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icml26/3105df16-98c9-46f1-9f54-b48ba2014a8a/assets.json

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icml26/3105df16-98c9-46f1-9f54-b48ba2014a8a/main_body_chunks.jsonl

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+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0000", "section": "Abstract", "page_start": 1, "page_end": 1, "type": "Text", "text": "Preference-based alignment methods (e.g., RLHF, DPO) typically optimize a single scalar objective, implicitly averaging over heterogeneous human preferences. In practice, systematic annotator and user-group disagreement makes mean-reward maximization brittle and susceptible to proxy over-optimization. We propose Disagreement-Aware Alignment via Risk-Constrained Decoding (DARC), a retraining-free inference-time method that frames response selection as distributionally robust, risk-sensitive decision making. Given multiple preference samples or scalable disagreement proxies, DARC reranks candidates by maximizing a KL-robust (entropic) satisfaction objective, and provides simple deployment controls that cap or penalize the corresponding entropic risk premium relative to the mean, enabling explicit risk budgets without retraining. We provide theoretical characterization linking this decoding rule to principled pessimism and KLbased distributionally robust optimization. Experiments on alignment benchmarks show that DARC reduces disagreement and tail risk while maintaining competitive average quality under noisy, heterogeneous feedback.", "source": "marker_v2", "marker_block_id": "/page/0/Text/4"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0001", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Preference data has become the dominant supervision signal for aligning large language models (Ouyang et al., 2022; Stiennon et al., 2020) . Most pipelines—RLHF with reward modeling and RL optimization (Christiano et al., 2017; Schulman et al., 2017) , offline preference objectives such as DPO and its refinements (Rafailov et al., 2023; Meng et al., 2024) , and reference-free single-stage variants such as ORPO (Hong et al., 2024) —share a common abstraction: preferences are treated as noisy observations of a single latent scalar utility (e.g., Bradley–Terry) (Bradley & Terry,", "source": "marker_v2", "marker_block_id": "/page/0/Text/6"}
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+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0003", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "FigureGroup", "text": "Figure 1. Score Distribution shift. Ridge plot showing human score densities on the high-disagreement subset. DARC variants (blue) shift the distribution to the right (higher mean µ) compared to the baseline (grey), with reduced spread (lower σ), indicating both increased satisfaction and reduced disagreement.", "source": "marker_v2", "marker_block_id": "/page/0/FigureGroup/586"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0004", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "1952) . This abstraction largely persists in newer reformulations such as KTO and IPO (Ethayarajh et al., 2024; Garg et al., 2025) , and even when reward models are made multidimensional via multi-head/objective designs (Wang et al., 2024a; Li et al., 2025; Yang et al., 2024) . Yet, treating feedback as perturbations around a single scalar provides limited guidance for inference-time response selection under heterogeneous preferences (Hung et al., 2025) , and it also lacks a unifying robust-optimization account for common risk-penalized decoding heuristics.", "source": "marker_v2", "marker_block_id": "/page/0/Text/12"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0005", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "However, real-world preferences are often heterogeneous rather than i.i.d. noise: annotators disagree for systematic reasons (Zhang et al., 2024; Chen et al., 2024) . Empirically, human ratings show substantial variance even on the raw Top-K candidate pool (Appendix H.1) , suggesting that uncertainty is intrinsic rather than an artifact of our selection rule. Under such plurality, maximizing the average reward µˆ can be brittle (Casper et al., 2023) , and the issue is exacerbated by proxy over-optimization, which can improve an imperfect preference proxy while degrading the underlying target (Gao et al., 2023; Rafailov et al., 2024) .", "source": "marker_v2", "marker_block_id": "/page/0/Text/13"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0006", "section": "1. Introduction", "page_start": 1, "page_end": 1, "type": "Text", "text": "Recent work further shows that proxy misspecification can induce inference-time reward hacking: as best-of-N (a widely used decoding primitive (Sun et al., 2024) ) or", "source": "marker_v2", "marker_block_id": "/page/0/Text/14"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0007", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "soft best-of-N becomes greedier, true utility can increase and then inevitably degrade (Huang et al., 2025a). Best-of-Poisson and HedgeTune mitigate this effect by tuning inference-time parameters (Khalaf et al., 2025); however, they primarily model risk through proxy-distortion trade-offs under a single reward signal, rather than preference heterogeneity. Closely related, pessimistic best-of-N rules penalize atypical candidates via an auxiliary error model to mitigate reward hacking (Anonymous, 2025), but they target distributional uncertainty of the reward model (e.g., atypicality/OOD) rather than disagreement-grounded risk across users.", "source": "marker_v2", "marker_block_id": "/page/1/Text/1"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0008", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "In parallel, robustness has been pursued through trainingtime objectives such as robust DPO under noisy preferences (Wu et al., 2024), which improve robustness via retraining and noise assumptions; group-robust objectives that protect minority preference groups (Ramesh et al., 2024), which rely on access to group structure; and uncertaintyaware reward modeling (Banerjee & Gopalan, 2024), which quantifies estimation uncertainty but does not by itself specify how to select responses under inference-time proxy shift (Ichihara et al., 2025). Taken together, these lines suggest a common lesson: when preferences are plural, the relevant object is not a deterministic score, but a random variable over users and annotation noise. Yet, a principled inference-time selection rule that is explicitly riskconstrained under heterogeneous preferences remains underdeveloped.", "source": "marker_v2", "marker_block_id": "/page/1/Text/2"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0009", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "We therefore study inference-time alignment under heterogeneous preferences through the lens of risk-constrained decision making (Chow et al., 2018; Tamar et al., 2015). Given a fixed candidate set and noisy preference or reward scores, we derive a finite-sample pessimistic rule based on a lower confidence bound, yielding high-probability guarantees for selecting a competitive response while controlling tail risk across prompts. This leads to Disagreement-Aware Alignment via Risk-Constrained Decoding (DARC), an inference-time-only, retraining-free procedure that plugs into any LM and preference estimator. DARC grounds risk in multi-annotator disagreement (Zhang et al., 2024) instantiated via validated proxy signals, improving robustness on high-disagreement prompts (Fig. 1). We include representative cases where Best-of-K is polarizing or unstable, whereas DARC yields consistently preferred responses (Appendix H.10).", "source": "marker_v2", "marker_block_id": "/page/1/Text/3"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0010", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "Beyond the statistical view, we give a distributionally robust optimization (DRO) characterization (Wiesemann et al., 2014; Rahimian & Mehrotra, 2019), viewing decoding as maximizing the worst-case expected satisfaction over local divergence neighborhoods (Namkoong & Duchi, 2016; Duchi et al., 2021). This yields a practical KL-robust instantiation and situates widely used mean—dispersion scoring", "source": "marker_v2", "marker_block_id": "/page/1/Text/4"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0011", "section": "1. Introduction", "page_start": 2, "page_end": 2, "type": "Text", "text": "rules within the same DRO perspective, clarifying the conditions under which they arise as principled risk-sensitive criteria (Duchi & Namkoong, 2019).", "source": "marker_v2", "marker_block_id": "/page/1/Text/5"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0012", "section": "Contributions.", "page_start": 2, "page_end": 2, "type": "ListGroup", "text": "Method. We formulate inference-time alignment as riskconstrained decision making under heterogeneous preferences, with risk induced by preference uncertainty and annotator disagreement. Theory. We connect LCB-based uniform pessimism to a KL-DRO view, yielding a closed-form entropic decoding objective and its constrained/penalized variants via an entropic risk premium. Empirics. Across benchmarks, DARC improves disagreement and prompt-level tail risk with competitive mean quality; a dual-robust multi-scorer extension hedges scorer shift and proxy over-optimization, with a KL-regularized DRO interpretation over scorers.", "source": "marker_v2", "marker_block_id": "/page/1/ListGroup/415"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0013", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Text", "text": "Let s denote a prompt (context) and let \\mathcal{Y}(s) be a realized candidate set produced by a fixed generator (e.g., sampling, beam variants, or a proposal model), with K := |\\mathcal{Y}(s)| .", "source": "marker_v2", "marker_block_id": "/page/1/Text/11"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0014", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Text", "text": "Conditioning on the candidate set. The generator may be stochastic; throughout the analysis we condition on the realized \\mathcal{Y}(s) . All probabilities below are taken over the evaluation randomness (human or otherwise), holding \\mathcal{Y}(s) fixed.", "source": "marker_v2", "marker_block_id": "/page/1/Text/12"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0015", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Text", "text": "Latent satisfaction under heterogeneous preferences. For each (s, y), let R(s, y) \\in \\mathbb{R} denote a (latent) user-satisfaction random variable capturing preference heterogeneity and evaluation noise, with mean \\mu(s, y) := \\mathbb{E}[R(s, y)] . Intuitively, \\mu(s, y) measures average quality.", "source": "marker_v2", "marker_block_id": "/page/1/Text/13"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0016", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Text", "text": "KL-robust (entropic) value and risk premium. For \\beta > 0 , define the entropic value", "source": "marker_v2", "marker_block_id": "/page/1/Text/14"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0017", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Equation", "text": "V_{\\beta}(s,y) := -\\frac{1}{\\beta} \\log \\mathbb{E} \\left[ \\exp \\left( -\\beta R(s,y) \\right) \\right], (1)", "source": "marker_v2", "marker_block_id": "/page/1/Equation/15"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0018", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Text", "text": "which is equivalent to a KL-based distributionally robust objective (Section 3.2). We define the entropic risk premium.", "source": "marker_v2", "marker_block_id": "/page/1/Text/16"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0019", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Equation", "text": "RP_{\\beta}(s,y) := \\mu(s,y) - V_{\\beta}(s,y) \\ge 0", "source": "marker_v2", "marker_block_id": "/page/1/Equation/17"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0020", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Text", "text": "Decision problem (risk-aware decoding). Conditioning on (s,\\mathcal{Y}(s)) , each candidate y\\in\\mathcal{Y}(s) induces an (unknown) satisfaction distribution over users/raters. Our population objective is to select an output by solving", "source": "marker_v2", "marker_block_id": "/page/1/Text/18"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0021", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Equation", "text": "y^* \\in \\arg \\max_{y \\in \\mathcal{Y}(s)} V_{\\beta}(s, y),", "source": "marker_v2", "marker_block_id": "/page/1/Equation/19"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0022", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Text", "text": "where entropic risk measure V_{\\beta} is defined in (1). We further consider explicit risk control via a budget or a penalty:", "source": "marker_v2", "marker_block_id": "/page/1/Text/20"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0023", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Equation", "text": "y_{\\tau}^{\\star} \\in \\arg\\max_{y \\in \\mathcal{Y}(s)} V_{\\beta}(s, y) s.t. \\mathrm{RP}_{\\beta}(s, y) \\leq \\tau ,", "source": "marker_v2", "marker_block_id": "/page/1/Equation/21"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0024", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Text", "text": "or in penalized (Lagrangian) form", "source": "marker_v2", "marker_block_id": "/page/1/Text/22"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0025", "section": "2. Problem setup", "page_start": 2, "page_end": 2, "type": "Equation", "text": "\\arg \\max_{y \\in \\mathcal{Y}(s)} V_{\\beta}(s, y) - \\lambda \\operatorname{RP}_{\\beta}(s, y).", "source": "marker_v2", "marker_block_id": "/page/1/Equation/23"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0026", "section": "3. Guarantees via Lower Confidence Bounds", "page_start": 3, "page_end": 3, "type": "Text", "text": "This section provides a statistical justification for disagreement-aware decoding by deriving high-probability lower confidence bounds (LCBs) on expected satisfaction under heterogeneous preferences. To contextualize the resulting pessimistic rules, we also give complementary distributionally robust optimization (DRO) characterizations.", "source": "marker_v2", "marker_block_id": "/page/2/Text/2"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0027", "section": "3. Guarantees via Lower Confidence Bounds", "page_start": 3, "page_end": 3, "type": "Text", "text": "Scalar satisfaction samples (guarantee setting). For each candidate y \\in \\mathcal{Y}(s) , we observe n i.i.d. scalar satisfaction samples \\{R_i(s,y)\\}_{i=1}^n drawn from the (unknown) distribution of R(s,y):", "source": "marker_v2", "marker_block_id": "/page/2/Text/3"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0028", "section": "3. Guarantees via Lower Confidence Bounds", "page_start": 3, "page_end": 3, "type": "Equation", "text": "R_i(s,y) \\stackrel{i.i.d.