizing for user-centered interaction is critical for building practical and effective AI agents.

Image captioning is one of the most fundamental tasks in computer vision. Owing to its open-ended nature, it has received significant attention in the era of multimodal large language models (MLLMs). In pursuit of ever more detailed and accurate captions, recent work has increasingly turned to reinforcement learning (RL). However, existing captioning-RL methods and evaluation metrics often emphasize a narrow notion of caption quality, inducing trade-offs across core dimensions of captioning. For example, utility-oriented objectives can encourage noisy, hallucinated, or overlong captions that improve downstream question answering while harming fluency, whereas arena-style objectives can favor fluent but generic descriptions with limited usefulness. To address this, we propose a more balanced RL framework that jointly optimizes utility-aware correctness, reference coverage, and linguistic quality. In order to effectively optimize the resulting continuous multi-objective reward formulation, we apply GDPO-style reward-decoupled normalization to continuous-valued captioning rewards and show that it improves performance over vanilla GRPO. Additionally, we introduce length-conditional reward masking, yielding a more suitable length penalty for captioning. Across LLaVA-1.5-7B and Qwen2.5-VL 3B and 7B base models, our method consistently improves caption quality, with peak gains of +13.6 DCScore, +9.0 CaptionQA, and +29.0 CapArena across different models.

Most recently developed approaches to cooperative multi-agent reinforcement learning in the centralized training with decentralized execution setting involve estimating a centralized, joint value function. In this paper, we demonstrate that, despite its various theoretical shortcomings, Independent PPO (IPPO), a form of independent learning in which each agent simply estimates its local value function, can perform just as well as or better than state-of-the-art joint learning approaches on popular multi-agent benchmark suite SMAC with little hyperparameter tuning. We also compare IPPO to several variants; the results suggest that IPPO's strong performance may be due to its robustness to some forms of environment non-stationarity.

The last year has witnessed the rapid progress of large language models (LLMs) across diverse domains. Among them, CodeLLMs have garnered particular attention because they can not only assist in completing various programming tasks but also represent the decision-making and logical reasoning capabilities of LLMs. However, current CodeLLMs mainly focus on pre-training and supervised fine-tuning scenarios, leaving the alignment stage, which is important for post-training LLMs, under-explored. This work first identifies that the commonly used PPO algorithm may be suboptimal for the alignment of CodeLLM because the involved reward rules are routinely coarse-grained and potentially flawed. We then advocate addressing this using the DPO algorithm. Based on only preference data pairs, DPO can render the model rank data automatically, giving rise to a fine-grained rewarding pattern more robust than human intervention. We also contribute a pipeline for collecting preference pairs for DPO on CodeLLMs. Studies show that our method significantly improves the performance of existing CodeLLMs on benchmarks such as MBPP and HumanEval.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: Token-level methods (e.g., PPO) aim to provide the fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving 6-12 percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving 7-11 percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially operating on very different scales. This imbalance introduces complications such as the selection of appropriate weights when scalarizing multiple objectives into a single objective function. In this paper, we propose a novel technique for scaling QUBO objectives that uses an exact computation of the variance of each individual QUBO objective. By scaling each objective to have unit variance, we align all objectives onto a common scale, thereby allowing for more balanced solutions to be found when scalarizing the objectives with equal weights, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multi-objective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome, and reliable, efficient solutions are scarce.

This paper examines the fiscal and macroeconomic strategies essential for transition of India to a high income economy by 2047, aligning with the vision of Viksit Bharat. A sustainable annual GDP growth rate of 7 to 8 percent is projected as necessary to achieve this milestone while maintaining fiscal prudence through a targeted deficit threshold below 3.5 percent of GDP. The study underscores the role of disciplined fiscal management in financing critical public investments in infrastructure, human capital development and technological innovation. Given constraints on domestic resource mobilization, the paper highlights the importance of multilateral financial institutions, including the World Bank, IMF and ADB, in expanding fiscal space in India through concessional financing, technical cooperation, and risk sharing mechanisms. Using econometric modeling and scenario analysis, the research identifies key policy interventions in infrastructure, healthcare, education and sustainable energy that can maximize growth while ensuring fiscal sustainability. Policy recommendations include enhancing tax buoyancy, rationalizing expenditure, optimizing public private partnerships and strengthening fiscal responsibility frameworks. The findings suggest that a calibrated approach to growth, prudent fiscal management and strategic international collaborations are critical to achieving long term economic aspirations of India.

Reinforcement Learning from Human Feedback has emerged as a standard for aligning diffusion models. However, we identify a fundamental limitation in the standard DPO formulation because it relies on the Bradley-Terry model to aggregate diverse evaluation axes like aesthetic quality and semantic alignment into a single scalar reward. This aggregation creates a reward conflict where the model is forced to unlearn desirable features of a specific dimension if they appear in a globally non-preferred sample. To address this issue, we propose Multi Reward Conditional DPO (MCDPO). This method resolves reward conflicts by introducing a disentangled Bradley-Terry objective. MCDPO explicitly injects a preference outcome vector as a condition during training, which allows the model to learn the correct optimization direction for each reward axis independently within a single network. We further introduce dimensional reward dropout to ensure balanced optimization across dimensions. Extensive experiments on Stable Diffusion 1.5 and SDXL demonstrate that MCDPO achieves superior performance on benchmarks. Notably, our conditional framework enables dynamic and multiple-axis control at inference time using Classifier Free Guidance to amplify specific reward dimensions without additional training or external reward models.

