papers/mrq/sau.json

{
  "paper_id": "mrq",
  "paper_title": "Towards General-Purpose Model-Free RL (MR.Q)",
  "D1": [
    {
      "id": "mrq-D1-001",
      "claim": "MR.Q Encoder Hyperparameters (Table 3, Appendix B.1): unrolling horizon H_Enc=5; loss weights λ_Reward=0.1, λ_Dynamics=0.1, λ_Terminal=0.1 (set to 0 until first terminal transition); pre-activation regularization λ_pre-activ=1e-5; encoder uses AdamW optimizer with lr=1e-4, weight decay=1e-4; activation=ELU throughout encoder sub-networks.",
      "source": "Appendix B.1, Table 3"
    },
    {
      "id": "mrq-D1-002",
      "claim": "MR.Q Value Function Hyperparameters (Table 3, Appendix B.1): multi-step return horizon H_Q=3; value function uses AdamW optimizer with lr=3e-4, weight decay=1e-4; target policy noise σ=0.2 (N(0, 0.2²)), noise clipping c=±0.3; gradient clip norm=20; value network activation=ELU.",
      "source": "Appendix B.1, Table 3; Section 4.2.2"
    },
    {
      "id": "mrq-D1-003",
      "claim": "MR.Q Policy Hyperparameters (Table 3, Appendix B.1): policy uses AdamW optimizer with lr=3e-4, weight decay=1e-4; Gumbel-Softmax temperature τ=10 for discrete actions, Tanh for continuous actions; policy network activation=ReLU.",
      "source": "Appendix B.1, Table 3; Section 4.2.3"
    },
    {
      "id": "mrq-D1-004",
      "claim": "MR.Q Common Hyperparameters (Table 3, Appendix B.1): discount factor γ=0.99; replay buffer capacity=1M transitions; minibatch size=256; target update frequency T_target=250; exploration noise N(0, 0.2²); initial random exploration=10k time steps; weight initialization=Xavier uniform; bias initialization=0.",
      "source": "Appendix B.1, Table 3"
    },
    {
      "id": "mrq-D1-005",
      "claim": "MR.Q Network Dimensions (Table 3, Appendix B.1): state embedding zs_dim=512, state-action embedding zsa_dim=512, internal action embedding za_dim=256; hidden dimension=512 throughout all MLP networks; CNN encoder: 4 conv layers, 32 output channels each, kernel size=3, strides=(2,2,2,1), flattened output=1568 fed into Linear(1568, 512).",
      "source": "Appendix B.1, Table 3; Appendix B.2"
    },
    {
      "id": "mrq-D1-006",
      "claim": "Experiment Setup Numbers (Appendix B.3): main results=10 seeds, design study=5 seeds; evaluation every 5k steps (Gym/DMC) or 100k steps (Atari), averaging over 10 episodes; Gym: 1M steps (no action repeat); DMC: 500k steps (1M frames with action repeat=2); Atari: 2.5M steps (10M frames with action repeat=4); 95% stratified bootstrap confidence interval.",
      "source": "Appendix B.3"
    },
    {
      "id": "mrq-D1-007",
      "claim": "Rainbow vs TD3 Hyperparameter Differences (Table 1 in Section 1): both use γ=0.99, Adam optimizer; Rainbow: lr=6.25e-5, Adam ε=1.5e-4, batch size=32, replay buffer=1M, target update every 8k steps (iterative); TD3: lr=1e-3, Adam ε=1e-8, batch size=100, replay buffer=1M, target update via EMA (τ=0.995, effective frequency=200). Table used to motivate need for general-purpose algorithm.",
      "source": "Section 1, Table 1"
    },
    {
      "id": "mrq-D1-008",
      "claim": "MR.Q Reward Scaling and Categorical Encoding (Table 3, Section 4.2.1): reward prediction uses categorical two-hot encoding with 65 bins over symexp-spaced range [-10, 10] (effective range [-22k, 22k] via symexp(x)=sign(x)(exp(|x|)-1)); value loss normalized by average absolute reward r̄ in replay buffer; target reward scale r̄' updated alongside target networks every T_target=250 steps.",