}{\\sim} R(s,y), \\qquad i = 1, \\dots, n.", "source": "marker_v2", "marker_block_id": "/page/2/Equation/4"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0029", "section": "3. Guarantees via Lower Confidence Bounds", "page_start": 3, "page_end": 3, "type": "Text", "text": "In this regime, the empirical mean and standard deviation \\hat{\\mu}_n(s,y) and \\hat{\\sigma}_n(s,y) estimate \\mu(s,y) and \\sigma(s,y) . Moreover, the plug-in estimator of (1) is", "source": "marker_v2", "marker_block_id": "/page/2/Text/5"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0030", "section": "3. Guarantees via Lower Confidence Bounds", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\widehat{V}_{\\beta}(s,y) := -\\frac{1}{\\beta} \\log \\left( \\frac{1}{n} \\sum_{i=1}^{n} \\exp\\left(-\\beta R_i(s,y)\\right) \\right), \\quad (2)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/6"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0031", "section": "3. Guarantees via Lower Confidence Bounds", "page_start": 3, "page_end": 3, "type": "Text", "text": "with the empirical risk premium", "source": "marker_v2", "marker_block_id": "/page/2/Text/7"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0032", "section": "3. Guarantees via Lower Confidence Bounds", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\widehat{RP}_{\\beta}(s,y) := \\hat{\\mu}_n(s,y) - \\widehat{V}_{\\beta}(s,y) \\ge 0. (3)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/8"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0033", "section": "3. Guarantees via Lower Confidence Bounds", "page_start": 3, "page_end": 3, "type": "Text", "text": "In practice, one may operate with approximate (proxy) estimates of these empirical quantities; the analysis below does not rely on proxy scores being independent, and any such approximation induces only an additive slack in the resulting LCB objective (Appendix A.12).", "source": "marker_v2", "marker_block_id": "/page/2/Text/9"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0034", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "Fix a prompt s and condition on \\mathcal{Y}=\\mathcal{Y}(s) with K:=|\\mathcal{Y}|. For readability, write R_i(y) for R_i(s,y) , and \\mu(y),\\sigma(y) for \\mu(s,y),\\sigma(s,y). For each y\\in\\mathcal{Y} , we observe n independent satisfaction samples with mean \\mu(y) and variance \\sigma^2(y) , and denote the empirical mean and standard deviation by \\hat{\\mu}_n(y):=\\frac{1}{n}\\sum_{i=1}^n R_i(y) and \\hat{\\sigma}_n^2(y):=\\frac{1}{n-1}\\sum_{i=1}^n (R_i(y)-\\hat{\\mu}_n(y))^2.", "source": "marker_v2", "marker_block_id": "/page/2/Text/11"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0035", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "Bridge to pairwise preferences. Our scalar-sample analysis can be viewed as operating on standard scalarizations of pairwise preferences (e.g., win-rate or fitted BT/Thurstone scores); see Appendix A.14. Empirically, our main conclusions are stable when replacing absolute scalar ratings with a pairwise scalarization against the base response (Table 6). Remark 3.1 (Shared annotators across candidates). Our guarantee requires independence across i for each fixed candidate y. Annotator overlap across candidates may induce dependence between \\{(\\hat{\\mu}_n(y), \\hat{\\sigma}_n(y))\\}_{y \\in \\mathcal{Y}} , but the uniform guarantee below follows from per-candidate concentration with a union bound and does not require independence across candidates.", "source": "marker_v2", "marker_block_id": "/page/2/Text/12"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0036", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "Assumption 3.2 (Bounded rewards). For all y \\in \\mathcal{Y} , the satisfaction samples are almost surely bounded:", "source": "marker_v2", "marker_block_id": "/page/2/Text/13"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0037", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Equation", "text": "R_i(y) \\in [a, b] a.s.", "source": "marker_v2", "marker_block_id": "/page/2/Equation/14"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0038", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "Boundedness matches typical rating scales and can be enforced for proxy scores via truncation (Appendix H.1); an analogous LCB holds under sub-Gaussian noise (Appendix A.4).", "source": "marker_v2", "marker_block_id": "/page/2/Text/15"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0039", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "Proposition 3.3 (Uniform LCB). There exists an absolute constant c > 0 such that for any \\delta \\in (0,1) , with probability at least 1 - \\delta , simultaneously for all y \\in \\mathcal{Y}(s) ,", "source": "marker_v2", "marker_block_id": "/page/2/Text/16"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0040", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\mu(y) \\ge \\hat{\\mu}_n(y) - c\\,\\hat{\\sigma}_n(y)\\sqrt{\\frac{\\log(K/\\delta)}{n}} - c\\,(b-a)\\frac{\\log(K/\\delta)}{n}. (4)", "source": "marker_v2", "marker_block_id": "/page/2/Equation/17"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0041", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "We denote the right-hand side by LCB<sub> \\delta </sub>(y).", "source": "marker_v2", "marker_block_id": "/page/2/Text/18"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0042", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "Proof. See Appendix A.2.", "source": "marker_v2", "marker_block_id": "/page/2/Text/19"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0043", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "Remark 3.4 (Variance governs estimation hardness). The LCB form (4) highlights a statistical driver of selection risk: the dominant estimation error scales with the standard deviation \\sigma(y) . The lower-order term decays as O(1/n), whereas the leading term scales as O(\\sigma(y)/\\sqrt{n}) . Consequently, low-disagreement candidates (small \\sigma(y) ) admit substantially tighter confidence bounds at the same sample size, while controversial candidates require many more samples to certify their mean. Penalizing \\hat{\\sigma}_n(y) therefore has an identification rationale: it discourages selecting candidates whose true quality is intrinsically harder to verify from limited feedback.", "source": "marker_v2", "marker_block_id": "/page/2/Text/20"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0044", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "Lower-tail interpretation. Maximizing a lower confidence bound is a principled way to avoid candidates with poor lower-tail satisfaction even when \\hat{\\mu}_n(y) is high (Boucheron et al., 2013; Vershynin, 2018). This is a statistical conservatism argument rather than an equivalence to coherent tail-risk measures such as CVaR (Artzner et al., 1999; Rockafellar et al., 2000). See Appendix A.4 for details.", "source": "marker_v2", "marker_block_id": "/page/2/Text/21"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0045", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "On constants and practical calibration. The uniform LCB in (4) is obtained via standard concentration plus a union bound over K candidates and is therefore conservative. We do not claim tight constants; instead, the bound motivates the functional form", "source": "marker_v2", "marker_block_id": "/page/2/Text/22"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0046", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Equation", "text": "\\lambda_{\\delta} \\propto \\sqrt{\\frac{\\log(K/\\delta)}{n}},", "source": "marker_v2", "marker_block_id": "/page/2/Equation/23"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0047", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "and the lower-order term c(b-a)\\frac{\\log(K/\\delta)}{n} is uniform across candidates and does not affect \\arg\\max_y decisions. In practice, we treat the coefficient as a risk-budget knob (optionally scaled by a factor \\alpha ) and fix it via a small held-out calibration, while reporting sensitivity of the resulting trade-off. Combined with the \\hat{\\sigma}_n(y) factor in (4), the uncertainty penalty scales as \\widetilde{O}(\\hat{\\sigma}_n(y)\\sqrt{\\log K/n}) , matching the intuition that more controversial candidates require larger risk budgets to be selected.", "source": "marker_v2", "marker_block_id": "/page/2/Text/24"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0048", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Text", "text": "LCB decoding and a mean–dispersion surrogate. We define the LCB decoder as", "source": "marker_v2", "marker_block_id": "/page/2/Text/25"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0049", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 3, "page_end": 3, "type": "Equation", "text": "y_{\\text{LCB}} \\in \\arg \\max_{y \\in \\mathcal{Y}} \\text{LCB}_{\\delta}(y).", "source": "marker_v2", "marker_block_id": "/page/2/Equation/26"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0050", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 4, "page_end": 4, "type": "Text", "text": "On the high-probability event of Proposition 3.3, this rule maximizes a valid lower bound on the true mean satisfaction \\mu(y) . Crucially, under bounded ratings, maximizing LCB_{\\delta}(y) is equivalent (up to a constant) to a mean-dispersion surrogate:", "source": "marker_v2", "marker_block_id": "/page/3/Text/1"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0051", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\arg \\max_{y \\in \\mathcal{Y}} (\\hat{\\mu}_n(y) - \\lambda \\hat{\\sigma}_n(y)).", "source": "marker_v2", "marker_block_id": "/page/3/Equation/2"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0052", "section": "3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate", "page_start": 4, "page_end": 4, "type": "Text", "text": "We provide the derivation in Corollary A.2 (Appendix A.3) and discuss the theoretical connection between this \\sigma -penalty (estimation uncertainty) and the entropic \\sigma^2 -penalty (risk aversion) in Remark A.3.", "source": "marker_v2", "marker_block_id": "/page/3/Text/3"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0053", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "KL-robust (entropic) decoding. We first consider a relative-entropy (KL) robustification of expected satisfaction. Let R \\in \\mathbb{R} be the (latent) satisfaction with reference distribution \\mathbb{P} . We consider worst-case distributions \\mathbb{Q} over R that are absolutely continuous w.r.t. \\mathbb{P} . For \\beta > 0 , define the KL-regularized robust value", "source": "marker_v2", "marker_block_id": "/page/3/Text/5"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0054", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\operatorname{Rob}_{\\beta}^{\\operatorname{KL}}(\\mathbb{P};R) := \\inf_{\\mathbb{Q} \\ll \\mathbb{P}} \\left\\{ \\mathbb{E}_{\\mathbb{Q}}[R] + \\beta^{-1} D_{\\operatorname{KL}}(\\mathbb{Q} \\| \\mathbb{P}) \\right\\}, \\quad (5)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/6"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0055", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "where \\mathbb{Q} \\ll \\mathbb{P} ensures the KL term is well-defined. This is standard in risk-sensitive control and large deviations (Dupuis & Ellis, 2011; Hansen & Sargent, 2011).", "source": "marker_v2", "marker_block_id": "/page/3/Text/7"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0056", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "Theorem 3.5 (KL-robust value equals an entropic objective). For any \\beta > 0 and any \\mathbb{P} such that \\mathbb{E}_{\\mathbb{P}}[\\exp(-\\beta R)] < \\infty ,", "source": "marker_v2", "marker_block_id": "/page/3/Text/8"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0057", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\operatorname{Rob}_{\\beta}^{\\mathrm{KL}}(\\mathbb{P}; R) = -\\frac{1}{\\beta} \\log \\mathbb{E}_{R \\sim \\mathbb{P}}[\\exp(-\\beta R)]. \\quad (6)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/9"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0058", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "In particular, for the empirical rater distribution \\widehat{\\mathbb{P}}_n^y , \\operatorname{Rob}_{\\beta}^{\\mathrm{KL}}(\\widehat{\\mathbb{P}}_n^y;R) = -\\frac{1}{\\beta}\\log(\\frac{1}{n}\\sum_{i=1}^n\\exp(-\\beta R_i(y))) = \\widehat{V}_{\\beta}(s,y) . See Appendix A.5 for the detailed proof.", "source": "marker_v2", "marker_block_id": "/page/3/Text/10"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0059", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "Relation to Expected Utility Theory (CARA). Maximizing the entropic value in (6) is equivalent to maximizing expected utility under a constant absolute risk aversion (CARA) utility, u(x) = -\\exp(-\\beta x) . A useful invariance is translation equivariance: for any constant c, V_{\\beta}(R+c) = V_{\\beta}(R) + c , hence the risk premium \\mu(R) - V_{\\beta}(R) is invariant to additive reward shifts. This is desirable in RLHF-style pipelines where learned reward models are often only identifiable up to an affine transformation.", "source": "marker_v2", "marker_block_id": "/page/3/Text/11"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0060", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "\\chi^2 -DRO yields a mean–dispersion special case. We now give a complementary robust-optimization view (Wiesemann et al., 2014; Rahimian & Mehrotra, 2019): under a \\chi^2 -divergence ambiguity set around \\mathbb{P} (Ben-Tal & Nemirovski, 2002), the worst-case expected satisfaction admits a mean–dispersion form. (Definitions and tightness conditions are deferred to Appendix B.)", "source": "marker_v2", "marker_block_id": "/page/3/Text/12"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0061", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "Proposition 3.6 ( \\chi^2 -DRO robust mean admits a mean–dispersion form). Let R be square-integrable under \\mathbb{P} with mean \\mu_{\\mathbb{P}} := \\mathbb{E}_{\\mathbb{P}}[R] and variance \\sigma_{\\mathbb{P}}^2 := \\operatorname{Var}_{\\mathbb{P}}(R) . For any", "source": "marker_v2", "marker_block_id": "/page/3/Text/13"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0062", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\rho \\ge 0, \\inf_{\\mathbb{Q} \\in \\mathcal{U}_{\\rho}(\\mathbb{P})} \\mathbb{E}_{\\mathbb{Q}}[R] \\ge \\mu_{\\mathbb{P}} - \\sqrt{\\rho} \\, \\sigma_{\\mathbb{P}}. (7)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/14"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0063", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "Specializing to \\mathbb{P} = \\widehat{\\mathbb{P}}_n^y yields the empirical closed form", "source": "marker_v2", "marker_block_id": "/page/3/Text/15"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0064", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\inf_{\\mathbb{Q}\\in\\mathcal{U}_{\\rho}(\\widehat{\\mathbb{P}}_{n}^{y})} \\mathbb{E}_{\\mathbb{Q}}[R] = \\widehat{\\mu}_{n}(y) - \\sqrt{\\rho} \\sqrt{\\widehat{v}_{n}(y)}, \\tag{8}", "source": "marker_v2", "marker_block_id": "/page/3/Equation/16"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0065", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "whenever the extremal density is nonnegative on the empirical support. Otherwise, the mean-dispersion form remains a valid lower bound (Remark B.1), ensuring the rule remains pessimistic.", "source": "marker_v2", "marker_block_id": "/page/3/Text/17"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0066", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "Proof and tightness conditions. See Appendix B for the extremal density characterization and a sufficient nonnegativity regime (e.g., bounded ratings imply tightness for small \\rho ).", "source": "marker_v2", "marker_block_id": "/page/3/Text/18"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0067", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "A unified pessimistic value (LCB as calibrated DRO). Define the candidate-wise pessimistic value", "source": "marker_v2", "marker_block_id": "/page/3/Text/19"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0068", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Equation", "text": "V_{\\delta}(y) := \\widehat{\\mu}_n(y) - c \\,\\widehat{\\sigma}_n(y) \\sqrt{\\frac{\\log(K/\\delta)}{n}} - c \\,(b-a) \\frac{\\log(K/\\delta)}{n}, (9)", "source": "marker_v2", "marker_block_id": "/page/3/Equation/20"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0069", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "which is a uniform lower confidence bound (LCB) under Proposition 3.3 (Appendix A.2). On the other hand, Proposition 3.6 implies that, up to the lower-order term in (9), V_{\\delta}(y) matches the \\chi^2 -DRO robust mean of the empirical rater distribution with radius", "source": "marker_v2", "marker_block_id": "/page/3/Text/21"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0070", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Equation", "text": "\\rho_{\\delta} \\asymp \\frac{\\log(K/\\delta)}{n},", "source": "marker_v2", "marker_block_id": "/page/3/Equation/22"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0071", "section": "3.2. Distributional risk: DRO characterizations of pessimistic value", "page_start": 4, "page_end": 4, "type": "Text", "text": "since \\sqrt{\\rho_\\delta} \\, \\widehat{\\sigma}_n(y) \\asymp \\widehat{\\sigma}_n(y) \\sqrt{\\log(K/\\delta)/n} (see Appendix C for a discussion distinguishing statistical estimation risk from intrinsic disagreement). This yields a unified interpretation of disagreement-aware decoding as calibrated pessimism :a statistical LCB rule that is equivalent (up to lower-order terms) to optimizing a local DRO objective. Thus, disagreement-aware decoding can be viewed equivalently as (i) maximizing a high-probability LCB on expected satisfaction (statistical pessimism), or (ii) maximizing a distributionally robust worst-case expected satisfaction over a local \\chi^2 neighborhood (adversarial robustness).", "source": "marker_v2", "marker_block_id": "/page/3/Text/23"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0072", "section": "4. Disagreement-Aware Risk-Constrained Decoding", "page_start": 4, "page_end": 4, "type": "Text", "text": "Motivated by the LCB and DRO characterization in §3–§3.2, we now present practical decoding rules that implement the KL-robust entropic objective (and its constrained/penalized variants) over a finite candidate set. For completeness, we also include a second-moment pessimistic surrogate implied by the LCB analysis in (18) as a computationally convenient ablation.", "source": "marker_v2", "marker_block_id": "/page/3/Text/25"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0073", "section": "4.1. From preference maximization to risk controls", "page_start": 4, "page_end": 4, "type": "Text", "text": "Standard reward-based reranking selects the highest estimated mean,", "source": "marker_v2", "marker_block_id": "/page/3/Text/27"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0074", "section": "4.1. From preference maximization to risk controls", "page_start": 4, "page_end": 4, "type": "Equation", "text": "y_{\\text{mean}}(s) \\in \\arg \\max_{y \\in \\mathcal{V}(s)} \\hat{\\mu}(s, y),", "source": "marker_v2", "marker_block_id": "/page/3/Equation/28"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0075", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Text", "text": "which optimizes average preference but may favor brittle outputs when disagreement is large.", "source": "marker_v2", "marker_block_id": "/page/4/Text/2"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0076", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Text", "text": "Risk-sensitive decoding (primary rule). Our primary decoder selects the candidate with the largest scorer-robust entropic value:", "source": "marker_v2", "marker_block_id": "/page/4/Text/3"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0077", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Equation", "text": "y_{\\text{Entropic}}(s) \\in \\arg \\max_{y \\in \\mathcal{Y}(s)} \\widehat{V}_{\\beta}(s, y), (10)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/4"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0078", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Text", "text": "where \\widehat{V}_{\\beta} is the entropic value defined in (2).", "source": "marker_v2", "marker_block_id": "/page/4/Text/5"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0079", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Text", "text": "Risk-constrained decoding via an entropic risk premium. We define explicit deployment knobs using the entropic risk premium \\widehat{RP}_{\\beta}(s,y) from (3). We consider two standard forms:", "source": "marker_v2", "marker_block_id": "/page/4/Text/6"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0080", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Equation", "text": "y_{\\tau}(s) \\in \\arg \\max_{y \\in \\mathcal{Y}(s)} \\widehat{V}_{\\beta}(s, y) \\quad \\text{s.t.