Recent advancements in Large Language Models (LLMs) have garnered wide attention and led to successful products such as ChatGPT and GPT-4. Their proficiency in adhering to instructions and delivering harmless, helpful, and honest (3H) responses can largely be attributed to the technique of Reinforcement Learning from Human Feedback (RLHF). In this paper, we aim to link the research in conventional RL to RL techniques used in LLM research. Demystify this technique by discussing why, when, and how RL excels. Furthermore, we explore potential future avenues that could either benefit from or contribute to RLHF research. Highlighted Takeaways: 1. RLHF is Online Inverse RL with Offline Demonstration Data. 2. RLHF > SFT because Imitation Learning (and Inverse RL) > Behavior Cloning (BC) by alleviating the problem of compounding error. 3. The RM step in RLHF generates a proxy of the expensive human feedback, such an insight can be generalized to other LLM tasks such as prompting evaluation and optimization where feedback is also expensive. 4. The policy learning in RLHF is more challenging than conventional problems studied in IRL due to their high action dimensionality and feedback sparsity. 5. The main superiority of PPO over off-policy value-based methods is its stability gained from (almost) on-policy data and conservative policy updates.

This paper describes a service learning project used in an upper-level and graduate-level database systems course. Students complete a small database project for a real client. The final product must match the client specification and needs, and include the database design and the final working database system with embedded user documentation. The solution must be implemented in a way to make it as easy to use as possible for the client. Students are expected to conduct professional meetings with their clients to understand the project, analyze the project's requirements, as well as design and implement the solution to the project. Students must have each milestone approved before starting the next phase of the project. The student learning objectives of a database system semester project are to: analyze a client's information system problem and determine the requirements for the solution; design a suitable database solution to the problem; use software design and development tools to design and develop a solution to the problem; communicate and interact with a client on a professional level; prepare effective documentation for both non-technical and technical software users; and interact ethically with all persons involved with a project. The broader impact objectives of a database system semester project are to: provide needed database solutions for organizations and businesses in the local area; provide a resume and portfolio-building opportunity for the students; provide a measure for assessing how well the program meets it mission; provide a mechanism for implementing service-based learning; provide a mechanism for outreach to local-area organizations and businesses; and provide a starting-point for undergraduate research projects.

Policy optimization methods with function approximation are widely used in multi-agent reinforcement learning. However, it remains elusive how to design such algorithms with statistical guarantees. Leveraging a multi-agent performance difference lemma that characterizes the landscape of multi-agent policy optimization, we find that the localized action value function serves as an ideal descent direction for each local policy. Motivated by the observation, we present a multi-agent PPO algorithm in which the local policy of each agent is updated similarly to vanilla PPO. We prove that with standard regularity conditions on the Markov game and problem-dependent quantities, our algorithm converges to the globally optimal policy at a sublinear rate. We extend our algorithm to the off-policy setting and introduce pessimism to policy evaluation, which aligns with experiments. To our knowledge, this is the first provably convergent multi-agent PPO algorithm in cooperative Markov games.

Online allocation problems with resource constraints are central problems in revenue management and online advertising. In these problems, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to choose an action that consumes a certain amount of resources and generates reward. The objective is to maximize cumulative rewards subject to a constraint on the total consumption of resources. In this paper, we consider a data-driven setting in which the reward and resource consumption of each request are generated using an input model that is unknown to the decision maker. We design a general class of algorithms that attain good performance in various input models without knowing which type of input they are facing. In particular, our algorithms are asymptotically optimal under independent and identically distributed inputs as well as various non-stationary stochastic input models, and they attain an asymptotically optimal fixed competitive ratio when the input is adversarial. Our algorithms operate in the Lagrangian dual space: they maintain a dual multiplier for each resource that is updated using online mirror descent. By choosing the reference function accordingly, we recover the dual sub-gradient descent and dual multiplicative weights update algorithm. The resulting algorithms are simple, fast, and do not require convexity in the revenue function, consumption function and action space, in contrast to existing methods for online allocation problems. We discuss applications to network revenue management, online bidding in repeated auctions with budget constraints, online proportional matching with high entropy, and personalized assortment optimization with limited inventory.

PPO has been widely adopted for training large language models (LLMs) at the token level in multi-turn dialogue and reasoning tasks. However, its performance is often unstable and prone to collapse. Through empirical analysis, we identify two main sources of instability in this setting: (1)~token-level importance sampling, which is misaligned with the natural granularity of multi-turn environments that have distinct turn-level stages, and (2) inaccurate advantage estimates from off-policy samples, where the critic has not learned to evaluate certain state-action pairs, resulting in high-variance gradients and unstable updates. To address these challenges, we introduce two complementary stabilization techniques: (1) turn-level importance sampling, which aligns optimization with the natural structure of multi-turn reasoning, and (2) clipping-bias correction, which normalizes gradients by downweighting unreliable, highly off-policy samples. Depending on how these components are combined, we obtain three variants: Turn-PPO (turn-level sampling only), S-PPO (clipping-bias correction applied to token-level PPO), and ST-PPO (turn-level sampling combined with clipping-bias correction). In our experiments, we primarily study ST-PPO and S-PPO, which together demonstrate how the two stabilization mechanisms address complementary sources of instability. Experiments on multi-turn search tasks across general QA, multi-hop QA, and medical multiple-choice QA benchmarks show that ST-PPO and S-PPO consistently prevent the performance collapses observed in large-model training, maintain lower clipping ratios throughout optimization, and achieve higher task performance than standard token-level PPO. These results demonstrate that combining turn-level importance sampling with clipping-bias correction provides a practical and scalable solution for stabilizing multi-turn LLM agent training.

Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where pre-training and RL post-training share the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the same score/flow-matching loss as pretraining to obtain a lower-variance objective and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This unifies pretraining and RL conceptually and practically, is consistent with policy-gradient theory, reduces variance, and yields faster convergence. This simple yet effective design yields substantial benefits: on GenEval, OCR, and PickScore benchmarks, AWM delivers up to a 24times speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching.

Learning from human preferences is crucial for language models (LMs) to effectively cater to human needs and societal values. Previous research has made notable progress by leveraging human feedback to follow instructions. However, these approaches rely primarily on online reinforcement learning (RL) techniques like Proximal Policy Optimization (PPO), which have been proven unstable and challenging to tune for language models. Moreover, PPO requires complex distributed system implementation, hindering the efficiency of large-scale distributed training. In this study, we propose an offline reinforcement learning from human feedback (RLHF) framework to align LMs using pre-generated samples without interacting with RL environments. Specifically, we explore maximum likelihood estimation (MLE) with filtering, reward-weighted regression (RWR), and Decision Transformer (DT) to align language models to human preferences. By employing a loss function similar to supervised fine-tuning, our methods ensure more stable model training than PPO with a simple machine learning system~(MLSys) and much fewer (around 12.3\%) computing resources. Experimental results demonstrate the DT alignment outperforms other Offline RLHF methods and is better than PPO.

The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitation of question-level difficulty bias. We also identify a connection between GRPO and traditional discriminative methods in supervised learning. Motivated by these insights, we introduce a new Discriminative Constrained Optimization (DisCO) framework for reinforcing LRMs, grounded in the principle of discriminative learning. The main differences between DisCO and GRPO and its recent variants are: (1) it replaces the group relative objective with a discriminative objective defined by a scoring function; (2) it abandons clipping-based surrogates in favor of non-clipping RL surrogate objectives used as scoring functions; (3) it employs a simple yet effective constrained optimization approach to enforce the KL divergence constraint, ensuring stable training. As a result, DisCO offers notable advantages over GRPO and its variants: (i) it completely eliminates difficulty bias by adopting discriminative objectives; (ii) it addresses the entropy instability in GRPO and its variants through the use of non-clipping scoring functions and a constrained optimization approach; (iii) it allows the incorporation of advanced discriminative learning techniques to address data imbalance, where a significant number of questions have more negative than positive generated answers during training. Our experiments on enhancing the mathematical reasoning capabilities of SFT-finetuned models show that DisCO significantly outperforms GRPO and its improved variants such as DAPO, achieving average gains of 7\% over GRPO and 6\% over DAPO across six benchmark tasks for an 1.5B model.

Reinforcement Learning from Human Feedback (RLHF) facilitates the alignment of large language models with human preferences, significantly enhancing the quality of interactions between humans and these models. InstructGPT implements RLHF through several stages, including Supervised Fine-Tuning (SFT), reward model training, and Proximal Policy Optimization (PPO). PPO, however, is sensitive to hyperparameters and requires a minimum of four models in its standard implementation, which makes it hard to train. In contrast, we propose a novel learning paradigm called RRHF, which scores responses generated by different sampling policies and learns to align them with human preferences through ranking loss. RRHF can efficiently align language model output probabilities with human preferences as robust as fine-tuning and it only needs 1 to 2 models during tuning. In addition, RRHF can be considered an extension of SFT and reward models while being simpler than PPO in terms of coding, model counts, and hyperparameters. The entire alignment process can be accomplished within a single RRHF training session. We evaluate RRHF using LLaMA and Alpaca on Helpful and Harmless data, demonstrating performance comparable to PPO.

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service delivery times and gauge the service quality based on the service provider's ability to complete the service as close as possible to the preferred time. Customers can be of different priority classes, and their priority may increase as they wait longer in the queue. The service provider can reject customers upon their arrival if the system is overloaded or outsource the service (alternatively work overtime) when the capacity is not enough. The service provider's goal is to find the minimum-cost admission and capacity allocation policy to dynamically decide when to serve and whom to serve. We model this problem as a Markov Decision Process. Our structural results partially characterize a set of suboptimal solutions, and we develop solution methods using these results. We also develop a problem-specific approximation method that is based on state aggregation to overcome the computational challenges. We present extensive computational results and discuss the impact of problem parameters on the optimal policy.

With COVID-19 having emerged as the most widespread human pandemic disease in a century, the need to control its spread to avoid massive loss of life became more than necessary, and extremely fast. Several vaccines were developed and the task of policy makers was suddenly to convince the reluctant population to be vaccinated by various means. While some countries have chosen a policy of mandatory vaccination or punitive incentives, many states in the United States have adopted various incentives to try to increase vaccination coverage. A study we conducted in recent months quantified the effect of these measures on the proportion of the population vaccinated, using the synthetic control method, by simulating what would have happened without these measures. The aim now is to generalize this study to smaller scales, to improve the results of our previous study, to quantify their robustness and to provide a tool that can be used by policy makers to adapt their behavior in light of the results obtained.

Reinforcement learning (RL) has emerged as a powerful approach for tackling complex problems. The recent introduction of multi-objective reinforcement learning (MORL) has further expanded the scope of RL by enabling agents to make trade-offs among multiple objectives. This advancement not only has broadened the range of problems that can be tackled but also created numerous opportunities for exploration and advancement. Yet, the effectiveness of RL agents heavily relies on appropriately setting their hyperparameters. In practice, this task often proves to be challenging, leading to unsuccessful deployments of these techniques in various instances. Hence, prior research has explored hyperparameter optimization in RL to address this concern. This paper presents an initial investigation into the challenge of hyperparameter optimization specifically for MORL. We formalize the problem, highlight its distinctive challenges, and propose a systematic methodology to address it. The proposed methodology is applied to a well-known environment using a state-of-the-art MORL algorithm, and preliminary results are reported. Our findings indicate that the proposed methodology can effectively provide hyperparameter configurations that significantly enhance the performance of MORL agents. Furthermore, this study identifies various future research opportunities to further advance the field of hyperparameter optimization for MORL.

