Performative Policy Gradient: Optimality in Performative Reinforcement Learning

Post-deployment machine learning algorithms often influence the environments that they act in, and thus, performatively shift the underlying dynamics that the standard Reinforcement Learning (RL) ignores. While designing optimal algorithms in this performative setting has been studied in supervised learning, the RL counterpart remains under-explored. In this paper, we prove the performative counterparts of the performance difference lemma and the policy gradient theorem in RL, and introduce the Performative Policy Gradient algorithm (PePG). PePG is the first policy gradient algorithm designed to account for performativity in RL. Under softmax parametrisation, and also with and without entropy regularisation, we prove that PePG converges to performatively optimal policies, i.e. policies that remain optimal under the distribution shifts induced by themselves. Thus, PePG significantly extends the prior works in Performative RL that achieves performative stability but not optimality. Our empirical analysis on standard performative RL environments validate that PePG outperforms the existing performative RL algorithms aiming for stability.