} \\quad \\widehat{\\mathrm{RP}}_{\\beta}(s, y) \\leq \\tau (11)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/7"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0081", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Equation", "text": "y_{\\lambda}(s) \\in \\arg\\max_{y \\in \\mathcal{Y}(s)} \\widehat{V}_{\\beta}(s, y) - \\lambda \\,\\widehat{\\mathrm{RP}}_{\\beta}(s, y), (12)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/8"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0082", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Text", "text": "where the penalty form is a Lagrangian relaxation. If the feasible set \\{y \\in \\mathcal{Y}(s) : \\widehat{\\mathrm{RP}}_\\beta(s,y) \\leq \\tau\\} is empty, we fall back to \\mathcal{Y}(s) , consistent with Algorithm 1. The constrained and penalized forms provide two equivalent ways to tune the reward–risk trade-off; their finite-candidate-set relationship is given in Appendix A.6.", "source": "marker_v2", "marker_block_id": "/page/4/Text/9"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0083", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Text", "text": "Disagreement as a risk proxy: interpretation and limitations. We use disagreement as a human-centric signal of preference heterogeneity, and implement risk sensitivity through the KL-robust entropic value (10) (a standard convex risk measure). The mean–dispersion form arises only as a finite-sample surrogate (via LCB pessimism) or as a \\chi^2 -DRO special case, rather than being the defining principle of our method.", "source": "marker_v2", "marker_block_id": "/page/4/Text/10"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0084", "section": "4.1. From preference maximization to risk controls", "page_start": 5, "page_end": 5, "type": "Text", "text": "Importantly, we do not claim that variance is a coherent risk measure (e.g., CVaR) (Artzner et al., 1999; Rockafellar et al., 2000) or that \\sigma is equivalent to a tail-risk functional in full generality. Instead, §3 shows that penalizing \\hat{\\sigma} arises naturally from maximizing a statistically justified lower confidence bound (LCB) on \\mu(s,y) , yielding a principled pessimistic selection rule under finite data. Moreover, §3.2 provides a complementary distributionally robust optimization characterization (Wiesemann et al., 2014; Rahimian & Mehrotra, 2019).", "source": "marker_v2", "marker_block_id": "/page/4/Text/11"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0085", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Text", "text": "Proxy robustness. When (\\hat{\\mu}, \\hat{\\sigma}) are obtained from scalable proxy scorers rather than i.i.d. human samples, a uniform proxy-error assumption yields a robust LCB guarantee; we defer the formal statement and proof to Appendix A.12.", "source": "marker_v2", "marker_block_id": "/page/4/Text/13"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0086", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Text", "text": "\\epsilon -rule as a constrained optimization. Our \\epsilon -tie-breaking is equivalent to", "source": "marker_v2", "marker_block_id": "/page/4/Text/14"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0087", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Equation", "text": "y_{\\epsilon}(s) \\in \\arg\\min_{y \\in \\mathcal{Y}(s)} \\widehat{\\sigma}(s, y) \\quad \\text{s.t.} \\quad \\widehat{V}_{\\beta}(s, y) \\ge \\widehat{V}_{\\max}(s) - \\epsilon, (13)", "source": "marker_v2", "marker_block_id": "/page/4/Equation/15"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0088", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Text", "text": "where \\widehat{V}_{\\max}(s) := \\max_{y \\in \\mathcal{Y}(s)} \\widehat{V}_{\\beta}(s, y) .", "source": "marker_v2", "marker_block_id": "/page/4/Text/16"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0089", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Text", "text": "Pareto view. Eq. (13) selects a Pareto-optimal point of", "source": "marker_v2", "marker_block_id": "/page/4/Text/17"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0090", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Text", "text": "the robust-value—disagreement trade-off: among candidates whose robust value is within \\epsilon of the best, it returns the least controversial one. Moreover, when the chosen point is sup-ported, the same solution can be written as a scalarization \\arg\\max_y\\left(\\widehat{V}_{\\beta,\\gamma}(s,y)-\\lambda_{\\epsilon}\\widehat{\\sigma}(s,y)\\right) for some \\lambda_{\\epsilon}\\geq 0 ; formal statements and proofs are deferred to Appendix A.13.", "source": "marker_v2", "marker_block_id": "/page/4/Text/18"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0091", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Text", "text": "Two-stage rule. To avoid sacrificing entropic value excessively for marginal robustness, we use:", "source": "marker_v2", "marker_block_id": "/page/4/Text/19"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0092", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\mathcal{F}_{\\epsilon}(s) := \\{ y \\in \\mathcal{Y}(s) \\mid \\widehat{V}_{\\beta}(s, y) \\ge \\widehat{V}_{\\max}(s) - \\epsilon \\}, y_{\\epsilon}(s) \\in \\arg \\min_{y \\in \\mathcal{F}_{\\epsilon}(s)} \\widehat{\\sigma}(s, y).", "source": "marker_v2", "marker_block_id": "/page/4/Equation/20"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0093", "section": "4.2. Practical decoding: \\epsilon -tie breaking", "page_start": 5, "page_end": 5, "type": "Text", "text": "This approximates the scalarized decoder \\max_y \\left(\\widehat{V}_\\beta(s,y) - \\lambda \\, \\widehat{\\sigma}(s,y)\\right) by enforcing near-optimality in entropic value and then selecting the least controversial candidate. In practice, we tune all risk parameters (\\beta,\\tau,\\epsilon) on a held-out development set; detailed tuning protocols are provided in Appendix H.4.", "source": "marker_v2", "marker_block_id": "/page/4/Text/21"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0094", "section": "4.3. Multi-scorer robustness", "page_start": 5, "page_end": 5, "type": "Text", "text": "Scorer-robust decoding (multi-reward models). In scalable proxy settings, satisfaction scores may come from learned reward models and be sensitive to model shift or proxy over-optimization. We optionally hedge this scorer ambiguity by using a family of M scorers indexed by m \\in [M] . For each candidate y \\in \\mathcal{Y}(s) , scorer m provides n scalar samples \\{R_{m,i}(s,y)\\}_{i=1}^n (e.g., via perturbations), from which we compute the scorer-specific entropic value \\widehat{V}_{\\beta,m}(s,y) and risk premium \\widehat{\\mathrm{RP}}_{\\beta,m}(s,y) . Because reward scales can differ across scorers, we apply a perprompt affine normalization (Appendix E). We then aggregate scorer-specific entropic values using a soft worst-case operator:", "source": "marker_v2", "marker_block_id": "/page/4/Text/23"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0095", "section": "4.3. Multi-scorer robustness", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\widetilde{V}_{\\beta,\\gamma}(s,y) := -\\frac{1}{\\gamma} \\log \\left( \\frac{1}{M} \\sum_{m=1}^{M} \\exp\\left(-\\gamma \\widehat{V}_{\\beta,m}(s,y)\\right) \\right), \\tag{14}", "source": "marker_v2", "marker_block_id": "/page/4/Equation/24"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0096", "section": "4.3. Multi-scorer robustness", "page_start": 5, "page_end": 5, "type": "Text", "text": "and aggregate risk premia pessimistically by \\widehat{RP}_{\\beta}(s,y) := \\max_{m \\in [M]} \\widehat{RP}_{\\beta,m}(s,y) . We decode by maximizing \\widetilde{V}_{\\beta,\\gamma}(s,y) subject to \\widehat{RP}_{\\beta}(s,y) \\leq \\tau (or its penalized form). Proposition 4.1 (Scorer aggregation as KL-regularized", "source": "marker_v2", "marker_block_id": "/page/4/Text/25"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0097", "section": "4.3. Multi-scorer robustness", "page_start": 5, "page_end": 5, "type": "Text", "text": "Proposition 4.1 (Scorer aggregation as KL-regularized DRO over scorers). Let v_m := \\hat{V}_{\\beta,m}(s,y) and \\mathbf{v} \\in \\mathbb{R}^M . Define \\mathbf{u} = (1/M, \\dots, 1/M) and the simplex \\Delta_M := \\{\\mathbf{q} \\in \\mathbb{R}^M_+ : \\sum_{m=1}^M q_m = 1\\} . Then the soft worst-case aggregation (14) admits the variational form", "source": "marker_v2", "marker_block_id": "/page/4/Text/26"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0098", "section": "4.3. Multi-scorer robustness", "page_start": 5, "page_end": 5, "type": "Equation", "text": "\\widetilde{V}_{\\beta,\\gamma}(s,y) = \\inf_{\\mathbf{q} \\in \\Delta_M} \\left\\{ \\sum_{m=1}^M q_m v_m + \\frac{1}{\\gamma} D_{\\mathrm{KL}}(\\mathbf{q} \\| \\mathbf{u}) \\right\\}. \\tag{15}", "source": "marker_v2", "marker_block_id": "/page/4/Equation/27"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0099", "section": "4.3. Multi-scorer robustness", "page_start": 5, "page_end": 5, "type": "Text", "text": "Interpretation. Eq. (15) shows that \\gamma interpolates between averaging across scores (\\gamma \\to 0) and a worst-case scorer (\\gamma \\to \\infty) , yielding a principled hedge against scorer shift. In particular, \\min_m v_m \\leq \\widetilde{V}_{\\beta,\\gamma}(s,y) \\leq \\frac{1}{M} \\sum_m v_m , and \\widetilde{V}_{\\beta,\\gamma}(s,y) is non-increasing in \\gamma .", "source": "marker_v2", "marker_block_id": "/page/4/Text/28"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0100", "section": "4.3. Multi-scorer robustness", "page_start": 6, "page_end": 6, "type": "TableGroup", "text": "Llama-3.1-8B-Instruct Qwen2.5-7B-Instruct Type Method M T-Bench Alp acaEval 2.0 ) M T-Bench Alpa caEval 2.0 Reward Risk↓ Tradeoff Len(tok) Reward Risk↓ Tradeoff Len(tok) Reward Risk↓ Tradeoff Len(tok) Reward Risk↓ Tradeoff Len(tok) Dataset: Overall Base (Best-of-K) 4.53 6.50 -8.47 315 4.52 7.46 -10.40 331 4.09 3.54 -2.99 244 3.29 3.11 -2.93 256 BoP(HedgeTune) 4.18 5.86 -7.54 316 4.12 6.24 -8.36 330 3.84 3.10 -2.36 231 3.14 2.68 -2.22 261 Inference Caution 4.09 5.43 -6.77 317 4.27 5.91 -7.55 320 3.89 3.21 -2.53 243 3.09 2.62 -2.15 259 DeAL 5.59 7.98 -10.37 309 5.66 8.74 -11.81 311 4.64 4.22 -3.80 256 4.02 3.74 -3.46 267 MC-Dropout 4.41 5.78 -7.15 315 4.37 6.31 -8.25 326 3.87 3.38 -2.89 247 3.13 2.79 -2.45 253 RBoN 4.43 5.62 -6.81 309 4.31 5.82 -7.33 321 3.93 3.22 -2.51 241 3.17 2.71 -2.25 257 DARC(ours) 4.46 5.41 -6.36 315 4.25 5.67 -7.33 319 4.01 3.14 -2.27 243 3.14 2.66 -2.18 256 DARC- \\tau (ours) 4.42 5.45 -6.48 313 4.49 6.21 -7.93 321 3.94 2.99 -2.04 232 3.12 2.48 -1.85 257 DARC- \\epsilon (ours) 4.46 5.29 -6.12 314 4.38 5.60 -6.82 319 3.96 2.96 -1.96 243 3.18 2.36 -1.54 261 cDPO (Best-of-K) 5.88 5.96 -6.04 300 5.86 6.97 -8.08 309 8.61 5.76 -2.91 258 5.30 6.63 -7.96 278 m · · cDPO + DARC- \\epsilon 5.81 5.65 -5.49 311 5.83 6.57 -7.31 290 8.53 5.49 -2.45 278 5.22 6.40 -7.58 274 Training rDPO (Best-of-K) 5.53 5.57 -5.61 260 11.62 7.10 -2.58 316 8.73 5.94 -3.15 294 5.77 6.90 -8.03 282 rDPO + DARC- \\epsilon 5.42 5.16 -4.90 258 11.58 6.78 -1.98 325 8.62 5.69 -2.76 288 5.68 6.68 -7.68 232 Dataset: High-Variance (Top 20%) Base (Best-of-K) 5.79 9.91 -14.03 382 7.48 10.22 -12.96 381 5.12 6.00 -7.12 308 2.79 5.46 -8.13 263 BoP(HedgeTune) 5.45 7.90 -10.35 382 7.28 8.12 -8.96 381 4.67 5.12 -5.57 307 2.53 4.09 -5.65 265 Inference Caution 5.41 7.42 -9.43 382 7.17 8.34 -9.51 381 4.80 5.39 -5.98 307 2.30 4.07 -5.84 264 DeAL 5.96 9.71 -13.46 374 7.89 10.15 -12.41 371 5.75 8.43 -11.11 316 3.45 6.89 -10.33 256 MC-Dropout 5.20 7.48 -9.76 384 7.19 8.15 -9.11 380 4.75 5.25 -5.25 306 2.35 4.00 -5.65 262 RBoN 5.28 7.30 -9.32 372 7.22 8.40 -9.58 376 4.90 5.45 -6.00 300 2.25 4.15 -6.05 258 DARC(ours) 5.32 7.33 -9.34 382 7.24 8.10 -8.96 381 4.99 5.05 -5.13 307 2.34 4.42 -6.50 263 DARC- \\tau (ours) 5.43 7.90 -10.37 382 7.21 8.55 -9.89 381 4.78 4.85 -4.92 294 2.31 3.84 -5.37 249 DARC- \\epsilon (ours) 5.49 7.00 -8.51 382 7.26 8.10 -8.94 381 5.03 4.77 -4.51 306 2.59 3.76 -4.93 265 cDPO (Best-of-K) 7.54 8.39 -9.24 312 8.88 9.40 -9.92 328 5.52 5.67 -5.82 317 7.17 7.30 -7.43 196 T cDPO + DARC- \\epsilon 7.51 8.11 -8.71 323 8.81 9.21 -9.61 328 5.42 5.17 -4.92 316 7.12 7.29 -7.46 196 Training rDPO (Best-of-K) 6.58 7.98 -9.38 337 11.60 9.05 -6.50 347 5.79 5.34 -4.89 304 7.80 7.72 -7.64 172 rDPO + DARC-e 6.41 7 16 -7 91 316 11.56 8 65 -5 74 329 5 56 5.03 -4 50 301 7.70 7.28 -6.86 164 Table 1. Evaluation on MT-Bench and AlpacaEval 2.0. Results across two generators families. We report mean reward, proxy risk (Risk), risk—reward tradeoff score (Tradeoff), and average length (Len(tok)).Blue/green highlight best/runner-up.", "source": "marker_v2", "marker_block_id": "/page/5/TableGroup/333"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0101", "section": "5.1. Experimental Setup and Implementation Details", "page_start": 6, "page_end": 6, "type": "Text", "text": "Candidate sets and evaluation protocol. For each prompt s, we generate a fixed candidate pool \\mathcal{Y}(s) of size K (shared across all methods), so differences arise solely from the inference-time selection rule. In the human-grounded setting, for each y \\in \\mathcal{Y}(s) we collect n scalar satisfaction ratings \\{r_i(s,y)\\}_{i=1}^n (Christiano et al., 2017; Stiennon et al., 2020; Ouyang et al., 2022), and split annotators into disjoint selection and evaluation sets \\mathcal{I}_{sel} and \\mathcal{I}_{eval} to avoid selection-evaluation leakage. All decoders operate on statistics computed from \\mathcal{I}_{sel} . Our entropic decoder uses the empirical entropic value in the human-grounded setting (where M=1 and V_{\\beta,\\gamma}=V_{\\beta} ), and uses the scorer-robust aggregated value V_{\\beta,\\gamma}(s,y) (and RP_{\\beta}(s,y) ) in proxy settings with multiple reward models. Second-moment baselines use only (\\hat{\\mu}_{sel}(s,y), \\hat{\\sigma}_{sel}(s,y)) (or their scorer-indexed analogues under proxies). All reported metrics are computed on held-out ratings in \\mathcal{I}_{eval} (definitions in Appendix H.3).", "source": "marker_v2", "marker_block_id": "/page/5/Text/6"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0102", "section": "5.1. Experimental Setup and Implementation Details", "page_start": 6, "page_end": 6, "type": "Text", "text": "Estimating mean and disagreement. We define (\\hat{\\mu}, \\hat{\\sigma}) as the mean and disagreement estimates, derived from either empirical samples or scorer proxies . DARC is inference-time only , modifying the selection over \\mathcal{Y}(s) without retraining. While our theory assumes multi-annotator feedback, we validate proxy uncertainty as a scalable approximation for human disagreement.", "source": "marker_v2", "marker_block_id": "/page/5/Text/7"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0103", "section": "5.1. Experimental Setup and Implementation Details", "page_start": 6, "page_end": 6, "type": "Text", "text": "Proxies, baselines, and hyperparameters. When multirater human scores are unavailable, we use scalable proxy", "source": "marker_v2", "marker_block_id": "/page/5/Text/8"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0104", "section": "5.1. Experimental Setup and Implementation Details", "page_start": 6, "page_end": 6, "type": "Text", "text": "scorers (e.g., ensembles / bootstrap reward models) to obtain a proxy mean together with either (i) a score distribution for computing V_{\\beta} , or (ii) a proxy disagreement diagnostic \\hat{\\sigma}_{proxy} (Kendall & Gal, 2017; Lakshminarayanan et al., 2017); we validate proxy-human alignment via rank correlation and stratified analyses (Uma et al., 2021). Inferencetime baselines include mean Best-of-K, inference-time hedging methods for reward hacking (Best-of-Poisson and HedgeTune) (Khalaf et al., 2025), pessimistic best-of-N reranking via an auxiliary error/atypicality model (Caution) (Anonymous, 2025), uncertainty-based reranking (e.g., MC-Dropout) (Gal & Ghahramani, 2016; Kendall & Gal, 2017), reward-regularized decoding (RBoN) (Jinnai et al., 2024) and DeAL (top-k lookahead reward-guided decoding) (Huang et al., 2025b); training-time baselines include cDPO/rDPO (Mitchell, 2023; Chowdhury et al., 2024). We report default settings and full tuning ranges (including our LCB- and DRO-instantiated decoding rules), along with complete baseline configurations and implementation details, in Appendix H.2 (see also