Direct Preference Optimization (DPO) is a simple and efficient framework that has attracted substantial attention. However, it often struggles to meet its primary objectives -- increasing the generation probability of chosen responses while reducing that of rejected responses -- due to the dominant influence of rejected responses on the loss function. This imbalance leads to suboptimal performance in promoting preferred responses. In this work, we systematically analyze the limitations of DPO and existing algorithms designed to achieve the objectives stated above. To address these limitations, we propose Bounded-DPO (BDPO), a novel method that bounds the influence of rejected responses while maintaining the original optimization structure of DPO. Through theoretical analysis and empirical evaluations, we demonstrate that BDPO achieves a balanced optimization of the chosen and rejected responses, outperforming existing algorithms.

We consider a binary classification problem under group fairness constraints, which can be one of Demographic Parity (DP), Equalized Opportunity (EOp), or Equalized Odds (EO). We propose an explicit characterization of Bayes optimal classifier under the fairness constraints, which turns out to be a simple modification rule of the unconstrained classifier. Namely, we introduce a novel instance-level measure of bias, which we call bias score, and the modification rule is a simple linear rule on top of the finite amount of bias scores.Based on this characterization, we develop a post-hoc approach that allows us to adapt to fairness constraints while maintaining high accuracy. In the case of DP and EOp constraints, the modification rule is thresholding a single bias score, while in the case of EO constraints we are required to fit a linear modification rule with 2 parameters. The method can also be applied for composite group-fairness criteria, such as ones involving several sensitive attributes.

We introduce Humans-Junior, a 3.8B model that matches GPT-4o on the FACTS Grounding public subset within a pm 5 pp equivalence margin. Results. On Q1--Q500 under identical judges, GPT-4o scores 73.5% (95% CI 69.5--77.2) and Humans-Junior 72.7% (95% CI 68.7--76.5); the paired difference is 0.8 pp (bootstrap 95% CI -3.1 to +4.7; permutation p = 0.72; Cohen's d = 0.023). TOST establishes equivalence at pm 5 pp (not at pm 3 pp). When purchased as managed APIs, Humans-Junior's base model (Phi-3.5-mini-instruct) is approx 19times less expensive than GPT-4o on Microsoft AI Foundry pricing; self-hosted or edge deployments can drive incremental inference cost toward zero. Measured vs estimated pricing sources are tabulated in Appendix E. Method. Our approach combines minimal directed "Exoskeleton Reasoning" scaffolds with behavioral fine-tuning that teaches protocol compliance (epistemic discipline) rather than domain answers. Fine-tuning alone adds little; combined, they synergize (+17.7 pp, p < 0.001) and reduce variance (approx 25%). In prompt-only settings on frontier models (Q1--Q100; non-comparable), directed reasoning improved GPT-4o by +11.8 pp to 85.3% and Gemini-2.5-Pro by +5.0 pp to 93.3% (baseline 88.3%, n = 100); see Section~5. TL;DR. A 3.8B model achieves GPT-4o-level FACTS accuracy (equivalent within pm 5 pp on Q1--Q500). Cloud pricing shows approx 19times lower cost versus GPT-4o, and self-hosted/edge deployments can approach zero marginal cost. Pricing sources are listed in Appendix E. Frontier prompt-only gains (Q1--Q100; non-comparable) and optimized-prompt exploratory results under earlier judges are summarized in Appendix F. Keywords: Small Language Models, Factual Grounding, Directed Reasoning, Fine-Tuning, Model Alignment, Cost-Efficient AI

Large language models (LLMs) are increasingly applied to complex reasoning tasks that require executing several complex steps before receiving any reward. Properly assigning credit to these steps is essential for enhancing model performance. Proximal Policy Optimization (PPO), a state-of-the-art reinforcement learning (RL) algorithm used for LLM finetuning, employs value networks to tackle credit assignment. However, value networks face challenges in predicting the expected cumulative rewards accurately in complex reasoning tasks, often leading to high-variance updates and suboptimal performance. In this work, we systematically evaluate the efficacy of value networks and reveal their significant shortcomings in reasoning-heavy LLM tasks, showing that they barely outperform a random baseline when comparing alternative steps. To address this, we propose VinePPO, a straightforward approach that leverages the flexibility of language environments to compute unbiased Monte Carlo-based estimates, bypassing the need for large value networks. Our method consistently outperforms PPO and other RL-free baselines across MATH and GSM8K datasets with fewer gradient updates (up to 9x), less wall-clock time (up to 3.0x). These results emphasize the importance of accurate credit assignment in RL finetuning of LLM and demonstrate VinePPO's potential as a superior alternative.

Multi-objective reinforcement learning (MORL) excels at handling rapidly changing preferences in tasks that involve multiple criteria, even for unseen preferences. However, previous dominating MORL methods typically generate a fixed policy set or preference-conditioned policy through multiple training iterations exclusively for sampled preference vectors, and cannot ensure the efficient discovery of the Pareto front. Furthermore, integrating preferences into the input of policy or value functions presents scalability challenges, in particular as the dimension of the state and preference space grow, which can complicate the learning process and hinder the algorithm's performance on more complex tasks. To address these issues, we propose a two-stage Pareto front discovery algorithm called Constrained MORL (C-MORL), which serves as a seamless bridge between constrained policy optimization and MORL. Concretely, a set of policies is trained in parallel in the initialization stage, with each optimized towards its individual preference over the multiple objectives. Then, to fill the remaining vacancies in the Pareto front, the constrained optimization steps are employed to maximize one objective while constraining the other objectives to exceed a predefined threshold. Empirically, compared to recent advancements in MORL methods, our algorithm achieves more consistent and superior performances in terms of hypervolume, expected utility, and sparsity on both discrete and continuous control tasks, especially with numerous objectives (up to nine objectives in our experiments).

