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Analytic Energy-Guided Policy Optimization for Offline Reinforcement Learning
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Proposes AEPO, which derives a closed-form-approximated intermediate energy for energy-guided diffusion policies via Taylor expansion and Gaussian moment-generating functions, and evaluates it on D4RL offline RL benchmarks.
Problem
Estimating the intermediate energy (log-expectation over posterior actions) in energy-guided diffusion policies for offline RL is intractable, so guidance is inexact.
Approach
Derives an analytic approximation of the intermediate energy log-expectation by linearizing Q around a constant action and using the Gaussian moment-generating function on the Gaussian posterior, then trains a neural intermediate energy network to regress this target, with guidance rescaling for robustness.
Key results
- AEPO achieves a mean normalized score of 87.4 on D4RL Gym-MuJoCo tasks versus 86.6 for QGPO (total 786.7 vs 779.2).
- On Maze2D, AEPO reaches a mean dense score of 127.5 and mean sparse score of 132.3, competitive with TCD and Diffuser.
- On Adroit, AEPO reports mean score 55.6 vs 54.6 for LD (total 667.5 vs 655.5).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use AEPO instead of QGPO | D4RL Gym-MuJoCo · D4RL Gym-MuJoCo | mean score: 86.6 -> 87.4 | Helped |
| Use AEPO instead of TCD | D4RL Pointmaze (Maze2D) sparse tasks · D4RL Pointmaze (Maze2D) | mean sparse score: 135.8 -> 132.3 | Hurt |
| Use AEPO instead of DD | D4RL Pointmaze (Maze2D) dense tasks · D4RL Pointmaze (Maze2D) | mean dense score: 61.5 -> 127.5 | Helped |
| Use AEPO instead of QGPO | D4RL Antmaze · D4RL Antmaze | mean score: 78.3 -> 80.6 | Helped |
| Use AEPO instead of LD | D4RL Adroit · D4RL Adroit | mean score: 54.6 -> 55.6 | Helped |
| Use Posterior 1 instead of Posterior 2 for posterior approximation (ablation) | AEPO · D4RL Gym-MuJoCo | holistic performance | Helped |
| Train the Q function with IQL rather than CQL or in-support softmax Q-learning (ablation) | AEPO · D4RL Gym-MuJoCo | holistic performance | Helped |
| Add intermediate guidance (ω = 0.1) rather than use no guidance (ω = 0) (ablation) | AEPO · D4RL Gym-MuJoCo | normalized score | Helped |
| Apply guidance rescaling rather than non-rescaling (ablation) | AEPO · D4RL Gym-MuJoCo | normalized score | Helped |
| Increase guidance degree ω with rescaling rather than without rescaling (ablation) | AEPO · D4RL Gym-MuJoCo | normalized score | Mixed |
| Vary β (ablation) | AEPO · D4RL Gym-MuJoCo | normalized score | No clear effect |
| Set expectile weight τ to 0.7 (ablation) | AEPO · D4RL Gym-MuJoCo | normalized score | Helped |
Surprising findings
- Posterior 2 variance estimate performs worse than Posterior 1 in ablations, which the authors attribute to dataset variance contamination.
Limitations
- Relies on a Taylor-expansion linear approximation of Q and mild assumptions for the posterior covariance.
- Performance gains over strong baselines are small on many tasks (e.g., AntMaze medium-play and large-play lower than QGPO/IDQL).
Experimental setup
Datasets: D4RL Gym-MuJoCo D4RL Maze2D D4RL AntMaze D4RL Adroit
Benchmarks: D4RL Gym-MuJoCo D4RL Maze2D D4RL AntMaze D4RL Adroit
Metrics: normalized score mean score total score
Baselines: QGPO D-QL DiffuserLite HD-DA IDQL AdaptDiffuser Consistency-AC HDMI TCD SfBC DD Diffuser
Builds on: Diffusion-QL QGPO Implicit Q-learning DPM-solver Diffuser
Closest papers by meaning
- Energy-Weighted Flow Matching for Offline Reinforcement Learning (ICLR 2025 · similarity 0.90)
- Offline Transition Modeling via Contrastive Energy Learning (ICML 2024 · similarity 0.90)
- Energy-Guided Diffusion Sampling for Offline-to-Online Reinforcement Learning (ICML 2024 · similarity 0.89)
- Prior-Guided Diffusion Planning for Offline Reinforcement Learning (NeurIPS 2025 · similarity 0.88)
- OCEAN-MBRL: Offline Conservative Exploration for Model-Based Offline Reinforcement Learning (AAAI 2024 · similarity 0.88)
- Reward-Consistent Dynamics Models are Strongly Generalizable for Offline Reinforcement Learning (ICLR 2024 · similarity 0.88)
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