Appendix F).", "source": "marker_v2", "marker_block_id": "/page/5/Text/9"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0105", "section": "5.1. Experimental Setup and Implementation Details", "page_start": 6, "page_end": 6, "type": "Text", "text": "Inference overhead. Disagreement estimation adds only a modest inference-time cost: in our implementation, using N_{\\rm aug} = 4/8/16 increases end-to-end latency by only \\approx 1.5\\%/2.0\\%/3.2\\% , since candidate generation dominates runtime (Appendix H.6, Table 7).", "source": "marker_v2", "marker_block_id": "/page/5/Text/10"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0106", "section": "5.1. Experimental Setup and Implementation Details", "page_start": 6, "page_end": 6, "type": "Text", "text": "Metrics (mean, risk, and tail). For each prompt s and candidate response y, we evaluate rewards on a held-out rater set \\mathcal{I}_{\\text{eval}} and report the empirical mean \\hat{\\mu}_{\\text{eval}}(s,y) . As a scalable proxy for robustness, we compute a perturbation -", "source": "marker_v2", "marker_block_id": "/page/5/Text/11"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0107", "section": "5.1. Experimental Setup and Implementation Details", "page_start": 7, "page_end": 7, "type": "Text", "text": "sensitivity statistic \\hat{\\sigma}_{sel}(s,y) as the standard deviation of rewards across N_{aug} style-preserving perturbations of y (see Appendix H.13). Human evaluation details are in Appendix I; the human mean is the average rating and the human variance is the sample variance across raters. We summarize performance via \\operatorname{Tradeoff}_{eval}(s,y) := \\hat{\\mu}_{eval}(s,y) - \\lambda \\hat{\\sigma}_{sel}(s,y) , using the same \\lambda for all methods (Appendix H.14). We also report \\operatorname{CVaR}_{10\\%} over prompts (Chow et al., 2015); see Appendix H.3.", "source": "marker_v2", "marker_block_id": "/page/6/Text/1"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0108", "section": "5.1. Experimental Setup and Implementation Details", "page_start": 7, "page_end": 7, "type": "TableGroup", "text": "Method Human Score ↑ Risk (Avg\\sigma) \\downarrow Tradeoff \\text{CVaR}_{10\\%}{\\uparrow} Dataset: Overall Base (Best-of- K ) 7.56 0.67 6.22 6.73 BoP(HedgeTune) 7.79 0.63 6.53 7.12 Caution 7.82 0.61 6.60 7.15 DeAL 7.83 0.72 6.39 7.08 MC-Dropout 7.73 0.64 6.45 7.19 RBoN 7.71 0.62 6.47 7.26 DARC(ours) 7.84 0.60 6.64 7.36 DARC- \\tau (ours) 7.83 0.58 6.67 7.46 DARC- \\epsilon (ours) 8.08 0.55 6.98 7.62 cDPO (Best-of-K) 7.80 0.65 6.50 7.11 cDPO + DARC- \\epsilon 8.03 0.54 6.95 7.41 rDPO (Best-of- K ) 8.17 0.69 6.79 7.20 rDPO + DARC- \\epsilon 8.15 0.58 6.99 7.60 Dataset: High-Disag greement (Top 20%) Base (Best-of- K ) 7.62 1.00 5.62 6.10 BoP(HedgeTune) 7.83 0.87 6.09 6.81 Caution 7.81 0.85 6.11 6.94 DeAL 7.99 1.13 5.73 7.33 MC-Dropout 7.88 0.84 6.20 7.25 RBoN 7.95 0.81 6.33 7.29 DARC(ours) 8.18 0.74 7.00 7.43 DARC- \\tau (ours) 8.11 0.65 6.81 7.35 DARC- \\epsilon (ours) 8.34 0.65 7.34 7.60 cDPO (Best-of-K) 7.96 0.89 6.18 7.15 cDPO + DARC- \\epsilon 8.31 0.63 7.05 7.54 rDPO (Best-of- K ) 8.25 0.91 6.43 7.02 rDPO + DARC- \\epsilon 8.72 0.67 7.38 7.48 Table 2. Human Evaluation Results. We report Human Mean Score, Disagreement Risk, Tradeoff, and \\text{CVaR}_{10\\%} (worst 10% prompt outcomes).", "source": "marker_v2", "marker_block_id": "/page/6/TableGroup/415"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0109", "section": "5.2. Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "347348", "source": "marker_v2", "marker_block_id": "/page/6/Text/28"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0110", "section": "5.2. Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "352353", "source": "marker_v2", "marker_block_id": "/page/6/Text/31"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0111", "section": "5.2. Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "357358", "source": "marker_v2", "marker_block_id": "/page/6/Text/35"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0112", "section": "5.2. Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "Automated proxy evaluation. Table 1 reports MT-Bench (Zheng et al., 2023) and AlpacaEval2.0 (Li et al., 2023; Dubois et al., 2024) results under two instructiontuned generators (Llama-3.1-8B-Instruct (Dubey et al., 2024), Qwen2.5-7B-Instruct (Qwen et al., 2025)). We evaluate each method by mean reward \\hat{\\mu} , proxy disagreement risk \\hat{\\sigma} (reward sensitivity to style-preserving perturbations), and a risk-reward tradeoff score Tradeoff = \\hat{\\mu} - \\lambda \\hat{\\sigma} with the same \\lambda across methods; we also report Len(tok) to control for length bias. Across both generators, inferencetime risk-aware selection improves robustness: DARC variants reduce \\hat{\\sigma} while keeping \\hat{\\mu} competitive, yielding higher Tradeoff than mean-only Best-of-K, with larger gains on the high-variance subset (top 20% prompts by baseline \\hat{\\sigma} ) and broadly stable Len(tok). Training-time robust policies (cDPO/rDPO) exhibit different trade-offs, and DARC remains complementary: applying DARC- \\epsilon as an inferencetime plug-in can further reduce \\hat{\\sigma} and improve Tradeoff in several cases, supporting a modular view where training", "source": "marker_v2", "marker_block_id": "/page/6/Text/5"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0113", "section": "5.2. Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "shapes the policy while DARC calibrates risk on a fixed candidate set.", "source": "marker_v2", "marker_block_id": "/page/6/Text/6"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0114", "section": "5.2. Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "Human-loop evaluation and tail robustness. We then close the loop with multi-annotator ratings on MT-Bench. Table 2 shows that DARC improves risk-sensitive criteria (Tradeoff and \\text{CVaR}_{10\\%} ) while maintaining competitive mean satisfaction. On the high-disagreement subset, disagreement-aware decoding yields substantial gains in tail robustness ( \\text{CVaR}_{10\\%} ) and conservative quality (Tradeoff), indicating that risk-controlled selection is particularly beneficial on genuinely controversial prompts. Figure 3 demonstrates that Risk-adjusted satisfaction( \\Delta Tradeoff) scale positively with disagreement, rising steadily from Q1 to Q5, peaking in the most controversial buckets (Q5). This confirms disagreement as an effective signal for allocating risk control, a trend corroborated by the CVaR results in Appendix Fig. 5.(See representative cases in Appendix H.10).)", "source": "marker_v2", "marker_block_id": "/page/6/Text/7"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0115", "section": "5.2. Results", "page_start": 7, "page_end": 7, "type": "FigureGroup", "text": "Figure 3. Gains concentrate on high-disagreement prompts. Mean improvement in lower-tail satisfaction ( \\Delta Tradeoff vs. base) across five prompt buckets ranked by baseline human disagreement \\hat{\\sigma} (low \\rightarrow high). Error bars denote 95% CIs.", "source": "marker_v2", "marker_block_id": "/page/6/FigureGroup/416"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0116", "section": "5.2. Results", "page_start": 7, "page_end": 7, "type": "Text", "text": "Validity of the disagreement proxy. We validate our perturbation-sensitivity proxy \\hat{\\sigma} against human disagreement measured by multiple independent rater scores on the same (prompt, response) pair. To avoid selection effects, we compute both proxy and human disagreement on the baseline candidate. As summarized in Figure 4, proxy disagreement shows a statistically significant rank-level consistency with human disagreement and remains positively associated even after controlling for mean reward and response length (strong and common confounders for RMbased signals). Moreover, the proxy serves as an effective risk filter for identifying prompts likely to exhibit preference heterogeneity, where risk-controlled decoding is designed to intervene: prompts identified as high-disagreement by the proxy substantially overlap with those identified by humans, far beyond random chance (Fig. 4). While mismatch cases exist (App. H.11)—often reflecting surface-form sensitivity (FP) or orthogonal validity/completeness issues (FN)—this is consistent with using \\hat{\\sigma} as a scalable screening signal to prioritize human verification rather than a fully calibrated estimator of disagreement magnitude. Consistently, this signal effectively allocates risk control: bucketed analysis", "source": "marker_v2", "marker_block_id": "/page/6/Text/10"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0117", "section": "5.2. Results", "page_start": 8, "page_end": 8, "type": "FigureGroup", "text": "Figure 2. Ablation Studies. Impact of key hyperparameters on risk mitigation performance. (a) Candidate pool size K. (b) Risk sensitivity coefficient \\beta . (c) Constraint threshold \\epsilon . (d) Perturbation budget N_{\\text{aug}} .", "source": "marker_v2", "marker_block_id": "/page/7/FigureGroup/417"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0118", "section": "5.2. Results", "page_start": 8, "page_end": 8, "type": "Text", "text": "shows a monotonic increase in \\Delta Tradeoff from low-to high-disagreement groups when bucketing by either human or proxy disagreement (App. H.7). We also stratify prompts by proxy-human disagreement alignment and find that, even in the worst-alignment bucket, DARC still achieves the best Tradeoff among all baselines (Appendix H.8, Table 8).", "source": "marker_v2", "marker_block_id": "/page/7/Text/3"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0119", "section": "5.2. Results", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Value Notes / p-value 0.6509 95% boot. CI [0.42, 0.70]; p < 10^{-10} 0.3130 p < 10^{-6} 0.4084 95% boot. CI [0.25, 0.45] 0.64 (64/100; random=0.20) 0.64 (symmetric at equal k) 0.47 (|A \\cap B|/|A \\cup B|) 64 hypergeom p = 2.6 \\times 10^{-29} Scatter: Human vs Proxy (Correlation \\rho = 0.674 ) Prompts Trend line 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6509 0.3130 0.4084 0.64 0.64 0.47 64 Figure 4. Proxy validity diagnostics. (Top) Rank correlation between proxy and human disagreement, with top-20% overlap. (Bottom) Top-q overlap (Left) and proxy vs. human disagreement scatter (Right).", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/418"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0120", "section": "5.2. Results", "page_start": 8, "page_end": 8, "type": "Text", "text": "Multi-scorer robust decoding To mitigate proxy overoptimization to a single reward model, we instantiate our decoder with a scorer family of size M = 3: RM1 (Skywork-reward-llama-3.1-8b (Liu et al., 2024a)), RM2 (nicholasKluge RewardModel (Corrêa, 2023)) and RM3(OpenAssistant (DeBERTa-v3-Large-v2) (Köpf et al., 2023)). At selection time, we compute V_{\\beta,m}(s,y) for each m \\in [M] (with within-prompt normalization), aggregate them into V_{\\beta,\\gamma}(s,y) via (14), and apply the same constrained/penalized rule using \\overline{RP}_{\\beta} in (27). For reporting, because absolute reward scales differ across RMs, we evaluate the selected outputs within each RM and report only within-RM differences to the baseline (mean \\Delta ) and Win/Tie/Loss rates (Table 3). We additionally provide a per-scorer breakdown of win/tie/loss and mean score differences under each evaluator reward model in Appendix H.9, confirming consistent gains across scorers.", "source": "marker_v2", "marker_block_id": "/page/7/Text/6"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0121", "section": "5.2. Results", "page_start": 8, "page_end": 8, "type": "TableGroup", "text": "Overa ıll High- \\hat{\\sigma} Subset Method W/T/L Mean \\Delta W/T/L Mean \\Delta Across scorers (aggregated) \\begin{array}{c} \\overline{\\text{DARC}} \\\\ \\overline{\\text{DARC-}\\tau} \\\\ \\overline{\\text{DARC-}\\epsilon} \\end{array} 278 / 173 / 49 257 / 192 / 51 296 / 168 / 36 0.124 0.128 0.161 32 / 63 / 5 36 / 60 / 4 44 / 54 / 2 0.303 0.259 0.386 Table 3. Multi-scorer robust decoding. DARC variants vs. Base (mean Best-of-K). \\Delta : per-prompt improvement over Base, aggregated across scorers (mean / min / mean— \\gamma std); W/T/L is on aggregated \\Delta . High- \\hat{\\sigma} uses the baseline disagreement proxy.", "source": "marker_v2", "marker_block_id": "/page/7/TableGroup/419"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0122", "section": "5.2. Results", "page_start": 8, "page_end": 8, "type": "Text", "text": "Scaling robustness. To assess scale robustness, we additionally evaluate our inference-time decoding rules on a stronger generator, Qwen2.5-14B-Instruct , using the same candidate-pool protocol and metrics. We observe consistent improvements over mean Best-of- K in risk-sensitive criteria (Tradeoff and prompt-level CVaR), with gains again concentrating on high-disagreement prompts (Table 14).", "source": "marker_v2", "marker_block_id": "/page/7/Text/9"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0123", "section": "5.2. Results", "page_start": 8, "page_end": 8, "type": "Text", "text": "Hyperparameter sensitivity and ablations. Figure 2 summarizes a sensitivity study over the main knobs of DARC- \\epsilon , reporting improvements over mean Best-of-K in \\Delta Tradeoff and \\Delta CVaR on fixed candidate pools. Increasing the candidate pool size K improves both metrics with diminishing returns (Fig. 2a). The risk sensitivity \\beta in the entropic robust value \\hat{V}_{\\beta} yields rapid robustness gains that plateau at moderate values (Fig. 2b). Fixing \\beta , enlarging the near-optimal set via \\epsilon further improves robustness up to saturation (with slight degradation when overly permissive) (Fig. 2c). Finally, the perturbation budget N_{\\rm aug} used to estimate proxy disagreement \\hat{\\sigma} saturates quickly; a small budget (e.g., 4–8) suffices, keeping inference overhead modest (Fig. 2d).", "source": "marker_v2", "marker_block_id": "/page/7/Text/10"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0124", "section": "6. Conclusion", "page_start": 8, "page_end": 8, "type": "Text", "text": "We cast decoding-time alignment under heterogeneous preferences as risk-constrained decision making. DARC uses a KL-robust (entropic) decoding rule with a conservative LCB/DRO interpretation, improving lower-tail outcomes while preserving mean quality. Limitations include a finite candidate pool and scorer bias; perturbation-based disagreement proxies are scalable screening signals, not calibrated human-disagreement estimates. Future work includes richer robustness signals and user/group-conditional risk control.", "source": "marker_v2", "marker_block_id": "/page/7/Text/12"}
+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0125", "section": "Impact Statement", "page_start": 9, "page_end": 9, "type": "Text", "text": "This paper presents work whose goal is to advance the field of machine learning. Our contributions focus on inferencetime response selection under preference heterogeneity. As with many machine learning methods, the proposed approach may exhibit uneven performance if the underlying proxies or learned scorers encode dataset- or populationspecific biases. We encourage reporting sensitivity to key design choices and auditing proxy/scorer behavior when the method is used in practice. Consequently, the method should be used and evaluated with appropriate care in deployment.", "source": "marker_v2", "marker_block_id": "/page/8/Text/2"}

icml26/3105df16-98c9-46f1-9f54-b48ba2014a8a/marker_meta.json

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+      "title": "DARC: Disagreement-Aware Alignment via Risk-Constrained Decoding",
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+      "title": "Abstract",
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+      "title": "1. Introduction",
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+      "title": "Contributions.",
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+      "title": "3. Guarantees via Lower Confidence Bounds",
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+      "title": "A. Additional Theoretical Details",
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icml26/3105df16-98c9-46f1-9f54-b48ba2014a8a/model_text_v3.txt

@@ -0,0 +1,377 @@
+[p. 1 | section: Abstract | type: Text]
+Preference-based alignment methods (e.g., RLHF, DPO) typically optimize a single scalar objective, implicitly averaging over heterogeneous human preferences. In practice, systematic annotator and user-group disagreement makes mean-reward maximization brittle and susceptible to proxy over-optimization. We propose Disagreement-Aware Alignment via Risk-Constrained Decoding (DARC), a retraining-free inference-time method that frames response selection as distributionally robust, risk-sensitive decision making. Given multiple preference samples or scalable disagreement proxies, DARC reranks candidates by maximizing a KL-robust (entropic) satisfaction objective, and provides simple deployment controls that cap or penalize the corresponding entropic risk premium relative to the mean, enabling explicit risk budgets without retraining. We provide theoretical characterization linking this decoding rule to principled pessimism and KLbased distributionally robust optimization. Experiments on alignment benchmarks show that DARC reduces disagreement and tail risk while maintaining competitive average quality under noisy, heterogeneous feedback.