      "source": "Appendix B.1, Table 3; Section 4.2.1 Eq 15; Section 4.2.2 Eq 19"
    },
    {
      "id": "mrq-D1-009",
      "claim": "MR.Q Observation Preprocessing (Appendix B.2, B.3): Gym vector state - no preprocessing; DMC Visual - last 3 frames resized to 84x84 RGB, action repeat=2; Atari - grayscale 84x84, max-pooled frames, last 4 frames as state, action repeat=4, sticky actions p=0.25; CNN encoder input normalization: state/255 - 0.5; LAP prioritized sampling: smoothing exponent α=0.4, minimum priority=1.",
      "source": "Appendix B.2, B.3"
    }
  ],
  "D2": [
    {
      "id": "mrq-D2-001",
      "claim": "(Eq 12) z_s'^t, r^t, d^t := g_ω(z^{t-1}, a^{t-1})^T · m, with z^0 := f_ω(s_0). Unrolls latent dynamics model over H_Enc: encodes initial state s_0, then repeatedly applies state-action encoder g_ω and linear MDP predictor m, outputting predicted next-state embedding z_s', reward r, and terminal signal d.",
      "source": "Section 4.2.1, Eq 12"
    },
    {
      "id": "mrq-D2-002",
      "claim": "(Eq 14) L_Enc = Σ_{t=1}^{H_Enc} [λ_Reward·L_Reward(r^t) + λ_Dynamics·L_Dynamics(z_s'^t) + λ_Terminal·L_Terminal(d^t)]. Sums reward, dynamics, terminal losses over unrolled horizon H_Enc=5, balanced by λ_Reward=λ_Dynamics=λ_Terminal=0.1. λ_Terminal=0 until first terminal (d=1) observed.",
      "source": "Section 4.2.1, Eq 14"
    },
    {
      "id": "mrq-D2-003",
      "claim": "(Eq 15) L_Reward(r) = CE(r, Two-Hot(r)), symexp(x)=sign(x)(exp(|x|)-1). Categorical reward prediction: cross-entropy between predicted logits and two-hot encoded target over 65 symexp-spaced bins on [-10,10] (effective range [-22k,22k]).",
      "source": "Section 4.2.1, Eq 15"
    },
    {
      "id": "mrq-D2-004",
      "claim": "(Eq 16) L_Dynamics(z_s') = (z_s' - z̄_s')². MSE between predicted next-state embedding z_s' (from encoder unrolling) and target embedding z̄_s' from target encoder f_ω'. State-only embedding z_s' (not z_{s'a'}) eliminates policy dependence; ω' synced every T_target=250.",
      "source": "Section 4.2.1, Eq 16"
    },
    {
      "id": "mrq-D2-005",
      "claim": "(Eq 17) L_Terminal(d̃) = (d̃ - d)². MSE between predicted scalar terminal signal d̃ and binary terminal indicator d ∈ {0,1} from the environment; active only after first terminal transition observed.",
      "source": "Section 4.2.1, Eq 17"
    },
    {
      "id": "mrq-D2-006",
      "claim": "(Eq 18) a_π = argmax a' (discrete) / clip(a', -1, 1) (continuous), where a' = π_φ'(s') + clip(ε, -c, c), ε ~ N(0, σ²), σ=0.2, c=±0.3. Target action with clipped Gaussian noise for value bootstrapping; for discrete actions, noise is added to each one-hot dimension before argmax.",
      "source": "Section 4.2.2, Eq 18"
    },
    {
      "id": "mrq-D2-007",
      "claim": "(Eq 19) L_Value(Q_i) = Huber(Q_i, (1/r̄)(Σ_{t=0}^{H_Q-1} γ^t·r_t + γ^{H_Q}·Q_j')), Q_j' = r̄'·min_{j=1,2} Q_{θ'_j}(z_{s_H,a_{H,π}}). Multi-step return H_Q=3, γ=0.99, Huber loss to debias prioritized sampling, clipped double Q (min over 2 target Q-nets), normalized by 1/r̄.",
      "source": "Section 4.2.2, Eq 19"
    },
    {
      "id": "mrq-D2-008",
