Entropy-Regularized Adjoint Matching for Offline Reinforcement Learning

Off-policy reinforcement learning of pretrained flow policies remains challenging due to the instability of optimization arising from the multi-step sampling process. Recently, Q-learning with Adjoint Matching (QAM) addressed this issue by reformulating into a memoryless stochastic optimal control (SOC) problem with a learned critic. However, QAM inherits a fundamental fragility of critic-guided improvement: small critic errors are amplified when critics are ill-conditioned, often leading to model collapse. This paper introduces Trust Region Q-Adjoint Matching (TRQAM), a stable off-policy fine-tuning algorithm that adaptively controls the path-space KL with pretrained flow policies through projected dual descent. Specifically, we optimize the trust-region parameter $λ$ in SOC dynamics, and theoretically show that the path-space KL can be represented by a closed-form function of $λ$. As a result, our method can precisely control the exact deviation from pretrained flow policies, achieving stable off-policy RL. Through experiments on 50 OGBench tasks, TRQAM consistently outperforms prior arts in both offline RL and offline-to-online RL. In particular, TRQAM achieves an overall success rate of 68% in offline RL, substantially improves the strongest baseline at 46%.

Many reinforcement learning (RL) tasks have discrete action spaces, but most generative policy methods based on diffusion and flow matching are designed for continuous control. Meanwhile, generative policies usually rely heavily on offline datasets and offline-to-online RL is itself challenging, as the policy must improve from new interaction without losing useful behavior learned from static data. To address those challenges, we introduce DRIFT, an online fine-tuning method that updates an offline pretrained continuous-time Markov chain (CTMC) policy with an advantage-weighted discrete flow matching loss. To preserve useful pretrained knowledge, we add a path-space penalty that regularizes the full CTMC trajectory distribution, rather than only the final action distribution. For large discrete action spaces, we introduce a candidate-set approximation that updates the actor over a small subset of actions sampled from reference-policy rollouts and uniform exploration. Our theoretical analysis shows that the candidate-set error is controlled by missing target probability mass, and the induced CTMC generator error decreases as the candidate set covers more high-probability actions. Experiments on prevailing discrete action RL task show that our method provides stable offline-to-online improvement across all tasks, achieving the highest average score on Jericho with a simple GRU encoder while outperforming methods that use pretrained language models. Controlled experiments further confirm that the path-space penalty remains bounded during fine-tuning and that the CTMC generator adapts to shifted rewards faster than deterministic baselines. The candidate-set mechanism is supported by a stability analysis showing that the generator error decreases exponentially with candidate coverage.

Score-based and flow-based generative models exhibit remarkable expressive capacity in capturing complex distributions, and have been extensively deployed in tasks ranging from image generation to reinforcement learning. Nevertheless, these models suffer from prolonged inference latency, which imposes a significant computational bottleneck in RL with iterative sampling. To overcome this limitation, we propose a new framework named Moment Matching Q-Learning (MoMa QL), which utilizes a technique from statistical hypothesis testing known as maximum mean discrepancy (MMD) that intend to match all orders of statistics between the original and target distribution. By enforcing strong regularization on all moment statistics, this algorithm guarantees distribution-level convergence for conditional score function and remains stable under various hyperparameters. Empirically, we show that our method MoMa QL is more computationally efficient with a comparable if not competitive performance in various D4RL tasks. Remarkably, by accelerating the action sampling process for flow-based policies, MoMa QL demonstrates superior performance in offline-to-online RL tasks because of faster and stronger adaptability for online interactive finetuning.