Performative Policy Gradient: Optimality in Performative Reinforcement Learning

Abstract

Post-deployment machine learning algorithms often influence the environments they act in, and thus *shift* the underlying dynamics that the standard reinforcement learning (RL) methods ignore. While designing optimal algorithms in this *performative* setting has recently 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.