      "claim": "(Eq 20) L_Policy(a_π) = -0.5·Σ_{i=1,2} Q_i(z_{sa_π}) + λ_pre-activ·z_π², a_π = activ(z_π). DPG maximizing avg Q across both Q-nets. Gumbel-Softmax(τ=10) for discrete actions, Tanh for continuous. λ_pre-activ=1e-5 L2 on pre-activation z_π to escape sparse-reward local minima.",
      "source": "Section 4.2.3, Eq 20"
    },
    {
      "id": "mrq-D2-009",
      "claim": "LAP (Fujimoto et al. 2020): P(i) ∝ (|δ_i| + ε)^α, α=0.4 smoothing exponent, min priority=1 floor. Transitions sampled proportional to TD error magnitude |δ_i| from Eq 19; importance-sampling weights corrected via Huber loss to eliminate prioritization bias.",
      "source": "Section 4.2, Section 4.2.2"
    },
    {
      "id": "mrq-D2-010",
      "claim": "(Pseudocode, Section 4.2): Every T_target=250 steps: θ'←θ, φ'←φ, ω'←ω, r̄'←r̄. Synchronized update keeps input and target output fixed within each iteration, reducing non-stationarity for downstream value function and policy optimization.",
      "source": "Section 4.2 (pseudocode block)"
    },
    {
      "id": "mrq-D2-011",
      "claim": "(App B.2) CNN Encoder f_ω(s): 4×Conv2d(32, k=3, strides 2,2,2,1) + ELU → Flatten(1568) → Linear(1568, 512) → LayerNorm → ELU → z_s ∈ R^512. Input: state/255 - 0.5. For pixel observations.",
      "source": "Section 4.2, Appendix B.2"
    },
    {
      "id": "mrq-D2-012",
      "claim": "(App B.2) MLP Encoder f_ω(s): 3-layer MLP = Linear(state_dim→512) → Linear(512→512) → Linear(512→512). Each layer: Linear → LayerNorm → ELU. Output z_s ∈ R^512. For vector/proprioceptive observations.",
      "source": "Section 4.2, Appendix B.2"
    },
    {
      "id": "mrq-D2-013",
      "claim": "(App B.2) State-Action Encoder g_ω(z_s, a): action → Linear(action_dim, 256) + ELU → concat with z_s → 3-layer MLP (768→512→512→512), LayerNorm+ELU after first 2 layers. Linear head outputs MDP predictions (z_s', r, d) and z_sa ∈ R^512.",
      "source": "Section 4.2.1, Appendix B.2"
    },
    {
      "id": "mrq-D2-014",
      "claim": "(App B.2) Value Network Q_θ(z_sa): 4-layer MLP = Linear(512→512→512→512→1). LayerNorm+ELU after first 3 layers, final Linear outputs scalar Q-value. Two identical networks (θ_1, θ_2) for clipped double Q: min_{j=1,2} Q_{θ'_j}.",
      "source": "Section 4.2.2, Appendix B.2"
    },
    {
      "id": "mrq-D2-015",
      "claim": "(App B.2) Policy Network π_φ(z_s): 3-layer MLP = Linear(512→512→512→action_dim). LayerNorm+ReLU after first 2 layers. Final activation: Gumbel-Softmax(τ=10) discrete / Tanh continuous. z_s gradient stopped (detached) so policy loss doesn't affect encoder.",
      "source": "Section 4.2.3, Appendix B.2"
    },
    {
      "id": "mrq-D2-016",
      "claim": "(Section 4.2.3): Exploration: a = activ(z_π) + ε, ε ~ N(0, σ²), σ=0.2. Continuous: clip perturbed action to [-1, 1]. Discrete: add noise to each one-hot dimension, argmax selects action. Initial 10k random exploration steps before policy learning begins.",
      "source": "Section 4.2.3"
    },
    {
      "id": "mrq-D2-017",
      "claim": "(Eq 3, Theorem 1-3): Q(s,a) ≈ z_sa^T·w (Eq 3, linear approximation). Theorem 1: linear model-based solution equals model-free TD fixed point. Theorem 3: for sufficiently rich features satisfying MDP homomorphism, non-linear Q_θ(z_sa) = Q^π(s,a). Embedding z_sa is learned to approximately linearize the value function; non-linear Q head compensates for residual approximation error.",