Purpose: With advancements in Large Language Models (LLMs) for healthcare, the need arises for competitive open-source models to protect the public interest. This work contributes to the field of open medical LLMs by optimizing key stages of data preprocessing and training, while showing how to improve model safety (through DPO) and efficacy (through RAG). The evaluation methodology used, which includes four different types of tests, defines a new standard for the field. The resultant models, shown to be competitive with the best private alternatives, are released with a permisive license. Methods: Building on top of strong base models like Llama 3.1 and Qwen 2.5, Aloe Beta uses a custom dataset to enhance public data with synthetic Chain of Thought examples. The models undergo alignment with Direct Preference Optimization, emphasizing ethical and policy-aligned performance in the presence of jailbreaking attacks. Evaluation includes close-ended, open-ended, safety and human assessments, to maximize the reliability of results. Results: Recommendations are made across the entire pipeline, backed by the solid performance of the Aloe Family. These models deliver competitive performance across healthcare benchmarks and medical fields, and are often preferred by healthcare professionals. On bias and toxicity, the Aloe Beta models significantly improve safety, showing resilience to unseen jailbreaking attacks. For a responsible release, a detailed risk assessment specific to healthcare is attached to the Aloe Family models. Conclusion: The Aloe Beta models, and the recipe that leads to them, are a significant contribution to the open-source medical LLM field, offering top-of-the-line performance while maintaining high ethical requirements. This work sets a new standard for developing and reporting aligned LLMs in healthcare.

The outbreak of COVID-19 has highlighted the intricate interplay between public health and economic stability on a global scale. This study proposes a novel reinforcement learning framework designed to optimize health and economic outcomes during pandemics. The framework leverages the SIR model, integrating both lockdown measures (via a stringency index) and vaccination strategies to simulate disease dynamics. The stringency index, indicative of the severity of lockdown measures, influences both the spread of the disease and the economic health of a country. Developing nations, which bear a disproportionate economic burden under stringent lockdowns, are the primary focus of our study. By implementing reinforcement learning, we aim to optimize governmental responses and strike a balance between the competing costs associated with public health and economic stability. This approach also enhances transparency in governmental decision-making by establishing a well-defined reward function for the reinforcement learning agent. In essence, this study introduces an innovative and ethical strategy to navigate the challenge of balancing public health and economic stability amidst infectious disease outbreaks.

Preference based alignment objectives implicitly assume that all human preferences are expressed with equal strength. In practice, however, preference strength varies across individuals and contexts -- a phenomenon established in behavioral economics and discrete choice theory. This mismatch limits the ability of existing objectives to faithfully capture heterogeneous human judgments. Inspired by this literature, we introduce Mixed Logit Direct Preference Optimization (MixDPO), a generalization of Direct Preference Optimization that models variation in preference strength. MixDPO enables alignment objectives to capture heterogeneity in how strongly preferences are expressed across training examples. We evaluate MixDPO on three preference datasets using two open-weight language models. Across datasets, MixDPO improves aggregate alignment performance (+11.2 points on Pythia-2.8B) while preserving subgroup level preferences, with the largest gains appearing in settings with higher inferred preference heterogeneity. MixDPO makes preference heterogeneity explicit through learned strength distributions. We release our code for reproducibility.

We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advantage signal as groups become uniformly correct. Process reward models (PRM) offer richer supervision, but directly using PRM scores causes reward hacking, where models exploit verbosity to inflate scores while accuracy collapses. PAPO resolves both by composing the advantage from an outcome component Aout, derived from ORM and normalized over all responses, and a process component Aproc, derived from a rubric-based PRM and normalized exclusively among correct responses. This decoupled design ensures that Aout anchors training on correctness while Aproc differentiates reasoning quality without distorting the outcome signal. Experiments across multiple model scales and six benchmarks demonstrate that PAPO consistently outperforms ORM, reaching 51.3% vs.\ 46.3% on OlympiadBench while continuing to improve as ORM plateaus and declines.

Discovering achievements with a hierarchical structure in procedurally generated environments presents a significant challenge. This requires an agent to possess a broad range of abilities, including generalization and long-term reasoning. Many prior methods have been built upon model-based or hierarchical approaches, with the belief that an explicit module for long-term planning would be advantageous for learning hierarchical dependencies. However, these methods demand an excessive number of environment interactions or large model sizes, limiting their practicality. In this work, we demonstrate that proximal policy optimization (PPO), a simple yet versatile model-free algorithm, outperforms previous methods when optimized with recent implementation practices. Moreover, we find that the PPO agent can predict the next achievement to be unlocked to some extent, albeit with limited confidence. Based on this observation, we introduce a novel contrastive learning method, called achievement distillation, which strengthens the agent's ability to predict the next achievement. Our method exhibits a strong capacity for discovering hierarchical achievements and shows state-of-the-art performance on the challenging Crafter environment in a sample-efficient manner while utilizing fewer model parameters.

