Bridging Successor Measure and Online Policy Learning with Flow Matching-Based Representations

The Successor Measure (SM), a powerful method in reinforcement learning (RL), describes discounted future state distributions under a policy, and it has recently been studied using generative modeling techniques. Although SM is a powerful predictive object, it lacks compact representations tailored for online RL. To address this, we introduce Successor Flow Features (SF2), a representation learning framework that bridges SM estimation with policy optimization. SF2 leverages flow-matching generative models to approximate successor measures, while enforcing a structured linear decomposition into a time-invariant embedding and a time-dependent projection. This yields compact, policy-aware state-action features that integrate readily into standard off-policy algorithms like TD3 and SAC. Experiments on DeepMind Control Suite tasks show that SF2 improves sample efficiency and training stability compared to strong successor feature baselines. We attribute these gains to the compact representation induced by flow matching, which reduces compounding errors in long-horizon predictions. The code is available on https://github.com/Shiien/successor-flow-representation-implementation .