FLAC: Maximum Entropy RL via Kinetic Energy Regularized Bridge Matching

TL;DR

FLAC introduces a likelihood-free reinforcement learning framework that uses kinetic energy regularization within a Schr"odinger Bridge formulation, enabling high-dimensional control without explicit action density estimation.

Contribution

It formulates maximum entropy RL as a Generalized Schr"odinger Bridge problem with kinetic energy regularization, providing a novel likelihood-free approach for iterative policies.

Findings

Achieves superior or comparable performance on high-dimensional benchmarks

Avoids explicit density estimation in policy optimization

Automatically tunes kinetic energy via dual mechanism

Abstract

Iterative generative policies, such as diffusion models and flow matching, offer superior expressivity for continuous control but complicate Maximum Entropy Reinforcement Learning because their action log-densities are not directly accessible. To address this, we propose Field Least-Energy Actor-Critic (FLAC), a likelihood-free framework that regulates policy stochasticity by penalizing the kinetic energy of the velocity field. Our key insight is to formulate policy optimization as a Generalized Schr\"odinger Bridge (GSB) problem relative to a high-entropy reference process (e.g., uniform). Under this view, the maximum-entropy principle emerges naturally as staying close to a high-entropy reference while optimizing return, without requiring explicit action densities. In this framework, kinetic energy serves as a physically grounded proxy for divergence from the reference: minimizing path-space energy bounds the deviation of the induced terminal action distribution. Building on this view, we derive an energy-regularized policy iteration scheme and a practical off-policy algorithm that automatically tunes the kinetic energy via a Lagrangian dual mechanism. Empirically, FLAC achieves superior or comparable performance on high-dimensional benchmarks relative to strong baselines, while avoiding explicit density estimation.