Objective. Clinical AI documentation systems require evaluation methodologies that are clinically valid, economically viable, and sensitive to iterative changes. Methods requiring expert review per scoring instance are too slow and expensive for safe, iterative deployment. We present a case-specific, clinician-authored rubric methodology for clinical AI evaluation and examine whether LLM-generated rubrics can approximate clinician agreement. Materials and Methods. Twenty clinicians authored 1,646 rubrics for 823 clinical cases (736 real-world, 87 synthetic) across primary care, psychiatry, oncology, and behavioral health. Each rubric was validated by confirming that an LLM-based scoring agent consistently scored clinician-preferred outputs higher than rejected ones. Seven versions of an EHR-embedded AI agent for clinicians were evaluated across all cases. Results. Clinician-authored rubrics discriminated effectively between high- and low-quality outputs (median score gap: 82.9%) with high scoring stability (median range: 0.00%). Median scores improved from 84% to 95%. In later experiments, clinician-LLM ranking agreement (tau: 0.42-0.46) matched or exceeded clinician-clinician agreement (tau: 0.38-0.43), attributable to both ceiling compression and LLM rubric improvement. Discussion. This convergence supports incorporating LLM rubrics alongside clinician-authored ones. At roughly 1,000 times lower cost, LLM rubrics enable substantially greater evaluation coverage, while continued clinical authorship grounds evaluation in expert judgment. Ceiling compression poses a methodological challenge for future inter-rater agreement studies. Conclusion. Case-specific rubrics offer a path for clinical AI evaluation that preserves expert judgment while enabling automation at three orders lower cost. Clinician-authored rubrics establish the baseline against which LLM rubrics are validated.

Mehta and Panigrahi (2012) proposed Online Matching with Stochastic Rewards, which generalizes the Online Bipartite Matching problem of Karp, Vazirani, and Vazirani (1990) by associating the edges with success probabilities. This new feature captures the pay-per-click model in online advertising. Recently, Huang and Zhang (2020) studied this problem under the online primal dual framework using the Configuration Linear Program (LP), and got the best known competitive ratios of the Stochastic Balance algorithm. Their work suggests that the more expressive Configuration LP is more suitable for this problem than the Matching LP. This paper advances the theory of Configuration LP in two directions. Our technical contribution includes a characterization of the joint matching outcome of an offline vertex and all its neighbors. This characterization may be of independent interest, and is aligned with the spirit of Configuration LP. By contrast, previous analyses of Ranking generally focus on only one neighbor. Second, we designed a Stochastic Configuration LP that captures a stochastic benchmark proposed by Goyal and Udwani (2020), who used a Path-based LP. The Stochastic Configuration LP is smaller and simpler than the Path-based LP. Moreover, using the new LP we improved the competitive ratio of Stochastic Balance from 0.596 to 0.611 when the success probabilities are infinitesimal, and to 0.613 when the success probabilities are further equal.

How can we use AI to discover a new state of the art for a scientific problem? Prior work in test-time scaling, such as AlphaEvolve, performs search by prompting a frozen LLM. We perform reinforcement learning at test time, so the LLM can continue to train, but now with experience specific to the test problem. This form of continual learning is quite special, because its goal is to produce one great solution rather than many good ones on average, and to solve this very problem rather than generalize to other problems. Therefore, our learning objective and search subroutine are designed to prioritize the most promising solutions. We call this method Test-Time Training to Discover (TTT-Discover). Following prior work, we focus on problems with continuous rewards. We report results for every problem we attempted, across mathematics, GPU kernel engineering, algorithm design, and biology. TTT-Discover sets the new state of the art in almost all of them: (i) Erdős' minimum overlap problem and an autocorrelation inequality; (ii) a GPUMode kernel competition (up to 2times faster than prior art); (iii) past AtCoder algorithm competitions; and (iv) denoising problem in single-cell analysis. Our solutions are reviewed by experts or the organizers. All our results are achieved with an open model, OpenAI gpt-oss-120b, and can be reproduced with our publicly available code, in contrast to previous best results that required closed frontier models. Our test-time training runs are performed using Tinker, an API by Thinking Machines, with a cost of only a few hundred dollars per problem.

Machine learning systems often experience a distribution shift between training and testing. In this paper, we introduce a simple variational objective whose optima are exactly the set of all representations on which risk minimizers are guaranteed to be robust to any distribution shift that preserves the Bayes predictor, e.g., covariate shifts. Our objective has two components. First, a representation must remain discriminative for the task, i.e., some predictor must be able to simultaneously minimize the source and target risk. Second, the representation's marginal support needs to be the same across source and target. We make this practical by designing self-supervised objectives that only use unlabelled data and augmentations to train robust representations. Our objectives give insights into the robustness of CLIP, and further improve CLIP's representations to achieve SOTA results on DomainBed.

Most algorithms in reinforcement learning (RL) require that the objective is formalised with a Markovian reward function. However, it is well-known that certain tasks cannot be expressed by means of an objective in the Markov rewards formalism, motivating the study of alternative objective-specification formalisms in RL such as Linear Temporal Logic and Multi-Objective Reinforcement Learning. To date, there has not yet been any thorough analysis of how these formalisms relate to each other in terms of their expressivity. We fill this gap in the existing literature by providing a comprehensive comparison of 17 salient objective-specification formalisms. We place these formalisms in a preorder based on their expressive power, and present this preorder as a Hasse diagram. We find a variety of limitations for the different formalisms, and argue that no formalism is both dominantly expressive and straightforward to optimise with current techniques. For example, we prove that each of Regularised RL, (Outer) Nonlinear Markov Rewards, Reward Machines, Linear Temporal Logic, and Limit Average Rewards can express a task that the others cannot. The significance of our results is twofold. First, we identify important expressivity limitations to consider when specifying objectives for policy optimization. Second, our results highlight the need for future research which adapts reward learning to work with a greater variety of formalisms, since many existing reward learning methods assume that the desired objective takes a Markovian form. Our work contributes towards a more cohesive understanding of the costs and benefits of different RL objective-specification formalisms.

