Analytic Energy-Guided Policy Optimization for Offline Reinforcement Learning (2505.01822v1)

Abstract: Conditional decision generation with diffusion models has shown powerful competitiveness in reinforcement learning (RL). Recent studies reveal the relation between energy-function-guidance diffusion models and constrained RL problems. The main challenge lies in estimating the intermediate energy, which is intractable due to the log-expectation formulation during the generation process. To address this issue, we propose the Analytic Energy-guided Policy Optimization (AEPO). Specifically, we first provide a theoretical analysis and the closed-form solution of the intermediate guidance when the diffusion model obeys the conditional Gaussian transformation. Then, we analyze the posterior Gaussian distribution in the log-expectation formulation and obtain the target estimation of the log-expectation under mild assumptions. Finally, we train an intermediate energy neural network to approach the target estimation of log-expectation formulation. We apply our method in 30+ offline RL tasks to demonstrate the effectiveness of our method. Extensive experiments illustrate that our method surpasses numerous representative baselines in D4RL offline reinforcement learning benchmarks.

Analytic Energy-Guided Policy Optimization for Offline Reinforcement Learning

The paper "Analytic Energy-Guided Policy Optimization for Offline Reinforcement Learning" addresses the challenge of optimizing decision-making using diffusion models in offline reinforcement learning (RL). It explores the relation between energy-function-guided diffusion models and constrained RL problems, presenting a novel approach called Analytic Energy-Guided Policy Optimization (AEPO) to facilitate this process.

Overview

Diffusion models have seen success in various domains such as image synthesis and robotics for their capacity to generate controllable decisions through guided sampling. In RL, however, the challenge lies in accurately estimating the intermediate energy during decision generation, which is often computationally infeasible due to the log-expectation formulation.

This paper proposes AEPO, which aims to analytically derive the intermediate guidance in diffusion processes when the model adheres to conditional Gaussian transformations. The authors establish a theoretical framework for estimating the log-expectation formulation, leading to an analytic expression of intermediate energy, which is then used for optimizing policy in offline RL tasks.

Key Contributions

• Theoretical Analysis: AEPO provides a comprehensive theoretical analysis of the intermediate guidance needed in diffusion processes. It derives the closed-form solution for estimating log-expectation under Gaussian diffusion models, addressing limitations present in existing approaches that rely heavily on imprecise intermediate energy estimates.
• Energy Neural Network Training: By training an intermediate energy neural network, AEPO is designed to accurately approximate the target estimation of the log-expectation, facilitating the generation of high-return action distributions.
• Experimental Evaluation: AEPO was tested across over 30 offline RL tasks from the D4RL benchmarks. Extensive experimentation demonstrated that AEPO consistently outperformed numerous existing methods, including classifier-guided and classifier-free-guided diffusion models, behavior cloning, and transformer-based models.

Numerical Results and Comparisons

The numerical performance of AEPO was robust across varied datasets in the D4RL benchmarks. It exceeded the performance of several state-of-the-art algorithms in most environments, showcasing the effectiveness of the proposed method. Importantly, AEPO demonstrated marked improvements over baselines like D-QL and DiffuserLite, reaffirming its potential in practical scenarios.

Implications and Future Directions

The implications of this research are substantial for the field of RL, particularly offline RL, where interaction with the environment is restricted to pre-existing datasets. AEPO's analytic approach to intermediate energy estimation paves the way for more effective policy generation under constrained scenarios. This paper enhances understanding of energy-guided decision-making, indicating that similar analytic methods could be adapted to online RL or hybrid settings involving dynamic environments.

For future research, this paper suggests exploring further the application of diffusion models in RL domains other than robotics, such as autonomous driving and complex sequential decision-making tasks. Moreover, extending this approach to handle non-Gaussian transformations could broaden AEPO’s applicability and efficiency in capturing more complex data distributions.

In conclusion, AEPO represents a significant advance in offline RL by demonstrating improved policy optimization through analytic energy-guidance. This paper not only addresses theoretical gaps but also marks a step toward more practical implementations of diffusion models in decision-making processes.