+
+[p. 1 | section: 1. Introduction | type: Text]
+Preference data has become the dominant supervision signal for aligning large language models (Ouyang et al., 2022; Stiennon et al., 2020) . Most pipelines—RLHF with reward modeling and RL optimization (Christiano et al., 2017; Schulman et al., 2017) , offline preference objectives such as DPO and its refinements (Rafailov et al., 2023; Meng et al., 2024) , and reference-free single-stage variants such as ORPO (Hong et al., 2024) —share a common abstraction: preferences are treated as noisy observations of a single latent scalar utility (e.g., Bradley–Terry) (Bradley & Terry,
+
+[p. 1 | section: 1. Introduction | type: Text]
+Score Distribution Shift on High-Disagreement Prompts
+
+[p. 1 | section: 1. Introduction | type: FigureGroup]
+Figure 1. Score Distribution shift. Ridge plot showing human score densities on the high-disagreement subset. DARC variants (blue) shift the distribution to the right (higher mean µ) compared to the baseline (grey), with reduced spread (lower σ), indicating both increased satisfaction and reduced disagreement.
+
+[p. 1 | section: 1. Introduction | type: Text]
+1952) . This abstraction largely persists in newer reformulations such as KTO and IPO (Ethayarajh et al., 2024; Garg et al., 2025) , and even when reward models are made multidimensional via multi-head/objective designs (Wang et al., 2024a; Li et al., 2025; Yang et al., 2024) . Yet, treating feedback as perturbations around a single scalar provides limited guidance for inference-time response selection under heterogeneous preferences (Hung et al., 2025) , and it also lacks a unifying robust-optimization account for common risk-penalized decoding heuristics.
+
+[p. 1 | section: 1. Introduction | type: Text]
+However, real-world preferences are often heterogeneous rather than i.i.d. noise: annotators disagree for systematic reasons (Zhang et al., 2024; Chen et al., 2024) . Empirically, human ratings show substantial variance even on the raw Top-K candidate pool (Appendix H.1) , suggesting that uncertainty is intrinsic rather than an artifact of our selection rule. Under such plurality, maximizing the average reward µˆ can be brittle (Casper et al., 2023) , and the issue is exacerbated by proxy over-optimization, which can improve an imperfect preference proxy while degrading the underlying target (Gao et al., 2023; Rafailov et al., 2024) .
+
+[p. 1 | section: 1. Introduction | type: Text]
+Recent work further shows that proxy misspecification can induce inference-time reward hacking: as best-of-N (a widely used decoding primitive (Sun et al., 2024) ) or
+
+[p. 2 | section: 1. Introduction | type: Text]
+soft best-of-N becomes greedier, true utility can increase and then inevitably degrade (Huang et al., 2025a). Best-of-Poisson and HedgeTune mitigate this effect by tuning inference-time parameters (Khalaf et al., 2025); however, they primarily model risk through proxy-distortion trade-offs under a single reward signal, rather than preference heterogeneity. Closely related, pessimistic best-of-N rules penalize atypical candidates via an auxiliary error model to mitigate reward hacking (Anonymous, 2025), but they target distributional uncertainty of the reward model (e.g., atypicality/OOD) rather than disagreement-grounded risk across users.
+
+[p. 2 | section: 1. Introduction | type: Text]
+In parallel, robustness has been pursued through trainingtime objectives such as robust DPO under noisy preferences (Wu et al., 2024), which improve robustness via retraining and noise assumptions; group-robust objectives that protect minority preference groups (Ramesh et al., 2024), which rely on access to group structure; and uncertaintyaware reward modeling (Banerjee & Gopalan, 2024), which quantifies estimation uncertainty but does not by itself specify how to select responses under inference-time proxy shift (Ichihara et al., 2025). Taken together, these lines suggest a common lesson: when preferences are plural, the relevant object is not a deterministic score, but a random variable over users and annotation noise. Yet, a principled inference-time selection rule that is explicitly riskconstrained under heterogeneous preferences remains underdeveloped.
+
+[p. 2 | section: 1. Introduction | type: Text]
+We therefore study inference-time alignment under heterogeneous preferences through the lens of risk-constrained decision making (Chow et al., 2018; Tamar et al., 2015). Given a fixed candidate set and noisy preference or reward scores, we derive a finite-sample pessimistic rule based on a lower confidence bound, yielding high-probability guarantees for selecting a competitive response while controlling tail risk across prompts. This leads to Disagreement-Aware Alignment via Risk-Constrained Decoding (DARC), an inference-time-only, retraining-free procedure that plugs into any LM and preference estimator. DARC grounds risk in multi-annotator disagreement (Zhang et al., 2024) instantiated via validated proxy signals, improving robustness on high-disagreement prompts (Fig. 1). We include representative cases where Best-of-K is polarizing or unstable, whereas DARC yields consistently preferred responses (Appendix H.10).
+
+[p. 2 | section: 1. Introduction | type: Text]
+Beyond the statistical view, we give a distributionally robust optimization (DRO) characterization (Wiesemann et al., 2014; Rahimian & Mehrotra, 2019), viewing decoding as maximizing the worst-case expected satisfaction over local divergence neighborhoods (Namkoong & Duchi, 2016; Duchi et al., 2021). This yields a practical KL-robust instantiation and situates widely used mean—dispersion scoring
+
+[p. 2 | section: 1. Introduction | type: Text]
+rules within the same DRO perspective, clarifying the conditions under which they arise as principled risk-sensitive criteria (Duchi & Namkoong, 2019).
+
+[p. 2 | section: Contributions. | type: ListGroup]
+Method. We formulate inference-time alignment as riskconstrained decision making under heterogeneous preferences, with risk induced by preference uncertainty and annotator disagreement. Theory. We connect LCB-based uniform pessimism to a KL-DRO view, yielding a closed-form entropic decoding objective and its constrained/penalized variants via an entropic risk premium. Empirics. Across benchmarks, DARC improves disagreement and prompt-level tail risk with competitive mean quality; a dual-robust multi-scorer extension hedges scorer shift and proxy over-optimization, with a KL-regularized DRO interpretation over scorers.
+
+[p. 2 | section: 2. Problem setup | type: Text]
+Let s denote a prompt (context) and let \mathcal{Y}(s) be a realized candidate set produced by a fixed generator (e.g., sampling, beam variants, or a proposal model), with K := |\mathcal{Y}(s)| .
+
+[p. 2 | section: 2. Problem setup | type: Text]
+Conditioning on the candidate set. The generator may be stochastic; throughout the analysis we condition on the realized \mathcal{Y}(s) . All probabilities below are taken over the evaluation randomness (human or otherwise), holding \mathcal{Y}(s) fixed.
+
+[p. 2 | section: 2. Problem setup | type: Text]
+Latent satisfaction under heterogeneous preferences. For each (s, y), let R(s, y) \in \mathbb{R} denote a (latent) user-satisfaction random variable capturing preference heterogeneity and evaluation noise, with mean \mu(s, y) := \mathbb{E}[R(s, y)] . Intuitively, \mu(s, y) measures average quality.
+
+[p. 2 | section: 2. Problem setup | type: Text]
+KL-robust (entropic) value and risk premium. For \beta > 0 , define the entropic value
+
+[p. 2 | section: 2. Problem setup | type: Equation]
+V_{\beta}(s,y) := -\frac{1}{\beta} \log \mathbb{E} \left[ \exp \left( -\beta R(s,y) \right) \right], (1)
+
+[p. 2 | section: 2. Problem setup | type: Text]
+which is equivalent to a KL-based distributionally robust objective (Section 3.2). We define the entropic risk premium.
+
+[p. 2 | section: 2. Problem setup | type: Equation]
+RP_{\beta}(s,y) := \mu(s,y) - V_{\beta}(s,y) \ge 0
+
+[p. 2 | section: 2. Problem setup | type: Text]
+Decision problem (risk-aware decoding). Conditioning on (s,\mathcal{Y}(s)) , each candidate y\in\mathcal{Y}(s) induces an (unknown) satisfaction distribution over users/raters. Our population objective is to select an output by solving
+
+[p. 2 | section: 2. Problem setup | type: Equation]
+y^* \in \arg \max_{y \in \mathcal{Y}(s)} V_{\beta}(s, y),
+
+[p. 2 | section: 2. Problem setup | type: Text]
+where entropic risk measure V_{\beta} is defined in (1). We further consider explicit risk control via a budget or a penalty:
+
+[p. 2 | section: 2. Problem setup | type: Equation]
+y_{\tau}^{\star} \in \arg\max_{y \in \mathcal{Y}(s)} V_{\beta}(s, y) s.t. \mathrm{RP}_{\beta}(s, y) \leq \tau ,
+
+[p. 2 | section: 2. Problem setup | type: Text]
+or in penalized (Lagrangian) form
+
+[p. 2 | section: 2. Problem setup | type: Equation]
+\arg \max_{y \in \mathcal{Y}(s)} V_{\beta}(s, y) - \lambda \operatorname{RP}_{\beta}(s, y).
+
+[p. 3 | section: 3. Guarantees via Lower Confidence Bounds | type: Text]
+This section provides a statistical justification for disagreement-aware decoding by deriving high-probability lower confidence bounds (LCBs) on expected satisfaction under heterogeneous preferences. To contextualize the resulting pessimistic rules, we also give complementary distributionally robust optimization (DRO) characterizations.
+
+[p. 3 | section: 3. Guarantees via Lower Confidence Bounds | type: Text]
+Scalar satisfaction samples (guarantee setting). For each candidate y \in \mathcal{Y}(s) , we observe n i.i.d. scalar satisfaction samples \{R_i(s,y)\}_{i=1}^n drawn from the (unknown) distribution of R(s,y):
+
+[p. 3 | section: 3. Guarantees via Lower Confidence Bounds | type: Equation]
+R_i(s,y) \stackrel{i.i.d.}{\sim} R(s,y), \qquad i = 1, \dots, n.
+
+[p. 3 | section: 3. Guarantees via Lower Confidence Bounds | type: Text]
+In this regime, the empirical mean and standard deviation \hat{\mu}_n(s,y) and \hat{\sigma}_n(s,y) estimate \mu(s,y) and \sigma(s,y) . Moreover, the plug-in estimator of (1) is
+
+[p. 3 | section: 3. Guarantees via Lower Confidence Bounds | type: Equation]
+\widehat{V}_{\beta}(s,y) := -\frac{1}{\beta} \log \left( \frac{1}{n} \sum_{i=1}^{n} \exp\left(-\beta R_i(s,y)\right) \right), \quad (2)
+
+[p. 3 | section: 3. Guarantees via Lower Confidence Bounds | type: Text]
+with the empirical risk premium
+
+[p. 3 | section: 3. Guarantees via Lower Confidence Bounds | type: Equation]
+\widehat{RP}_{\beta}(s,y) := \hat{\mu}_n(s,y) - \widehat{V}_{\beta}(s,y) \ge 0. (3)
+
+[p. 3 | section: 3. Guarantees via Lower Confidence Bounds | type: Text]
+In practice, one may operate with approximate (proxy) estimates of these empirical quantities; the analysis below does not rely on proxy scores being independent, and any such approximation induces only an additive slack in the resulting LCB objective (Appendix A.12).
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+Fix a prompt s and condition on \mathcal{Y}=\mathcal{Y}(s) with K:=|\mathcal{Y}|. For readability, write R_i(y) for R_i(s,y) , and \mu(y),\sigma(y) for \mu(s,y),\sigma(s,y). For each y\in\mathcal{Y} , we observe n independent satisfaction samples with mean \mu(y) and variance \sigma^2(y) , and denote the empirical mean and standard deviation by \hat{\mu}_n(y):=\frac{1}{n}\sum_{i=1}^n R_i(y) and \hat{\sigma}_n^2(y):=\frac{1}{n-1}\sum_{i=1}^n (R_i(y)-\hat{\mu}_n(y))^2.
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+Bridge to pairwise preferences. Our scalar-sample analysis can be viewed as operating on standard scalarizations of pairwise preferences (e.g., win-rate or fitted BT/Thurstone scores); see Appendix A.14. Empirically, our main conclusions are stable when replacing absolute scalar ratings with a pairwise scalarization against the base response (Table 6). Remark 3.1 (Shared annotators across candidates). Our guarantee requires independence across i for each fixed candidate y. Annotator overlap across candidates may induce dependence between \{(\hat{\mu}_n(y), \hat{\sigma}_n(y))\}_{y \in \mathcal{Y}} , but the uniform guarantee below follows from per-candidate concentration with a union bound and does not require independence across candidates.
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+Assumption 3.2 (Bounded rewards). For all y \in \mathcal{Y} , the satisfaction samples are almost surely bounded:
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Equation]
+R_i(y) \in [a, b] a.s.
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+Boundedness matches typical rating scales and can be enforced for proxy scores via truncation (Appendix H.1); an analogous LCB holds under sub-Gaussian noise (Appendix A.4).
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+Proposition 3.3 (Uniform LCB). There exists an absolute constant c > 0 such that for any \delta \in (0,1) , with probability at least 1 - \delta , simultaneously for all y \in \mathcal{Y}(s) ,
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Equation]
+\mu(y) \ge \hat{\mu}_n(y) - c\,\hat{\sigma}_n(y)\sqrt{\frac{\log(K/\delta)}{n}} - c\,(b-a)\frac{\log(K/\delta)}{n}. (4)
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+We denote the right-hand side by LCB<sub> \delta </sub>(y).
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+Proof. See Appendix A.2.
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+Remark 3.4 (Variance governs estimation hardness). The LCB form (4) highlights a statistical driver of selection risk: the dominant estimation error scales with the standard deviation \sigma(y) . The lower-order term decays as O(1/n), whereas the leading term scales as O(\sigma(y)/\sqrt{n}) . Consequently, low-disagreement candidates (small \sigma(y) ) admit substantially tighter confidence bounds at the same sample size, while controversial candidates require many more samples to certify their mean. Penalizing \hat{\sigma}_n(y) therefore has an identification rationale: it discourages selecting candidates whose true quality is intrinsically harder to verify from limited feedback.
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+Lower-tail interpretation. Maximizing a lower confidence bound is a principled way to avoid candidates with poor lower-tail satisfaction even when \hat{\mu}_n(y) is high (Boucheron et al., 2013; Vershynin, 2018). This is a statistical conservatism argument rather than an equivalence to coherent tail-risk measures such as CVaR (Artzner et al., 1999; Rockafellar et al., 2000). See Appendix A.4 for details.
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+On constants and practical calibration. The uniform LCB in (4) is obtained via standard concentration plus a union bound over K candidates and is therefore conservative. We do not claim tight constants; instead, the bound motivates the functional form
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Equation]
+\lambda_{\delta} \propto \sqrt{\frac{\log(K/\delta)}{n}},
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+and the lower-order term c(b-a)\frac{\log(K/\delta)}{n} is uniform across candidates and does not affect \arg\max_y decisions. In practice, we treat the coefficient as a risk-budget knob (optionally scaled by a factor \alpha ) and fix it via a small held-out calibration, while reporting sensitivity of the resulting trade-off. Combined with the \hat{\sigma}_n(y) factor in (4), the uncertainty penalty scales as \widetilde{O}(\hat{\sigma}_n(y)\sqrt{\log K/n}) , matching the intuition that more controversial candidates require larger risk budgets to be selected.