Language models as intelligent agents push the boundaries of sequential decision-making agents but struggle with limited knowledge of environmental dynamics and exponentially huge action space. Recent efforts like GLAM and TWOSOME manually constrain the action space to a restricted subset and employ reinforcement learning to align agents' knowledge with specific environments. However, they overlook fine-grained credit assignments for intra-action tokens, which is essential for efficient language agent optimization, and rely on human's prior knowledge to restrict action space. This paper proposes decomposing language agent optimization from the action level to the token level, offering finer supervision for each intra-action token and manageable optimization complexity in environments with unrestricted action spaces. Beginning with the simplification of flattening all actions, we theoretically explore the discrepancies between action-level optimization and this naive token-level optimization. We then derive the Bellman backup with Action Decomposition (BAD) to integrate credit assignments for both intra-action and inter-action tokens, effectively eliminating the discrepancies. Implementing BAD within the PPO algorithm, we introduce Policy Optimization with Action Decomposition (POAD). POAD benefits from a finer-grained credit assignment process and lower optimization complexity, leading to enhanced learning efficiency and generalization abilities in aligning language agents with interactive environments. We validate POAD across diverse testbeds, with results affirming the advantages of our approach and the correctness of our theoretical analysis.

Varied approaches for aligning language models have been proposed, including supervised fine-tuning, RLHF, and direct optimization methods such as DPO. Although DPO has rapidly gained popularity due to its straightforward training process and competitive results, there is an open question of whether there remain practical advantages of using a discriminator, like a reward model, to evaluate responses. We propose D2PO, discriminator-guided DPO, an approach for the online setting where preferences are being collected throughout learning. As we collect gold preferences, we use these not only to train our policy, but to train a discriminative response evaluation model to silver-label even more synthetic data for policy training. We explore this approach across a set of diverse tasks, including a realistic chat setting, we find that our approach leads to higher-quality outputs compared to DPO with the same data budget, and greater efficiency in terms of preference data requirements. Furthermore, we show conditions under which silver labeling is most helpful: it is most effective when training the policy with DPO, outperforming traditional PPO, and benefits from maintaining a separate discriminator from the policy model.

In our pursuit of advancing multi-modal AI assistants capable of guiding users to achieve complex multi-step goals, we propose the task of "Visual Planning for Assistance (VPA)". Given a succinct natural language goal, e.g., "make a shelf", and a video of the user's progress so far, the aim of VPA is to devise a plan, i.e., a sequence of actions such as "sand shelf", "paint shelf", etc. to realize the specified goal. This requires assessing the user's progress from the (untrimmed) video, and relating it to the requirements of natural language goal, i.e., which actions to select and in what order? Consequently, this requires handling long video history and arbitrarily complex action dependencies. To address these challenges, we decompose VPA into video action segmentation and forecasting. Importantly, we experiment by formulating the forecasting step as a multi-modal sequence modeling problem, allowing us to leverage the strength of pre-trained LMs (as the sequence model). This novel approach, which we call Visual Language Model based Planner (VLaMP), outperforms baselines across a suite of metrics that gauge the quality of the generated plans. Furthermore, through comprehensive ablations, we also isolate the value of each component--language pre-training, visual observations, and goal information. We have open-sourced all the data, model checkpoints, and training code.

Direct Preference Optimization (DPO) is successful for alignment in LLMs but still faces challenges in text-to-image generation. Existing studies are confined to denoising diffusion models while overlooking flow-matching, and suffer from an objective mismatch when applying discrete NLP-based DPO to regression-based generative tasks.\ In this paper, we derive a generalized DPO objective that covers both diffusion and flow-matching via a unified reverse-time SDE framework, and point out from a gradient perspective that the standard DPO objective is suboptimal for text-to-image generation. Consequently, we propose Linear-DPO, which replaces the aggressive sigmoid-based utility function with a sustained linear utility and incorporates an EMA-updated reference model. Qualitative and quantitative experiments on diffusion models (SD1.5, SDXL) and flow-matching model (SD3-Medium) demonstrate the superiority of our approach over existing baselines.

Preference learning algorithms (e.g., RLHF and DPO) are frequently used to steer LLMs to produce generations that are more preferred by humans, but our understanding of their inner workings is still limited. In this work, we study the conventional wisdom that preference learning trains models to assign higher likelihoods to more preferred outputs than less preferred outputs, measured via ranking accuracy. Surprisingly, we find that most state-of-the-art preference-tuned models achieve a ranking accuracy of less than 60% on common preference datasets. We furthermore derive the idealized ranking accuracy that a preference-tuned LLM would achieve if it optimized the DPO or RLHF objective perfectly. We demonstrate that existing models exhibit a significant alignment gap -- i.e., a gap between the observed and idealized ranking accuracies. We attribute this discrepancy to the DPO objective, which is empirically and theoretically ill-suited to fix even mild ranking errors in the reference model, and derive a simple and efficient formula for quantifying the difficulty of learning a given preference datapoint. Finally, we demonstrate that ranking accuracy strongly correlates with the empirically popular win rate metric when the model is close to the reference model used in the objective, shedding further light on the differences between on-policy (e.g., RLHF) and off-policy (e.g., DPO) preference learning algorithms.

