Title: Performative Policy Gradient: Ascent to Optimality in Performative Reinforcement Learning
Primary area: reinforcement learning
Keywords: Reinforcement Learning, Performative Reinforcement Learning, Markov Decision Process, Policy Gradient, Convergence, Optimality

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 further 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. Furthermore, our empirical analysis on standard performative RL environments validate that PePG outperforms standard policy gradient algorithms and the existing performative RL algorithms aiming for stability.

TL;DR: First performative policy gradient algorithm designed to provably attain performative optimality with softmax parameterisation.