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+LCB decoding and a mean–dispersion surrogate. We define the LCB decoder as
+
+[p. 3 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Equation]
+y_{\text{LCB}} \in \arg \max_{y \in \mathcal{Y}} \text{LCB}_{\delta}(y).
+
+[p. 4 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+On the high-probability event of Proposition 3.3, this rule maximizes a valid lower bound on the true mean satisfaction \mu(y) . Crucially, under bounded ratings, maximizing LCB_{\delta}(y) is equivalent (up to a constant) to a mean-dispersion surrogate:
+
+[p. 4 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Equation]
+\arg \max_{y \in \mathcal{Y}} (\hat{\mu}_n(y) - \lambda \hat{\sigma}_n(y)).
+
+[p. 4 | section: 3.1. Estimation risk: uniform LCB and a mean-dispersion surrogate | type: Text]
+We provide the derivation in Corollary A.2 (Appendix A.3) and discuss the theoretical connection between this \sigma -penalty (estimation uncertainty) and the entropic \sigma^2 -penalty (risk aversion) in Remark A.3.
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+KL-robust (entropic) decoding. We first consider a relative-entropy (KL) robustification of expected satisfaction. Let R \in \mathbb{R} be the (latent) satisfaction with reference distribution \mathbb{P} . We consider worst-case distributions \mathbb{Q} over R that are absolutely continuous w.r.t. \mathbb{P} . For \beta > 0 , define the KL-regularized robust value
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Equation]
+\operatorname{Rob}_{\beta}^{\operatorname{KL}}(\mathbb{P};R) := \inf_{\mathbb{Q} \ll \mathbb{P}} \left\{ \mathbb{E}_{\mathbb{Q}}[R] + \beta^{-1} D_{\operatorname{KL}}(\mathbb{Q} \| \mathbb{P}) \right\}, \quad (5)
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+where \mathbb{Q} \ll \mathbb{P} ensures the KL term is well-defined. This is standard in risk-sensitive control and large deviations (Dupuis & Ellis, 2011; Hansen & Sargent, 2011).
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+Theorem 3.5 (KL-robust value equals an entropic objective). For any \beta > 0 and any \mathbb{P} such that \mathbb{E}_{\mathbb{P}}[\exp(-\beta R)] < \infty ,
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Equation]
+\operatorname{Rob}_{\beta}^{\mathrm{KL}}(\mathbb{P}; R) = -\frac{1}{\beta} \log \mathbb{E}_{R \sim \mathbb{P}}[\exp(-\beta R)]. \quad (6)
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+In particular, for the empirical rater distribution \widehat{\mathbb{P}}_n^y , \operatorname{Rob}_{\beta}^{\mathrm{KL}}(\widehat{\mathbb{P}}_n^y;R) = -\frac{1}{\beta}\log(\frac{1}{n}\sum_{i=1}^n\exp(-\beta R_i(y))) = \widehat{V}_{\beta}(s,y) . See Appendix A.5 for the detailed proof.
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+Relation to Expected Utility Theory (CARA). Maximizing the entropic value in (6) is equivalent to maximizing expected utility under a constant absolute risk aversion (CARA) utility, u(x) = -\exp(-\beta x) . A useful invariance is translation equivariance: for any constant c, V_{\beta}(R+c) = V_{\beta}(R) + c , hence the risk premium \mu(R) - V_{\beta}(R) is invariant to additive reward shifts. This is desirable in RLHF-style pipelines where learned reward models are often only identifiable up to an affine transformation.
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+\chi^2 -DRO yields a mean–dispersion special case. We now give a complementary robust-optimization view (Wiesemann et al., 2014; Rahimian & Mehrotra, 2019): under a \chi^2 -divergence ambiguity set around \mathbb{P} (Ben-Tal & Nemirovski, 2002), the worst-case expected satisfaction admits a mean–dispersion form. (Definitions and tightness conditions are deferred to Appendix B.)
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+Proposition 3.6 ( \chi^2 -DRO robust mean admits a mean–dispersion form). Let R be square-integrable under \mathbb{P} with mean \mu_{\mathbb{P}} := \mathbb{E}_{\mathbb{P}}[R] and variance \sigma_{\mathbb{P}}^2 := \operatorname{Var}_{\mathbb{P}}(R) . For any
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Equation]
+\rho \ge 0, \inf_{\mathbb{Q} \in \mathcal{U}_{\rho}(\mathbb{P})} \mathbb{E}_{\mathbb{Q}}[R] \ge \mu_{\mathbb{P}} - \sqrt{\rho} \, \sigma_{\mathbb{P}}. (7)
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+Specializing to \mathbb{P} = \widehat{\mathbb{P}}_n^y yields the empirical closed form
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Equation]
+\inf_{\mathbb{Q}\in\mathcal{U}_{\rho}(\widehat{\mathbb{P}}_{n}^{y})} \mathbb{E}_{\mathbb{Q}}[R] = \widehat{\mu}_{n}(y) - \sqrt{\rho} \sqrt{\widehat{v}_{n}(y)}, \tag{8}
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+whenever the extremal density is nonnegative on the empirical support. Otherwise, the mean-dispersion form remains a valid lower bound (Remark B.1), ensuring the rule remains pessimistic.
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+Proof and tightness conditions. See Appendix B for the extremal density characterization and a sufficient nonnegativity regime (e.g., bounded ratings imply tightness for small \rho ).
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+A unified pessimistic value (LCB as calibrated DRO). Define the candidate-wise pessimistic value
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Equation]
+V_{\delta}(y) := \widehat{\mu}_n(y) - c \,\widehat{\sigma}_n(y) \sqrt{\frac{\log(K/\delta)}{n}} - c \,(b-a) \frac{\log(K/\delta)}{n}, (9)
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+which is a uniform lower confidence bound (LCB) under Proposition 3.3 (Appendix A.2). On the other hand, Proposition 3.6 implies that, up to the lower-order term in (9), V_{\delta}(y) matches the \chi^2 -DRO robust mean of the empirical rater distribution with radius
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Equation]
+\rho_{\delta} \asymp \frac{\log(K/\delta)}{n},
+
+[p. 4 | section: 3.2. Distributional risk: DRO characterizations of pessimistic value | type: Text]
+since \sqrt{\rho_\delta} \, \widehat{\sigma}_n(y) \asymp \widehat{\sigma}_n(y) \sqrt{\log(K/\delta)/n} (see Appendix C for a discussion distinguishing statistical estimation risk from intrinsic disagreement). This yields a unified interpretation of disagreement-aware decoding as calibrated pessimism :a statistical LCB rule that is equivalent (up to lower-order terms) to optimizing a local DRO objective. Thus, disagreement-aware decoding can be viewed equivalently as (i) maximizing a high-probability LCB on expected satisfaction (statistical pessimism), or (ii) maximizing a distributionally robust worst-case expected satisfaction over a local \chi^2 neighborhood (adversarial robustness).
+
+[p. 4 | section: 4. Disagreement-Aware Risk-Constrained Decoding | type: Text]
+Motivated by the LCB and DRO characterization in §3–§3.2, we now present practical decoding rules that implement the KL-robust entropic objective (and its constrained/penalized variants) over a finite candidate set. For completeness, we also include a second-moment pessimistic surrogate implied by the LCB analysis in (18) as a computationally convenient ablation.
+
+[p. 4 | section: 4.1. From preference maximization to risk controls | type: Text]
+Standard reward-based reranking selects the highest estimated mean,
+
+[p. 4 | section: 4.1. From preference maximization to risk controls | type: Equation]
+y_{\text{mean}}(s) \in \arg \max_{y \in \mathcal{V}(s)} \hat{\mu}(s, y),
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Text]
+which optimizes average preference but may favor brittle outputs when disagreement is large.
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Text]
+Risk-sensitive decoding (primary rule). Our primary decoder selects the candidate with the largest scorer-robust entropic value:
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Equation]
+y_{\text{Entropic}}(s) \in \arg \max_{y \in \mathcal{Y}(s)} \widehat{V}_{\beta}(s, y), (10)
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Text]
+where \widehat{V}_{\beta} is the entropic value defined in (2).
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Text]
+Risk-constrained decoding via an entropic risk premium. We define explicit deployment knobs using the entropic risk premium \widehat{RP}_{\beta}(s,y) from (3). We consider two standard forms:
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Equation]
+y_{\tau}(s) \in \arg \max_{y \in \mathcal{Y}(s)} \widehat{V}_{\beta}(s, y) \quad \text{s.t.} \quad \widehat{\mathrm{RP}}_{\beta}(s, y) \leq \tau (11)
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Equation]
+y_{\lambda}(s) \in \arg\max_{y \in \mathcal{Y}(s)} \widehat{V}_{\beta}(s, y) - \lambda \,\widehat{\mathrm{RP}}_{\beta}(s, y), (12)
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Text]
+where the penalty form is a Lagrangian relaxation. If the feasible set \{y \in \mathcal{Y}(s) : \widehat{\mathrm{RP}}_\beta(s,y) \leq \tau\} is empty, we fall back to \mathcal{Y}(s) , consistent with Algorithm 1. The constrained and penalized forms provide two equivalent ways to tune the reward–risk trade-off; their finite-candidate-set relationship is given in Appendix A.6.
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Text]
+Disagreement as a risk proxy: interpretation and limitations. We use disagreement as a human-centric signal of preference heterogeneity, and implement risk sensitivity through the KL-robust entropic value (10) (a standard convex risk measure). The mean–dispersion form arises only as a finite-sample surrogate (via LCB pessimism) or as a \chi^2 -DRO special case, rather than being the defining principle of our method.
+
+[p. 5 | section: 4.1. From preference maximization to risk controls | type: Text]
+Importantly, we do not claim that variance is a coherent risk measure (e.g., CVaR) (Artzner et al., 1999; Rockafellar et al., 2000) or that \sigma is equivalent to a tail-risk functional in full generality. Instead, §3 shows that penalizing \hat{\sigma} arises naturally from maximizing a statistically justified lower confidence bound (LCB) on \mu(s,y) , yielding a principled pessimistic selection rule under finite data. Moreover, §3.2 provides a complementary distributionally robust optimization characterization (Wiesemann et al., 2014; Rahimian & Mehrotra, 2019).
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Text]
+Proxy robustness. When (\hat{\mu}, \hat{\sigma}) are obtained from scalable proxy scorers rather than i.i.d. human samples, a uniform proxy-error assumption yields a robust LCB guarantee; we defer the formal statement and proof to Appendix A.12.
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Text]
+\epsilon -rule as a constrained optimization. Our \epsilon -tie-breaking is equivalent to
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Equation]
+y_{\epsilon}(s) \in \arg\min_{y \in \mathcal{Y}(s)} \widehat{\sigma}(s, y) \quad \text{s.t.} \quad \widehat{V}_{\beta}(s, y) \ge \widehat{V}_{\max}(s) - \epsilon, (13)
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Text]
+where \widehat{V}_{\max}(s) := \max_{y \in \mathcal{Y}(s)} \widehat{V}_{\beta}(s, y) .
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Text]
+Pareto view. Eq. (13) selects a Pareto-optimal point of
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Text]
+the robust-value—disagreement trade-off: among candidates whose robust value is within \epsilon of the best, it returns the least controversial one. Moreover, when the chosen point is sup-ported, the same solution can be written as a scalarization \arg\max_y\left(\widehat{V}_{\beta,\gamma}(s,y)-\lambda_{\epsilon}\widehat{\sigma}(s,y)\right) for some \lambda_{\epsilon}\geq 0 ; formal statements and proofs are deferred to Appendix A.13.
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Text]
+Two-stage rule. To avoid sacrificing entropic value excessively for marginal robustness, we use:
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Equation]
+\mathcal{F}_{\epsilon}(s) := \{ y \in \mathcal{Y}(s) \mid \widehat{V}_{\beta}(s, y) \ge \widehat{V}_{\max}(s) - \epsilon \}, y_{\epsilon}(s) \in \arg \min_{y \in \mathcal{F}_{\epsilon}(s)} \widehat{\sigma}(s, y).
+
+[p. 5 | section: 4.2. Practical decoding: \epsilon -tie breaking | type: Text]
+This approximates the scalarized decoder \max_y \left(\widehat{V}_\beta(s,y) - \lambda \, \widehat{\sigma}(s,y)\right) by enforcing near-optimality in entropic value and then selecting the least controversial candidate. In practice, we tune all risk parameters (\beta,\tau,\epsilon) on a held-out development set; detailed tuning protocols are provided in Appendix H.4.
+
+[p. 5 | section: 4.3. Multi-scorer robustness | type: Text]
+Scorer-robust decoding (multi-reward models). In scalable proxy settings, satisfaction scores may come from learned reward models and be sensitive to model shift or proxy over-optimization. We optionally hedge this scorer ambiguity by using a family of M scorers indexed by m \in [M] . For each candidate y \in \mathcal{Y}(s) , scorer m provides n scalar samples \{R_{m,i}(s,y)\}_{i=1}^n (e.g., via perturbations), from which we compute the scorer-specific entropic value \widehat{V}_{\beta,m}(s,y) and risk premium \widehat{\mathrm{RP}}_{\beta,m}(s,y) . Because reward scales can differ across scorers, we apply a perprompt affine normalization (Appendix E). We then aggregate scorer-specific entropic values using a soft worst-case operator:
+
+[p. 5 | section: 4.3. Multi-scorer robustness | type: Equation]
+\widetilde{V}_{\beta,\gamma}(s,y) := -\frac{1}{\gamma} \log \left( \frac{1}{M} \sum_{m=1}^{M} \exp\left(-\gamma \widehat{V}_{\beta,m}(s,y)\right) \right), \tag{14}
+
+[p. 5 | section: 4.3. Multi-scorer robustness | type: Text]
+and aggregate risk premia pessimistically by \widehat{RP}_{\beta}(s,y) := \max_{m \in [M]} \widehat{RP}_{\beta,m}(s,y) . We decode by maximizing \widetilde{V}_{\beta,\gamma}(s,y) subject to \widehat{RP}_{\beta}(s,y) \leq \tau (or its penalized form). Proposition 4.1 (Scorer aggregation as KL-regularized
+
+[p. 5 | section: 4.3. Multi-scorer robustness | type: Text]
+Proposition 4.1 (Scorer aggregation as KL-regularized DRO over scorers). Let v_m := \hat{V}_{\beta,m}(s,y) and \mathbf{v} \in \mathbb{R}^M . Define \mathbf{u} = (1/M, \dots, 1/M) and the simplex \Delta_M := \{\mathbf{q} \in \mathbb{R}^M_+ : \sum_{m=1}^M q_m = 1\} . Then the soft worst-case aggregation (14) admits the variational form
+
+[p. 5 | section: 4.3. Multi-scorer robustness | type: Equation]
+\widetilde{V}_{\beta,\gamma}(s,y) = \inf_{\mathbf{q} \in \Delta_M} \left\{ \sum_{m=1}^M q_m v_m + \frac{1}{\gamma} D_{\mathrm{KL}}(\mathbf{q} \| \mathbf{u}) \right\}. \tag{15}
+
+[p. 5 | section: 4.3. Multi-scorer robustness | type: Text]
+Interpretation. Eq. (15) shows that \gamma interpolates between averaging across scores (\gamma \to 0) and a worst-case scorer (\gamma \to \infty) , yielding a principled hedge against scorer shift. In particular, \min_m v_m \leq \widetilde{V}_{\beta,\gamma}(s,y) \leq \frac{1}{M} \sum_m v_m , and \widetilde{V}_{\beta,\gamma}(s,y) is non-increasing in \gamma .