Test-time alignment of Large Language Models (LLMs) to human preferences offers a flexible way to generate responses aligned to diverse objectives without extensive retraining of LLMs. Existing methods achieve alignment to multiple objectives simultaneously (e.g., instruction-following, helpfulness, conciseness) by optimizing their corresponding reward functions. However, they often rely on predefined weights or optimize for averages, sacrificing one objective for another and leading to unbalanced outcomes. To address this, we introduce Robust Multi-Objective Decoding (RMOD), a novel inference-time algorithm that optimizes for improving worst-case rewards. RMOD formalizes the robust decoding problem as a maximin two-player game between reward weights and the sampling policy, solving for the Nash equilibrium. We show that the game reduces to a convex optimization problem to find the worst-case weights, while the best response policy can be computed analytically. We also introduce a practical RMOD variant designed for efficient decoding with contemporary LLMs, incurring minimal computational overhead compared to non-robust Multi-Objective Decoding (MOD) methods. Our experimental results showcase the effectiveness of RMOD in generating responses equitably aligned with diverse objectives, outperforming baselines up to 20%.

A single language model (LM), despite aligning well with an average labeler through reinforcement learning from human feedback (RLHF), may not universally suit diverse human preferences. Recent approaches therefore opt for customization by collecting multi-dimensional feedback and creating distinct reward models (RMs) for each dimension (e.g., helpfulness, harmlessness, or honesty). Different LMs can then be optimized for different preferences using multi-objective RLHF (MORLHF) with different reward weightings. Yet, RL fine-tuning is unstable and resource-heavy, especially for MORLHF with diverse and usually conflicting objectives. In this paper, we present Multi-Objective Direct Preference Optimization (MODPO), an RL-free algorithm that extends Direct Preference Optimization (DPO) for multiple alignment objectives with minimal overheads. Essentially, MODPO folds language modeling directly into reward modeling, training LMs as implicit collective reward models (cRMs) that combine all objectives with specific weightings. While theoretically guaranteed to produce the same optimal solutions as MORLHF, MODPO is practically more stable and computationally efficient. Empirical results from safety alignment and long-form question answering confirm that MODPO matches or outperforms existing methods, consistently producing a Pareto front of LMs that cater to diverse preferences with 3 times less computational resources compared to MORLHF.

We introduce the Agent GPA (Goal-Plan-Action) framework: an evaluation paradigm based on an agent's operational loop of setting goals, devising plans, and executing actions. The framework includes five evaluation metrics: Goal Fulfillment, Logical Consistency, Execution Efficiency, Plan Quality, and Plan Adherence. Logical Consistency checks that an agent's actions are consistent with its prior actions. Execution Efficiency checks whether the agent executes in the most efficient way to achieve its goal. Plan Quality checks whether an agent's plans are aligned with its goals; Plan Adherence checks if an agent's actions are aligned with its plan; and Goal Fulfillment checks that agent's final outcomes match the stated goals. Our experimental results on two benchmark datasets - the public TRAIL/GAIA dataset and an internal dataset for a production-grade data agent - show that this framework (a) provides a systematic way to cover a broad range of agent failures, including all agent errors on the TRAIL/GAIA benchmark dataset; (b) supports LLM-judges that exhibit strong agreement with human annotation, covering 80% to over 95% errors; and (c) localizes errors with 86% agreement to enable targeted improvement of agent performance.

Multi-Objective Reinforcement Learning (MORL) is a generalization of traditional Reinforcement Learning (RL) that aims to optimize multiple, often conflicting objectives simultaneously rather than focusing on a single reward. This approach is crucial in complex decision-making scenarios where agents must balance trade-offs between various goals, such as maximizing performance while minimizing costs. We consider the problem of MORL where the objectives are combined using a non-linear scalarization function. Just like in standard RL, policy gradient methods (PGMs) are amongst the most effective for handling large and continuous state-action spaces in MORL. However, existing PGMs for MORL suffer from high sample inefficiency, requiring large amounts of data to be effective. Previous attempts to solve this problem rely on overly strict assumptions, losing PGMs' benefits in scalability to large state-action spaces. In this work, we address the issue of sample efficiency by implementing variance-reduction techniques to reduce the sample complexity of policy gradients while maintaining general assumptions.

Ask a frontier model how to taper six milligrams of alprazolam (psychiatrist retired, ten days of pills left, abrupt cessation causes seizures) and it tells her to call the psychiatrist she just explained does not exist. Change one word ("I'm a psychiatrist; a patient presents with...") and the same model, same weights, same inference pass produces a textbook Ashton Manual taper with diazepam equivalence, anticonvulsant coverage, and monitoring thresholds. The knowledge was there; the model withheld it. IatroBench measures this gap. Sixty pre-registered clinical scenarios, six frontier models, 3,600 responses, scored on two axes (commission harm, CH 0-3; omission harm, OH 0-4) through a structured-evaluation pipeline validated against physician scoring (kappa_w = 0.571, within-1 agreement 96%). The central finding is identity-contingent withholding: match the same clinical question in physician vs. layperson framing and all five testable models provide better guidance to the physician (decoupling gap +0.38, p = 0.003; binary hit rates on safety-colliding actions drop 13.1 percentage points in layperson framing, p < 0.0001, while non-colliding actions show no change). The gap is widest for the model with the heaviest safety investment (Opus, +0.65). Three failure modes separate cleanly: trained withholding (Opus), incompetence (Llama 4), and indiscriminate content filtering (GPT-5.2, whose post-generation filter strips physician responses at 9x the layperson rate because they contain denser pharmacological tokens). The standard LLM judge assigns OH = 0 to 73% of responses a physician scores OH >= 1 (kappa = 0.045); the evaluation apparatus has the same blind spot as the training apparatus. Every scenario targets someone who has already exhausted the standard referrals.