Flow Matching for Offline Reinforcement Learning with Discrete Actions

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 focusing on a small set of high probability actions can reduce computation while keeping the approximation error small, making our method practical for large action spaces. We evaluate on macro-action MinAtar games where offline-pretrained DRIFT outperforms its online-only counterpart across all five games and achieves the highest mean return on three and on oracle free Jericho, DRIFT achieves a mean normalized score of 7.3% with a lightweight GRU encoder, outperforming the evaluated pretrained language-model baselines. Ablations demonstrate the importance of appropriately weighted path-space regularization and reference-guided candidate construction.

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 popularity bias that can suppress high-reward actions in low-density regions, and creates a support binding that restricts off-manifold exploration. Existing workarounds, such as appending residual Gaussian policies, often re-introduce the expressivity bottlenecks associated with unimodal distributions. In this work, we propose Maximum Entropy Adjoint 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 Mixture Behavior 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.

Offline reinforcement learning aims to learn effective policies from fixed datasets without environment interaction. Although generative models such as diffusion and flow matching enhance policy expressiveness, they typically start from uninformative Gaussian noise and generate actions through multi-step iteration, leading to high computational costs and failing to effectively leverage suboptimal trajectories in datasets. We propose MeanFlow2Better (MF2B), which reformulates offline RL as generative decision chunk optimization from current performance status to better performance status in a high-level latent decision space. MF2B maps trajectory chunks to high-level latent decision representations through an encoder, placing generation starting points within a structured decision space sculpted by behavioral data. The model learns a shared conditional mean velocity field in this space, constructing two flow mappings: from Gaussian-Induced Decision Sources toward positive behavioral decision regions, and from suboptimal decisions toward high-value decision regions. Both flow mappings complete decision refinement through one-step ODE integration over the unit time interval $Δt=1$, requiring neither multi-step iterative sampling nor backpropagation through time. Furthermore, we propose hierarchical chunk-level advantage to guide the flow direction toward high-return regions, where the high-level decisions cover multiple low-level actions, leading to sequence length compression from $T$ to $K \approx T/H$ and significantly lower computational overhead. On the D4RL Gym-MuJoCo benchmark, MF2B achieves an average score of 90.91, matching or surpassing strong baselines.