Entropy-Regularized Adjoint Matching for Offline Reinforcement Learning

Integrating expressive generative policies, such as flow-matching models, into offline reinforcement learning (RL) allows agents to capture complex, multi-modal behaviors. While Q-learning with Adjoint Matching (QAM) stabilizes policy optimization via the continuous adjoint method, it remains inherently bound to the fixed behavior distribution. This dependence induces a $\mathit{\text{popularity}}\mathit{\text{bias}}$ that can suppress high-reward actions in low-density regions, and creates a $\mathit{\text{support}}\mathit{\text{binding}}$ that restricts off-manifold exploration. Existing workarounds, such as appending $\mathit{\text{residual}}$ Gaussian policies, often re-introduce the expressivity bottlenecks associated with unimodal distributions. In this work, we propose $\mathit{\text{Maximum}}\mathit{\text{Entropy}}\mathit{\text{Adjoint}}\mathit{\text{Matching}}$ (ME-AM), a unified framework that addresses these limitations within the continuous flow formulation. ME-AM incorporates two mechanisms: (1) a Mirror Descent entropy maximization objective that mitigates the popularity bias to facilitate the extraction of optimal policies from offline datasets, and (2) a $\mathit{\text{Mixture}}\mathit{\text{Behavior}}\mathit{\text{Prior}}$ that broadens the geometric support to encompass out-of-distribution high-reward regions. By exploring this extended geometry, ME-AM identifies robust actions while preserving the absolute continuity of the generative vector field. Empirically, ME-AM demonstrates competitive or superior performance compared to prior state-of-the-art (SOTA) methods across a diverse suite of sparse-reward continuous control environments.