      "source": "Section 4.1, Section 4.2.2"
    }
  ],
  "D3": [
    {
      "id": "mrq-D3-001",
      "claim": "Purpose: Evaluate general model-free RL on Gym locomotion with continuous actions and vector states. Data: Gym MuJoCo Locomotion (-v4): 5 tasks: Ant-v4, HalfCheetah-v4, Hopper-v4, Humanoid-v4, Walker2d-v4. State space: low-level proprioceptive states (vector), Action space: continuous | Baselines: TD7 (domain-specific SOTA for Gym, author-provided results), TD-MPC2 (general model-based, re-run by authors using episodic branch, 10 seeds), DreamerV3 (general model-based, re-run by authors with DMC hyperparameters, 10 seeds), PPO (general model-free, Stable Baselines 3 default MLP policy) | Metric: TD3-Normalized score = (x - random_score) / (TD3_score - random_score), with random and TD3 reference scores from TD7 (Fujimoto et al., 2024); aggregate mean/median/IQM, 10 seeds, 95% stratified bootstrap CI, agents trained for 1M steps without preprocessing.",
      "source": "Section 5.1, Appendix B.3, B.4"
    },
    {
      "id": "mrq-D3-002",
      "claim": "Purpose: Evaluate general model-free RL on proprioceptive continuous control tasks. Data: DeepMind Control Suite: 28 tasks (all default tasks used by either TD-MPC2 or DreamerV3), Tasks include: acrobot-swingup, ball_in_cup-catch, cartpole (balance, balance_sparse, swingup, swingup_sparse), cheetah-run, dog (run, stand, trot, walk), finger (spin, turn_easy, turn_hard), fish-swim, hopper (hop, stand), humanoid (run, stand, walk), pendulum-swingup, quadruped (run, walk), reacher (easy, hard), walker (run, stand, walk). State space: proprioceptive (vector), Action space: continuous | Baselines: TD7 (re-run by authors, 10 seeds), TD-MPC2 (re-run by authors, 10 seeds), DreamerV3 (re-run by authors with DMC hyperparameters, 10 seeds), PPO (Stable Baselines 3 default MLP policy, 10 seeds) | Metric: raw episode return capped at 1000, aggregate mean/median/IQM over 10 seeds, 95% stratified bootstrap CI, agents trained for 500k steps (1M frames with action repeat=2).",
      "source": "Section 5.1, Appendix B.3, B.4"
    },
    {
      "id": "mrq-D3-003",
      "claim": "Purpose: Evaluate general model-free RL on image-based continuous control tasks. Data: DeepMind Control Suite: 28 tasks (same as proprioceptive benchmark). State space: image-based (last 3 observations, RGB 84x84, action repeat=2), Action space: continuous | Baselines: DrQ-v2 (domain-specific SOTA model-free for visual DMC, author-reported results where available, re-run for missing, 10 seeds), TD-MPC2 (general model-based, re-run by authors, 10 seeds), DreamerV3 (general model-based, re-run by authors, 10 seeds), PPO (general model-free, Stable Baselines 3 default CNN policy, 10 seeds) | Metric: raw episode return capped at 1000, aggregate mean/median/IQM over 10 seeds, 95% stratified bootstrap CI, agents trained for 500k steps (1M frames with action repeat=2).",
      "source": "Section 5.1, Appendix B.3, B.4"
    },
    {
      "id": "mrq-D3-004",
