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Enhancing Value Function Estimation through First-Order State-Action Dynamics in Offline Reinforcement Learning
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Adds a first-order (gradient) consistency loss, derived from the HJB equation and finite-difference dataset dynamics, to discrete-time actor-critic value learning for offline RL, applied to ReBrac (TD3-based) and EDAC/SAC.
Problem
Offline RL value functions learned with the discrete-time Bellman equation extrapolate poorly to unvisited states and actions, causing wrong value landscapes and policies.
Approach
Regularize the Q-function so its state and action gradients align with dataset finite-difference dynamics (s'-s, a'-a) as implied by the HJB first-order condition, avoiding explicit reward/dynamics models and PDE solving, plus weighting, nearby-state consistency, and an action-gradient threshold.
Key results
- Ours reaches 82.6 MuJoCo performance versus 79.4 for ReBrac, and 85.7 vs 76.9 on AntMaze.
- Ours reaches 79.6 on Adroit vs 75.0 for ReBrac and 63.3 on Franka Kitchen (partial/complete average) versus 44.7 for the best listed baseline.
- On the stochastic variant built on EDAC, first-order consistency improves Walker2d-medium from 92.5 to 95.1 and Halfcheetah-medium from 65.9 to 70.0 (per Table 3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add first-order consistency to ReBrac | Offline RL on D4RL · Mujoco Performance | normalized score: 79.4 -> 82.6 | Helped |
| Add first-order consistency to ReBrac | Offline RL on D4RL · Antmaze Performance | normalized score: 76.9 -> 85.7 | Helped |
| Add first-order consistency to ReBrac | Offline RL on D4RL · Adroit Performance | normalized score: 75.0 -> 79.6 | Helped |
| Add first-order consistency | Offline RL on D4RL · Franka Performance | normalized score: 44.7 -> 63.3 | Helped |
| Add first-order consistency to EDAC | Stochastic offline RL · Walker2d-medium and Walker2d-medium-replay | normalized score: 92.5 ± 0.8 -> 95.1 ± 1.4; 87.1 ± 2.4 -> 94.1 ± 2.0 | Helped |
| Add first-order consistency to EDAC | Stochastic offline RL · Halfcheetah-medium and Halfcheetah-medium-replay | normalized score: 65.9 ± 0.6 -> 70.0 ± 0.2; 61.3 ±1 .9 -> 66.0 ± 0.4 | Helped |
| Add first-order consistency to EDAC | Stochastic offline RL · Adroit Relocate-expert and Door-expert | normalized score: -0.3 ± 0.0 -> 63.7 ± 8.4; -0.3 ± 0.1 -> 107.6 ± 0.3 | Helped |
| Add nearby state consistency (ablation) | First-order consistency · Antmaze diverse datasets | normalized score: 91.4 ± 3.5 -> 94.0 ± 2.2; 75.6 ± 18.7 -> 88.2 ± 3.5; 48.5 ± 30.0 -> 70.4 ± 4.4 | Helped |
| Add state consistency (ablation) | First-order consistency · Antmaze diverse datasets | normalized score: 80.4 ± 17.2 -> 94.0 ± 2.2; 84.4 ± 4.5 -> 88.2 ± 3.5; 50.6 ± 20.7 -> 70.4 ± 4.4 | Helped |
| Add action indicator (ablation) | First-order consistency · Antmaze diverse datasets | normalized score: 95.2 ± 2.1 -> 94.0 ± 2.2; 75.6 ± 17.9 -> 88.2 ± 3.5; 63.4 ± 6.2 -> 70.4 ± 4.4 | Mixed |
| Add action consistency (ablation) | First-order consistency · Antmaze diverse datasets | normalized score: 93.6 ± 1.9 -> 94.0 ± 2.2; 77.2 ± 20.7 -> 88.2 ± 3.5; 66.2 ± 14.7 -> 70.4 ± 4.4 | Helped |
| Normalize state consistency gradients (ablation) | First-order consistency · Antmaze diverse datasets | normalized score: 72.0 ± 18.2 -> 94.0 ± 2.2; 80.6 ± 17.3 -> 88.2 ± 3.5 | Mixed |
Surprising findings
- Ablation shows removing action indicator or action consistency can sometimes slightly improve the Umaze-diverse score (95.2 without action consistency vs 94.0 full).
Limitations
- Gains are mixed across tasks; some ablation variants score higher on individual Antmaze datasets.
- Relies on finite-difference approximations of dynamics and action derivatives assuming constant time step (Delta t = 1).
- Requires tuning of several extra hyperparameters (weights, action gradient threshold, weighting function).
Experimental setup
Datasets: D4RL Gym-MuJoCo D4RL AntMaze D4RL Adroit D4RL Franka Kitchen
Benchmarks: D4RL Gym-MuJoCo D4RL AntMaze D4RL Adroit D4RL Franka Kitchen
Metrics: normalized score
Baselines: ReBrac RVS IQL DT TD3+BC CQL F-BRC EDAC SAC-N SAC-RND SAC ATAC
Builds on: ReBrac TD3 SAC EDAC F-BRC
Closest papers by meaning
- A Perspective of Q-value Estimation on Offline-to-Online Reinforcement Learning (AAAI 2024 · similarity 0.91)
- Is Value Learning Really the Main Bottleneck in Offline RL? (NeurIPS 2024 · similarity 0.90)
- The Edge-of-Reach Problem in Offline Model-Based Reinforcement Learning (NeurIPS 2024 · similarity 0.90)
- Pessimistic Nonlinear Least-Squares Value Iteration for Offline Reinforcement Learning (ICLR 2024 · similarity 0.90)
- Minimax Optimal and Computationally Efficient Algorithms for Distributionally Robust Offline Reinforcement Learning (NeurIPS 2024 · similarity 0.90)
- A Clean Slate for Offline Reinforcement Learning (NeurIPS 2025 · similarity 0.90)
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