We present \(\varepsilon \) -retrain, a general exploration strategy for reinforcement learning (RL) that encourages adherence to behavioral preferences while preserving the convergence guarantees of the underlying RL algorithm. \(\varepsilon \) -retrain maintains a dynamic collection of retrain areas—regions of the state space where the agent previously violated a specified preference—and mixes the standard uniform restart distribution with states from these areas, according to a decaying parameter \(\varepsilon \) . This mixed retraining thus focuses on enforcing the desired behaviors in the collected areas. We develop the theory for both policy and value-based methods, showing that: (i) in policy-based settings, our method retains monotonic improvement bounds; and (ii) in value-based settings, \(\varepsilon \) -retrain preserves convergence properties without additional assumptions. The approach is simple to integrate into existing RL algorithms and improves sample efficiency and behavioral adherence in the locomotion, power systems, and navigation tasks tested. These results establish \(\varepsilon \) -retrain as a lightweight, theoretically grounded mechanism for incorporating behavioral preferences into RL.
