RL-Inf: Tracking Non-local Training Data Influence for Online Reinforcement Learning

Online reinforcement learning (RL) has achieved significant success in decision-making tasks, but modern online RL remains highly sensitive to the quality of training experience. Understanding the role of training data in online RL is challenging because the training distribution evolves together with the policy, causing the influence of the training data to propagate across future optimization and future data collection. Existing data-attribution methods for online RL primarily focus on local influence within a single training round, overlooking the non-local data influence across multiple training rounds. In this work, we formalize data attribution in online RL through a trajectory-level leave-one-out quantity, RL-LOO, which measures how one training sample influences a downstream target after subsequent online updates have taken place. We then derive RL-Inf, a first-order estimator that propagates data influence through both optimization effects and policy-induced sampling effects, and provide theoretical guarantees on its approximation accuracy under smoothness assumptions. Our analysis further disentangles these two effects and shows both theoretically and empirically that the full RL-Inf estimator can often be well approximated using the optimization effect alone. Building on this observation, we develop RINSE, a practical data filtering method for online RL. Experiments on standard control benchmarks and an RLHF-style toxicity-mitigation setting show that RINSE improves training efficiency and final performance over standard PPO and local attribution baselines. These results suggest that RL-Inf provides a practical and principled framework for understanding and improving online RL.