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A Diffusion Model Framework for Maximum Entropy Reinforcement Learning

Sebastian Sanokowski, Kaustubh Patil, Alois Knoll

TL;DR

This paper reframes Maximum Entropy Reinforcement Learning as a diffusion-based sampling problem, establishing a principled reverse KL objective that ties diffusion dynamics to MaxEntRL. It develops a unified DMERL framework and derives three practical algorithms—DiffPPO, DiffSAC, and DiffWPO—achieving higher sample efficiency and better returns on continuous-control benchmarks with minimal implementation changes. Theoretical contributions include linking the MaxEntRL surrogate to the Log Variance loss and formulating a diffusion-based Wasserstein optimization approach, plus a tractable diffusion-augmented MDP. Empirical results demonstrate robust improvements across Humanoid tasks, with ablations confirming that more diffusion steps yield better performance, suggesting diffusion-based policies are a strong direction for sample-efficient, multimodal action modeling in RL.

Abstract

Diffusion models have achieved remarkable success in data-driven learning and in sampling from complex, unnormalized target distributions. Building on this progress, we reinterpret Maximum Entropy Reinforcement Learning (MaxEntRL) as a diffusion model-based sampling problem. We tackle this problem by minimizing the reverse Kullback-Leibler (KL) divergence between the diffusion policy and the optimal policy distribution using a tractable upper bound. By applying the policy gradient theorem to this objective, we derive a modified surrogate objective for MaxEntRL that incorporates diffusion dynamics in a principled way. This leads to simple diffusion-based variants of Soft Actor-Critic (SAC), Proximal Policy Optimization (PPO) and Wasserstein Policy Optimization (WPO), termed DiffSAC, DiffPPO and DiffWPO. All of these methods require only minor implementation changes to their base algorithm. We find that on standard continuous control benchmarks, DiffSAC, DiffPPO and DiffWPO achieve better returns and higher sample efficiency than SAC and PPO.

A Diffusion Model Framework for Maximum Entropy Reinforcement Learning

TL;DR

This paper reframes Maximum Entropy Reinforcement Learning as a diffusion-based sampling problem, establishing a principled reverse KL objective that ties diffusion dynamics to MaxEntRL. It develops a unified DMERL framework and derives three practical algorithms—DiffPPO, DiffSAC, and DiffWPO—achieving higher sample efficiency and better returns on continuous-control benchmarks with minimal implementation changes. Theoretical contributions include linking the MaxEntRL surrogate to the Log Variance loss and formulating a diffusion-based Wasserstein optimization approach, plus a tractable diffusion-augmented MDP. Empirical results demonstrate robust improvements across Humanoid tasks, with ablations confirming that more diffusion steps yield better performance, suggesting diffusion-based policies are a strong direction for sample-efficient, multimodal action modeling in RL.

Abstract

Diffusion models have achieved remarkable success in data-driven learning and in sampling from complex, unnormalized target distributions. Building on this progress, we reinterpret Maximum Entropy Reinforcement Learning (MaxEntRL) as a diffusion model-based sampling problem. We tackle this problem by minimizing the reverse Kullback-Leibler (KL) divergence between the diffusion policy and the optimal policy distribution using a tractable upper bound. By applying the policy gradient theorem to this objective, we derive a modified surrogate objective for MaxEntRL that incorporates diffusion dynamics in a principled way. This leads to simple diffusion-based variants of Soft Actor-Critic (SAC), Proximal Policy Optimization (PPO) and Wasserstein Policy Optimization (WPO), termed DiffSAC, DiffPPO and DiffWPO. All of these methods require only minor implementation changes to their base algorithm. We find that on standard continuous control benchmarks, DiffSAC, DiffPPO and DiffWPO achieve better returns and higher sample efficiency than SAC and PPO.

Paper Structure

This paper contains 46 sections, 107 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Problem Description
  3. Reinforcement Learning as Reverse Kullback--Leibler Divergence Minimization
  4. Proximal Policy Optimization (PPO)
  5. Soft Actor-Critic (SAC)
  6. Connection between the Log Variance Loss and Off-Policy Surrogate Objectives
  7. Maximum Entropy Wasserstein Policy Optimization
  8. Diffusion Samplers
  9. Continuous-Time Formulation.
  10. Discrete-Time Approximation.
  11. Intractability of the Marginal.
  12. Method
  13. Diffusion-Based Maximum Entropy Reinforcement Learning MDP
  14. Diffusion-based Maximum Entropy Wasserstein Policy Optimization
  15. Experiments
  16. ...and 31 more sections

Figures (2)

  • Figure 1: Effect of varying the number of diffusion steps K on the Humanoid-v4 environment for DiffPPO, DiffSAC and DiffWPO. The average and standard deviation are taken over four seeds.
  • Figure 2: Performance comparison of diffusion-augmented RL algorithms and their vanilla counterparts. Curves are averaged over four independent seeds; shaded areas denote standard deviation.