      "claim": "Purpose: Evaluate general model-free RL on discrete-action pixel-based Atari games. Data: Atari-57 benchmark: 55 games evaluated (Defender and Surround omitted from DQN/Rainbow comparison due to absence in Dopamine). State space: pixel observations (grayscale 84x84, stack of last 4 max-pooled observations with action repeat=4), Action space: discrete (per-game action count), Environment version: -v5, Sticky actions enabled (p=0.25) | Baselines: DreamerV3 (general model-based, author-reported results), DQN (model-free, results from Dopamine framework), Rainbow (model-free, results from Dopamine framework), PPO (general model-free, Stable Baselines 3 default CNN policy) | Metric: Human-Normalized score = (x - random_score) / (human_score - random_score) with human scores from Wang et al. 2016; aggregate mean/median/IQM, 10 seeds, 95% stratified bootstrap CI, agents trained for 2.5M steps (10M frames with action repeat=4).",
      "source": "Section 5.1, Appendix B.3, B.4"
    },
    {
      "id": "mrq-D3-005",
      "claim": "Purpose: Quantify the impact of individual design choices and hyperparameters on MR.Q performance. Data: All four benchmarks: Gym Locomotion (5 tasks), DMC Proprioceptive (28 tasks), DMC Visual (28 tasks), Atari (55 games) | Baselines: default MR.Q configuration as reference; variations tested: Linear value function, Dynamics target (state-action instead of state-only), No target encoder, Revert (all three combined), Non-linear model, MSE reward loss, No reward scaling, No min (mean instead of min over Q-networks), No LAP, No MR (model-based representation removed), 1-step return, No unroll (H_Enc=1) | Metric: Average difference in normalized performance from default MR.Q, over 5 seeds. Impact categories: Negative [-0.01, -0.2), Damaging [-0.2, -0.5), Catastrophic (<=-0.5), Positive (>0.01). Gym: TD3-Normalized, DMC: Raw reward, Atari: Human-Normalized, 95% bootstrap CI.",
      "source": "Section 5.2, Table 2"
    }
  ],
  "D4": [
    {
      "id": "mrq-D4-001",
      "claim": "Phase 1 (Encoder with latent dynamics unrolling): Encode s→z_s via f_ω. Per step t=1..H_Enc: z_sa=g_ω(z_{t-1},a_{t-1}), then MDP predictions (z_s',r,d)=z_sa^T·m. Loss = Σ λ_Reward·CE + λ_Dynamics·MSE(z̃_s',z̄_s') + λ_Terminal·MSE(d̃,d), λ_Terminal=0 until first terminal seen. Target z̄_s' from target encoder f_ω' (state-only). (Section 4.2.1)",
      "source": "Section 4.2.1, Eq 12-17"
    },
    {
      "id": "mrq-D4-002",
      "claim": "Phase 2 (Target synchronization every T_target=250 steps): Copy θ'←θ, φ'←φ, ω'←ω, r̄'←r̄. Keeps input/target fixed within each iteration to reduce non-stationarity. Transitions sampled via LAP prioritized replay (α=0.4, min priority=1), buffer capacity 1M, batch size 256, 10k initial random steps. (Section 4.2 pseudocode)",
      "source": "Section 4.2 pseudocode block"
    },
    {
      "id": "mrq-D4-003",
      "claim": "Phase 3 (Value update with clipped double Q + multi-step return): Target action a_π=π_φ'(s')+clip(ε,-0.3,0.3), ε~N(0,0.2²). Multi-step return over H_Q=3 with γ=0.99, Huber loss, normalized by 1/r̄. Clipped double Q: min_{j=1,2} Q_θ'_j for bootstrap. Gradient clip norm=20. AdamW lr=3e-4. (Section 4.2.2, Eq 18-19)",
      "source": "Section 4.2.2, Eq 18-19"
    },
    {
      "id": "mrq-D4-004",
      "claim": "Phase 4 (Policy update via deterministic policy gradient + exploration): Policy π_φ: 3-layer MLP on z_s, Gumbel-Softmax(τ=10) discrete / Tanh continuous. Loss=-0.5·Σ_i Q_θ_i(z_{s,a_π})+λ·z_π², grad stopped from z_s. Exploration: add Gaussian noise N(0,0.2²) to actions during training. AdamW lr=3e-4. (Section 4.2.3, Eq 20)",
      "source": "Section 4.2.3, Eq 20"
    }
  ]
}