+
+[p. 6 | section: 4.3. Multi-scorer robustness | type: TableGroup]
+Llama-3.1-8B-Instruct Qwen2.5-7B-Instruct Type Method M T-Bench Alp acaEval 2.0 ) M T-Bench Alpa caEval 2.0 Reward Risk↓ Tradeoff Len(tok) Reward Risk↓ Tradeoff Len(tok) Reward Risk↓ Tradeoff Len(tok) Reward Risk↓ Tradeoff Len(tok) Dataset: Overall Base (Best-of-K) 4.53 6.50 -8.47 315 4.52 7.46 -10.40 331 4.09 3.54 -2.99 244 3.29 3.11 -2.93 256 BoP(HedgeTune) 4.18 5.86 -7.54 316 4.12 6.24 -8.36 330 3.84 3.10 -2.36 231 3.14 2.68 -2.22 261 Inference Caution 4.09 5.43 -6.77 317 4.27 5.91 -7.55 320 3.89 3.21 -2.53 243 3.09 2.62 -2.15 259 DeAL 5.59 7.98 -10.37 309 5.66 8.74 -11.81 311 4.64 4.22 -3.80 256 4.02 3.74 -3.46 267 MC-Dropout 4.41 5.78 -7.15 315 4.37 6.31 -8.25 326 3.87 3.38 -2.89 247 3.13 2.79 -2.45 253 RBoN 4.43 5.62 -6.81 309 4.31 5.82 -7.33 321 3.93 3.22 -2.51 241 3.17 2.71 -2.25 257 DARC(ours) 4.46 5.41 -6.36 315 4.25 5.67 -7.33 319 4.01 3.14 -2.27 243 3.14 2.66 -2.18 256 DARC- \tau (ours) 4.42 5.45 -6.48 313 4.49 6.21 -7.93 321 3.94 2.99 -2.04 232 3.12 2.48 -1.85 257 DARC- \epsilon (ours) 4.46 5.29 -6.12 314 4.38 5.60 -6.82 319 3.96 2.96 -1.96 243 3.18 2.36 -1.54 261 cDPO (Best-of-K) 5.88 5.96 -6.04 300 5.86 6.97 -8.08 309 8.61 5.76 -2.91 258 5.30 6.63 -7.96 278 m · · cDPO + DARC- \epsilon 5.81 5.65 -5.49 311 5.83 6.57 -7.31 290 8.53 5.49 -2.45 278 5.22 6.40 -7.58 274 Training rDPO (Best-of-K) 5.53 5.57 -5.61 260 11.62 7.10 -2.58 316 8.73 5.94 -3.15 294 5.77 6.90 -8.03 282 rDPO + DARC- \epsilon 5.42 5.16 -4.90 258 11.58 6.78 -1.98 325 8.62 5.69 -2.76 288 5.68 6.68 -7.68 232 Dataset: High-Variance (Top 20%) Base (Best-of-K) 5.79 9.91 -14.03 382 7.48 10.22 -12.96 381 5.12 6.00 -7.12 308 2.79 5.46 -8.13 263 BoP(HedgeTune) 5.45 7.90 -10.35 382 7.28 8.12 -8.96 381 4.67 5.12 -5.57 307 2.53 4.09 -5.65 265 Inference Caution 5.41 7.42 -9.43 382 7.17 8.34 -9.51 381 4.80 5.39 -5.98 307 2.30 4.07 -5.84 264 DeAL 5.96 9.71 -13.46 374 7.89 10.15 -12.41 371 5.75 8.43 -11.11 316 3.45 6.89 -10.33 256 MC-Dropout 5.20 7.48 -9.76 384 7.19 8.15 -9.11 380 4.75 5.25 -5.25 306 2.35 4.00 -5.65 262 RBoN 5.28 7.30 -9.32 372 7.22 8.40 -9.58 376 4.90 5.45 -6.00 300 2.25 4.15 -6.05 258 DARC(ours) 5.32 7.33 -9.34 382 7.24 8.10 -8.96 381 4.99 5.05 -5.13 307 2.34 4.42 -6.50 263 DARC- \tau (ours) 5.43 7.90 -10.37 382 7.21 8.55 -9.89 381 4.78 4.85 -4.92 294 2.31 3.84 -5.37 249 DARC- \epsilon (ours) 5.49 7.00 -8.51 382 7.26 8.10 -8.94 381 5.03 4.77 -4.51 306 2.59 3.76 -4.93 265 cDPO (Best-of-K) 7.54 8.39 -9.24 312 8.88 9.40 -9.92 328 5.52 5.67 -5.82 317 7.17 7.30 -7.43 196 T cDPO + DARC- \epsilon 7.51 8.11 -8.71 323 8.81 9.21 -9.61 328 5.42 5.17 -4.92 316 7.12 7.29 -7.46 196 Training rDPO (Best-of-K) 6.58 7.98 -9.38 337 11.60 9.05 -6.50 347 5.79 5.34 -4.89 304 7.80 7.72 -7.64 172 rDPO + DARC-e 6.41 7 16 -7 91 316 11.56 8 65 -5 74 329 5 56 5.03 -4 50 301 7.70 7.28 -6.86 164 Table 1. Evaluation on MT-Bench and AlpacaEval 2.0. Results across two generators families. We report mean reward, proxy risk (Risk), risk—reward tradeoff score (Tradeoff), and average length (Len(tok)).Blue/green highlight best/runner-up.
+
+[p. 6 | section: 5.1. Experimental Setup and Implementation Details | type: Text]
+Candidate sets and evaluation protocol. For each prompt s, we generate a fixed candidate pool \mathcal{Y}(s) of size K (shared across all methods), so differences arise solely from the inference-time selection rule. In the human-grounded setting, for each y \in \mathcal{Y}(s) we collect n scalar satisfaction ratings \{r_i(s,y)\}_{i=1}^n (Christiano et al., 2017; Stiennon et al., 2020; Ouyang et al., 2022), and split annotators into disjoint selection and evaluation sets \mathcal{I}_{sel} and \mathcal{I}_{eval} to avoid selection-evaluation leakage. All decoders operate on statistics computed from \mathcal{I}_{sel} . Our entropic decoder uses the empirical entropic value in the human-grounded setting (where M=1 and V_{\beta,\gamma}=V_{\beta} ), and uses the scorer-robust aggregated value V_{\beta,\gamma}(s,y) (and RP_{\beta}(s,y) ) in proxy settings with multiple reward models. Second-moment baselines use only (\hat{\mu}_{sel}(s,y), \hat{\sigma}_{sel}(s,y)) (or their scorer-indexed analogues under proxies). All reported metrics are computed on held-out ratings in \mathcal{I}_{eval} (definitions in Appendix H.3).
+
+[p. 6 | section: 5.1. Experimental Setup and Implementation Details | type: Text]
+Estimating mean and disagreement. We define (\hat{\mu}, \hat{\sigma}) as the mean and disagreement estimates, derived from either empirical samples or scorer proxies . DARC is inference-time only , modifying the selection over \mathcal{Y}(s) without retraining. While our theory assumes multi-annotator feedback, we validate proxy uncertainty as a scalable approximation for human disagreement.
+
+[p. 6 | section: 5.1. Experimental Setup and Implementation Details | type: Text]
+Proxies, baselines, and hyperparameters. When multirater human scores are unavailable, we use scalable proxy
+
+[p. 6 | section: 5.1. Experimental Setup and Implementation Details | type: Text]
+scorers (e.g., ensembles / bootstrap reward models) to obtain a proxy mean together with either (i) a score distribution for computing V_{\beta} , or (ii) a proxy disagreement diagnostic \hat{\sigma}_{proxy} (Kendall & Gal, 2017; Lakshminarayanan et al., 2017); we validate proxy-human alignment via rank correlation and stratified analyses (Uma et al., 2021). Inferencetime baselines include mean Best-of-K, inference-time hedging methods for reward hacking (Best-of-Poisson and HedgeTune) (Khalaf et al., 2025), pessimistic best-of-N reranking via an auxiliary error/atypicality model (Caution) (Anonymous, 2025), uncertainty-based reranking (e.g., MC-Dropout) (Gal & Ghahramani, 2016; Kendall & Gal, 2017), reward-regularized decoding (RBoN) (Jinnai et al., 2024) and DeAL (top-k lookahead reward-guided decoding) (Huang et al., 2025b); training-time baselines include cDPO/rDPO (Mitchell, 2023; Chowdhury et al., 2024). We report default settings and full tuning ranges (including our LCB- and DRO-instantiated decoding rules), along with complete baseline configurations and implementation details, in Appendix H.2 (see also Appendix F).
+
+[p. 6 | section: 5.1. Experimental Setup and Implementation Details | type: Text]
+Inference overhead. Disagreement estimation adds only a modest inference-time cost: in our implementation, using N_{\rm aug} = 4/8/16 increases end-to-end latency by only \approx 1.5\%/2.0\%/3.2\% , since candidate generation dominates runtime (Appendix H.6, Table 7).
+
+[p. 6 | section: 5.1. Experimental Setup and Implementation Details | type: Text]
+Metrics (mean, risk, and tail). For each prompt s and candidate response y, we evaluate rewards on a held-out rater set \mathcal{I}_{\text{eval}} and report the empirical mean \hat{\mu}_{\text{eval}}(s,y) . As a scalable proxy for robustness, we compute a perturbation -
+
+[p. 7 | section: 5.1. Experimental Setup and Implementation Details | type: Text]
+sensitivity statistic \hat{\sigma}_{sel}(s,y) as the standard deviation of rewards across N_{aug} style-preserving perturbations of y (see Appendix H.13). Human evaluation details are in Appendix I; the human mean is the average rating and the human variance is the sample variance across raters. We summarize performance via \operatorname{Tradeoff}_{eval}(s,y) := \hat{\mu}_{eval}(s,y) - \lambda \hat{\sigma}_{sel}(s,y) , using the same \lambda for all methods (Appendix H.14). We also report \operatorname{CVaR}_{10\%} over prompts (Chow et al., 2015); see Appendix H.3.
+
+[p. 7 | section: 5.1. Experimental Setup and Implementation Details | type: TableGroup]
+Method Human Score ↑ Risk (Avg\sigma) \downarrow Tradeoff \text{CVaR}_{10\%}{\uparrow} Dataset: Overall Base (Best-of- K ) 7.56 0.67 6.22 6.73 BoP(HedgeTune) 7.79 0.63 6.53 7.12 Caution 7.82 0.61 6.60 7.15 DeAL 7.83 0.72 6.39 7.08 MC-Dropout 7.73 0.64 6.45 7.19 RBoN 7.71 0.62 6.47 7.26 DARC(ours) 7.84 0.60 6.64 7.36 DARC- \tau (ours) 7.83 0.58 6.67 7.46 DARC- \epsilon (ours) 8.08 0.55 6.98 7.62 cDPO (Best-of-K) 7.80 0.65 6.50 7.11 cDPO + DARC- \epsilon 8.03 0.54 6.95 7.41 rDPO (Best-of- K ) 8.17 0.69 6.79 7.20 rDPO + DARC- \epsilon 8.15 0.58 6.99 7.60 Dataset: High-Disag greement (Top 20%) Base (Best-of- K ) 7.62 1.00 5.62 6.10 BoP(HedgeTune) 7.83 0.87 6.09 6.81 Caution 7.81 0.85 6.11 6.94 DeAL 7.99 1.13 5.73 7.33 MC-Dropout 7.88 0.84 6.20 7.25 RBoN 7.95 0.81 6.33 7.29 DARC(ours) 8.18 0.74 7.00 7.43 DARC- \tau (ours) 8.11 0.65 6.81 7.35 DARC- \epsilon (ours) 8.34 0.65 7.34 7.60 cDPO (Best-of-K) 7.96 0.89 6.18 7.15 cDPO + DARC- \epsilon 8.31 0.63 7.05 7.54 rDPO (Best-of- K ) 8.25 0.91 6.43 7.02 rDPO + DARC- \epsilon 8.72 0.67 7.38 7.48 Table 2. Human Evaluation Results. We report Human Mean Score, Disagreement Risk, Tradeoff, and \text{CVaR}_{10\%} (worst 10% prompt outcomes).
+
+[p. 7 | section: 5.2. Results | type: Text]
+347348
+
+[p. 7 | section: 5.2. Results | type: Text]
+352353
+
+[p. 7 | section: 5.2. Results | type: Text]
+357358
+
+[p. 7 | section: 5.2. Results | type: Text]
+Automated proxy evaluation. Table 1 reports MT-Bench (Zheng et al., 2023) and AlpacaEval2.0 (Li et al., 2023; Dubois et al., 2024) results under two instructiontuned generators (Llama-3.1-8B-Instruct (Dubey et al., 2024), Qwen2.5-7B-Instruct (Qwen et al., 2025)). We evaluate each method by mean reward \hat{\mu} , proxy disagreement risk \hat{\sigma} (reward sensitivity to style-preserving perturbations), and a risk-reward tradeoff score Tradeoff = \hat{\mu} - \lambda \hat{\sigma} with the same \lambda across methods; we also report Len(tok) to control for length bias. Across both generators, inferencetime risk-aware selection improves robustness: DARC variants reduce \hat{\sigma} while keeping \hat{\mu} competitive, yielding higher Tradeoff than mean-only Best-of-K, with larger gains on the high-variance subset (top 20% prompts by baseline \hat{\sigma} ) and broadly stable Len(tok). Training-time robust policies (cDPO/rDPO) exhibit different trade-offs, and DARC remains complementary: applying DARC- \epsilon as an inferencetime plug-in can further reduce \hat{\sigma} and improve Tradeoff in several cases, supporting a modular view where training
+
+[p. 7 | section: 5.2. Results | type: Text]
+shapes the policy while DARC calibrates risk on a fixed candidate set.
+
+[p. 7 | section: 5.2. Results | type: Text]
+Human-loop evaluation and tail robustness. We then close the loop with multi-annotator ratings on MT-Bench. Table 2 shows that DARC improves risk-sensitive criteria (Tradeoff and \text{CVaR}_{10\%} ) while maintaining competitive mean satisfaction. On the high-disagreement subset, disagreement-aware decoding yields substantial gains in tail robustness ( \text{CVaR}_{10\%} ) and conservative quality (Tradeoff), indicating that risk-controlled selection is particularly beneficial on genuinely controversial prompts. Figure 3 demonstrates that Risk-adjusted satisfaction( \Delta Tradeoff) scale positively with disagreement, rising steadily from Q1 to Q5, peaking in the most controversial buckets (Q5). This confirms disagreement as an effective signal for allocating risk control, a trend corroborated by the CVaR results in Appendix Fig. 5.(See representative cases in Appendix H.10).)
+
+[p. 7 | section: 5.2. Results | type: FigureGroup]
+Figure 3. Gains concentrate on high-disagreement prompts. Mean improvement in lower-tail satisfaction ( \Delta Tradeoff vs. base) across five prompt buckets ranked by baseline human disagreement \hat{\sigma} (low \rightarrow high). Error bars denote 95% CIs.
+
+[p. 7 | section: 5.2. Results | type: Text]
+Validity of the disagreement proxy. We validate our perturbation-sensitivity proxy \hat{\sigma} against human disagreement measured by multiple independent rater scores on the same (prompt, response) pair. To avoid selection effects, we compute both proxy and human disagreement on the baseline candidate. As summarized in Figure 4, proxy disagreement shows a statistically significant rank-level consistency with human disagreement and remains positively associated even after controlling for mean reward and response length (strong and common confounders for RMbased signals). Moreover, the proxy serves as an effective risk filter for identifying prompts likely to exhibit preference heterogeneity, where risk-controlled decoding is designed to intervene: prompts identified as high-disagreement by the proxy substantially overlap with those identified by humans, far beyond random chance (Fig. 4). While mismatch cases exist (App. H.11)—often reflecting surface-form sensitivity (FP) or orthogonal validity/completeness issues (FN)—this is consistent with using \hat{\sigma} as a scalable screening signal to prioritize human verification rather than a fully calibrated estimator of disagreement magnitude. Consistently, this signal effectively allocates risk control: bucketed analysis
+
+[p. 8 | section: 5.2. Results | type: FigureGroup]
+Figure 2. Ablation Studies. Impact of key hyperparameters on risk mitigation performance. (a) Candidate pool size K. (b) Risk sensitivity coefficient \beta . (c) Constraint threshold \epsilon . (d) Perturbation budget N_{\text{aug}} .
+
+[p. 8 | section: 5.2. Results | type: Text]
+shows a monotonic increase in \Delta Tradeoff from low-to high-disagreement groups when bucketing by either human or proxy disagreement (App. H.7). We also stratify prompts by proxy-human disagreement alignment and find that, even in the worst-alignment bucket, DARC still achieves the best Tradeoff among all baselines (Appendix H.8, Table 8).
