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Local and Global Stability in Performative Reinforcement Learning

arXiv · AI, language, vision and robotics · article · Sep 6, 2026 · UTC

In performative reinforcement learning the deployed policy shapes the environment that generates the learner's future data, and the natural solution concept is a performatively stable policy that is optimal in the environment it induces. Existing convergence guarantees rely on Lipschitz sensitivity assumptions on the environment map $π\mapsto (P_π, r_π)$, which are hard to verify and fail in settings such as multi-agent best-response dynamics. We instead study stability for mixtures of policies, and show that the resulting picture is fundamentally different from performative prediction, where

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