+
+[p. 8 | section: 5.2. Results | type: TableGroup]
+Value Notes / p-value 0.6509 95% boot. CI [0.42, 0.70]; p < 10^{-10} 0.3130 p < 10^{-6} 0.4084 95% boot. CI [0.25, 0.45] 0.64 (64/100; random=0.20) 0.64 (symmetric at equal k) 0.47 (|A \cap B|/|A \cup B|) 64 hypergeom p = 2.6 \times 10^{-29} Scatter: Human vs Proxy (Correlation \rho = 0.674 ) Prompts Trend line 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6509 0.3130 0.4084 0.64 0.64 0.47 64 Figure 4. Proxy validity diagnostics. (Top) Rank correlation between proxy and human disagreement, with top-20% overlap. (Bottom) Top-q overlap (Left) and proxy vs. human disagreement scatter (Right).
+
+[p. 8 | section: 5.2. Results | type: Text]
+Multi-scorer robust decoding To mitigate proxy overoptimization to a single reward model, we instantiate our decoder with a scorer family of size M = 3: RM1 (Skywork-reward-llama-3.1-8b (Liu et al., 2024a)), RM2 (nicholasKluge RewardModel (Corrêa, 2023)) and RM3(OpenAssistant (DeBERTa-v3-Large-v2) (Köpf et al., 2023)). At selection time, we compute V_{\beta,m}(s,y) for each m \in [M] (with within-prompt normalization), aggregate them into V_{\beta,\gamma}(s,y) via (14), and apply the same constrained/penalized rule using \overline{RP}_{\beta} in (27). For reporting, because absolute reward scales differ across RMs, we evaluate the selected outputs within each RM and report only within-RM differences to the baseline (mean \Delta ) and Win/Tie/Loss rates (Table 3). We additionally provide a per-scorer breakdown of win/tie/loss and mean score differences under each evaluator reward model in Appendix H.9, confirming consistent gains across scorers.
+
+[p. 8 | section: 5.2. Results | type: TableGroup]
+Overa ıll High- \hat{\sigma} Subset Method W/T/L Mean \Delta W/T/L Mean \Delta Across scorers (aggregated) \begin{array}{c} \overline{\text{DARC}} \\ \overline{\text{DARC-}\tau} \\ \overline{\text{DARC-}\epsilon} \end{array} 278 / 173 / 49 257 / 192 / 51 296 / 168 / 36 0.124 0.128 0.161 32 / 63 / 5 36 / 60 / 4 44 / 54 / 2 0.303 0.259 0.386 Table 3. Multi-scorer robust decoding. DARC variants vs. Base (mean Best-of-K). \Delta : per-prompt improvement over Base, aggregated across scorers (mean / min / mean— \gamma std); W/T/L is on aggregated \Delta . High- \hat{\sigma} uses the baseline disagreement proxy.
+
+[p. 8 | section: 5.2. Results | type: Text]
+Scaling robustness. To assess scale robustness, we additionally evaluate our inference-time decoding rules on a stronger generator, Qwen2.5-14B-Instruct , using the same candidate-pool protocol and metrics. We observe consistent improvements over mean Best-of- K in risk-sensitive criteria (Tradeoff and prompt-level CVaR), with gains again concentrating on high-disagreement prompts (Table 14).
+
+[p. 8 | section: 5.2. Results | type: Text]
+Hyperparameter sensitivity and ablations. Figure 2 summarizes a sensitivity study over the main knobs of DARC- \epsilon , reporting improvements over mean Best-of-K in \Delta Tradeoff and \Delta CVaR on fixed candidate pools. Increasing the candidate pool size K improves both metrics with diminishing returns (Fig. 2a). The risk sensitivity \beta in the entropic robust value \hat{V}_{\beta} yields rapid robustness gains that plateau at moderate values (Fig. 2b). Fixing \beta , enlarging the near-optimal set via \epsilon further improves robustness up to saturation (with slight degradation when overly permissive) (Fig. 2c). Finally, the perturbation budget N_{\rm aug} used to estimate proxy disagreement \hat{\sigma} saturates quickly; a small budget (e.g., 4–8) suffices, keeping inference overhead modest (Fig. 2d).
+
+[p. 8 | section: 6. Conclusion | type: Text]
+We cast decoding-time alignment under heterogeneous preferences as risk-constrained decision making. DARC uses a KL-robust (entropic) decoding rule with a conservative LCB/DRO interpretation, improving lower-tail outcomes while preserving mean quality. Limitations include a finite candidate pool and scorer bias; perturbation-based disagreement proxies are scalable screening signals, not calibrated human-disagreement estimates. Future work includes richer robustness signals and user/group-conditional risk control.
+
+[p. 9 | section: Impact Statement | type: Text]
+This paper presents work whose goal is to advance the field of machine learning. Our contributions focus on inferencetime response selection under preference heterogeneity. As with many machine learning methods, the proposed approach may exhibit uneven performance if the underlying proxies or learned scorers encode dataset- or populationspecific biases. We encourage reporting sensitivity to key design choices and auditing proxy/scorer behavior when the method is used in practice. Consequently, the method should be used and evaluated with appropriate care in deployment.

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+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0132", "section": "References", "page_start": 11, "page_end": 11, "type": "ListGroup", "text": "Song, Y., Swamy, G., Singh, A., Bagnell, J., and Sun, W. The importance of online data: Understanding preference fine-tuning via coverage. Advances in Neural Information Processing Systems , 37:12243–12270, 2024. Stiennon, N., Ouyang, L., Wu, J., Ziegler, D., Lowe, R., Voss, C., Radford, A., Amodei, D., and Christiano, P. F. Learning to summarize with human feedback. Advances in neural information processing systems , 33:3008–3021, 2020. Sun, H., Haider, M., Zhang, R., Yang, H., Qiu, J., Yin, M., Wang, M., Bartlett, P., and Zanette, A. Fast best-of-n decoding via speculative rejection. Advances in Neural Information Processing Systems , 37:32630–32652, 2024. Tamar, A., Chow, Y., Ghavamzadeh, M., and Mannor, S. Policy gradient for coherent risk measures. Advances in neural information processing systems , 28, 2015. Uma, A. N., Fornaciari, T., Hovy, D., Paun, S., Plank, B., and Poesio, M. Learning from disagreement: A survey. Journal of Artificial Intelligence Research , 72:1385–1470, 2021. Vershynin, R. High-dimensional probability: An introduc tion with applications in data science , volume 47. Cambridge university press, 2018. Wang, H., Xiong, W., Xie, T., Zhao, H., and Zhang, T. Interpretable preferences via multi-objective reward modeling and mixture-of-experts. arXiv preprint arXiv:2406.12845 , 2024a. Wang, Z., Bukharin, A., Delalleau, O., Egert, D., Shen, G., Zeng, J., Kuchaiev, O., and Dong, Y. Helpsteer2 preference: Complementing ratings with preferences. arXiv preprint arXiv:2410.01257 , 2024b. Wang, Z., Dong, Y., Zeng, J., Adams, V., Sreedhar, M. N., Egert, D., Delalleau, O., Scowcroft, J., Kant, N., Swope, A., et al. Helpsteer: Multi-attribute helpfulness dataset for steerlm. In Proceedings of the 2024 Conference of the North American Chapter of the Association for Com putational Linguistics: Human Language Technologies (Volume 1: Long Papers) , pp. 3371–3384, 2024c. Wiesemann, W., Kuhn, D., and Sim, M. Distributionally robust convex optimization. Operations research , 62(6): 1358–1376, 2014. Wu, J., Xie, Y., Yang, Z., Wu, J., Chen, J., Gao, J., Ding, B., Wang, X., and He, X. Towards robust alignment of language models: Distributionally robustifying direct preference optimization. arXiv preprint arXiv:2407.07880 , 2024.", "source": "marker_v2", "marker_block_id": "/page/10/ListGroup/488"}
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+{"paper_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a", "chunk_id": "3105df16-98c9-46f1-9f54-b48ba2014a8a:0134", "section": "References", "page_start": 12, "page_end": 12, "type": "ListGroup", "text": "Zhang, M. J., Wang, Z., Hwang, J. D., Dong, Y., Delalleau, O., Choi, Y., Choi, E., Ren, X., and Pyatkin, V. Diverging preferences: When do annotators disagree and do models know? arXiv preprint arXiv:2410.14632 , 2024. Zheng, L., Chiang, W.-L., Sheng, Y., Zhuang, S., Wu, Z., Zhuang, Y., Lin, Z., Li, Z., Li, D., Xing, E., et al. Judging llm-as-a-judge with mt-bench and chatbot arena. Ad vances in neural information processing systems , 36: 46595–46623, 2023. Zhou, E., Zheng, G., Wang, B., Xi, Z., Dou, S., Bao, R., Shen, W., Xiong, L., Fan, J., Mou, Y., et al. Rmb: Comprehensively benchmarking reward models in llm alignment. arXiv preprint arXiv:2410.09893 , 2024.", "source": "marker_v2", "marker_block_id": "/page/11/ListGroup/238"}

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+Chakraborty, S., Qiu, J., Yuan, H., Koppel, A., Huang, F., Manocha, D., Bedi, A. S., and Wang, M. Maxminrlhf: Alignment with diverse human preferences. arXiv preprint arXiv:2402.08925 , 2024. Chen, D., Chen, Y., Rege, A., and Vinayak, R. K. Pal: Pluralistic alignment framework for learning from heterogeneous preferences. arXiv preprint arXiv:2406.08469 , 2024. Chow, Y., Tamar, A., Mannor, S., and Pavone, M. Risksensitive and robust decision-making: a cvar optimization approach. Advances in neural information processing systems , 28, 2015. Chow, Y., Ghavamzadeh, M., Janson, L., and Pavone, M. Risk-constrained reinforcement learning with percentile risk criteria. Journal of Machine Learning Research , 18 (167):1–51, 2018. Chowdhury, S. R., Kini, A., and Natarajan, N. Provably robust dpo: Aligning language models with noisy feedback. arXiv preprint arXiv:2403.00409 , 2024. Christiano, P. F., Leike, J., Brown, T., Martic, M., Legg, S., and Amodei, D. Deep reinforcement learning from human preferences. Advances in neural information pro cessing systems , 30, 2017. Correa, N. K. Aira, 2023. URL ˆ com/Nkluge-correa/Aira . Dubey, A., Jauhri, A., Pandey, A., Kadian, A., Al-Dahle, A., Letman, A., Mathur, A., Schelten, A., Yang, A., Fan, A., et al. The llama 3 herd of models. arXiv e-prints , pp. arXiv–2407, 2024. Dubois, Y., Galambosi, B., Liang, P., and Hashimoto, T. B. Length-controlled alpacaeval: A simple way to debias automatic evaluators. arXiv preprint arXiv:2404.04475 , 2024. Duchi, J. and Namkoong, H. Variance-based regularization with convex objectives. Journal of Machine Learning Research , 20(68):1–55, 2019. Duchi, J. C. and Namkoong, H. Learning models with uniform performance via distributionally robust optimization. The Annals of Statistics , 49(3):1378–1406, 2021. Duchi, J. C., Glynn, P. W., and Namkoong, H. Statistics of robust optimization: A generalized empirical likelihood approach. Mathematics of Operations Research , 46(3): 946–969, 2021. Dupuis, P. and Ellis, R. S. A weak convergence approach to the theory of large deviations . John Wiley & Sons, 2011.
+
+[p. 10 | section: References | type: Text]
+495 496 497 Ethayarajh, K., Xu, W., Muennighoff, N., Jurafsky, D., and Kiela, D. Kto: Model alignment as prospect theoretic optimization. arXiv preprint arXiv:2402.01306 , 2024.
+
+[p. 10 | section: References | type: ListGroup]
+Gal, Y. and Ghahramani, Z. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In international conference on machine learning , pp. 1050–1059. PMLR, 2016. Gao, L., Schulman, J., and Hilton, J. Scaling laws for reward model overoptimization. In International Conference on Machine Learning , pp. 10835–10866. PMLR, 2023. Garg, S., Singh, A., Singh, S., and Chopra, P. Ipo: Your language model is secretly a preference classifier. arXiv preprint arXiv:2502.16182 , 2025. Guo, Y., Cui, G., Yuan, L., Ding, N., Sun, Z., Sun, B., Chen, H., Xie, R., Zhou, J., Lin, Y., et al. Controllable preference optimization: Toward controllable multi-objective alignment. arXiv preprint arXiv:2402.19085 , 2024. Hansen, L. P. and Sargent, T. J. Robustness. In Robustness . Princeton university press, 2011. Hong, J., Lee, N., and Thorne, J. Orpo: Monolithic preference optimization without reference model. arXiv preprint arXiv:2403.07691 , 2024. Huang, A., Block, A., Liu, Q., Jiang, N., Krishnamurthy, A., and Foster, D. J. Is best-of-n the best of them? coverage, scaling, and optimality in inference-time alignment. arXiv preprint arXiv:2503.21878 , 2025a. Huang, J. Y., Sengupta, S., Bonadiman, D., Lai, Y.-a., Gupta, A., Pappas, N., Mansour, S., Kirchhoff, K., and Roth, D. Deal: Decoding-time alignment for large language models. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) , pp. 26280–26300, 2025b. Hung, C.-Y., Majumder, N., Mehrish, A., and Poria, S. Reward-guided tree search for inference time alignment of large language models. In Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers) , pp. 12575–12593, 2025. Ichihara, Y., Jinnai, Y., Morimura, T., Ariu, K., Abe, K., Sakamoto, M., and Uchibe, E. Evaluation of best-of-n sampling strategies for language model alignment. arXiv preprint arXiv:2502.12668 , 2025. Jin, Z., Yuan, H., Men, T., Cao, P., Chen, Y., Xu, J., Li, H., Jiang, X., Liu, K., and Zhao, J. Rag-rewardbench: Benchmarking reward models in retrieval augmented generation for preference alignment. In Findings of the Association
+
+[p. 10 | section: References | type: ListGroup]
+for Computational Linguistics: ACL 2025 , pp. 17061– 17090, 2025. Jinnai, Y., Morimura, T., Ariu, K., and Abe, K. Regularized best-of-n sampling to mitigate reward hacking for language model alignment. In ICML 2024 Workshop on Models of Human Feedback for AI Alignment , 2024. Kendall, A. and Gal, Y. What uncertainties do we need in bayesian deep learning for computer vision? Advances in neural information processing systems , 30, 2017. Khalaf, H., Verdun, C. M., Oesterling, A., Lakkaraju, H., and Calmon, F. d. P. Inference-time reward hacking in large language models. arXiv preprint arXiv:2506.19248 , 2025. Kopf, A., Kilcher, Y., Von R ¨ utte, D., Anagnostidis, S., ¨ Tam, Z. R., Stevens, K., Barhoum, A., Nguyen, D., Stanley, O., Nagyfi, R., et al. Openassistant conversationsdemocratizing large language model alignment. Ad vances in neural information processing systems , 36: 47669–47681, 2023. Lakshminarayanan, B., Pritzel, A., and Blundell, C. Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems , 30, 2017. Lambert, N., Pyatkin, V., Morrison, J., Miranda, L. J. V., Lin, B. Y., Chandu, K., Dziri, N., Kumar, S., Zick, T., Choi, Y., et al. Rewardbench: Evaluating reward models for language modeling. In Findings of the Association for Computational Linguistics: NAACL 2025 , pp. 1755– 1797, 2025. Levy, D., Carmon, Y., Duchi, J. C., and Sidford, A. Largescale methods for distributionally robust optimization. Advances in neural information processing systems , 33: 8847–8860, 2020. Li, X., Zhang, T., Dubois, Y., Taori, R., Gulrajani, I., Guestrin, C., Liang, P., and Hashimoto, T. B. Alpacaeval: An automatic evaluator of instruction-following models, 2023. Li, X., Chen, X., Fan, J., Jiang, E. H., and Gao, M. Multi-head reward aggregation guided by entropy. arXiv preprint arXiv:2503.20995 , 2025. Liu, C. Y., Zeng, L., Liu, J., Yan, R., He, J., Wang, C., Yan, S., Liu, Y., and Zhou, Y. Skywork-reward: Bag of tricks for reward modeling in llms. arXiv preprint arXiv:2410.18451 , 2024a. Liu, Y., Yao, Z., Min, R., Cao, Y., Hou, L., and Li, J. Rmbench: Benchmarking reward models of language models with subtlety and style. arXiv preprint arXiv:2410.16184 , 2024b.
+
+[p. 11 | section: References | type: Text]
+550 Meng, Y., Xia, M., and Chen, D. Simpo: Simple preference optimization with a reference-free reward. Advances in Neural Information Processing Systems , 37:124198– 124235, 2024.
+
+[p. 11 | section: References | type: ListGroup]
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