A Closed-Loop Non-Asymptotic Convergence Analysis of PPO with Learned Critics and Clipping

2026-10-07

AI Summary

This study addresses the challenges of hyperparameter tuning and poorly understood interaction mechanisms in Proximal Policy Optimization (PPO) by establishing its first closed-loop, non-asymptotic convergence theory. Methodologically, we construct synchronous and asynchronous analysis frameworks to systematically characterize error propagation arising from actor-critic coupling, the clipping mechanism, and finite-batch reuse. Furthermore, we rigorously model Generalized Advantage Estimation (GAE) and Monte Carlo targets under explicit coverage assumptions. Our analysis reveals error amplification bounds and temporal dependency conditions, proving polynomial sample complexity. Ultimately, we derive an $O(T^{-2/5})$ bound on stationarity and tracking accuracy, providing solid theoretical guidance for PPO practice.

Abstract

Despite its widespread use, Proximal Policy Optimization with clipping (PPO-Clip) remains difficult to tune, and the interactions among critic learning, clipping, and rollout reuse remain incompletely understood. We develop a \emph{non-asymptotic} analysis of PPO-Clip as a \emph{closed-loop actor--critic} system. It captures actor--critic coupling, nonsmooth probability-ratio clipping, finite-batch reuse, and predictable early stopping under explicit coverage and critic regularity assumptions, using raw GAE and Monte Carlo critic targets. Our synchronous and asynchronous guarantees jointly characterize policy stationarity and the tracking accuracy of the learned critic, with explicit dependence on algorithmic parameters. A sufficient coupling condition gives optimization, critic tracking, clipping, and finite-batch errors a common amplification bound. The asynchronous result also requires a delay-dependent critic stepsize restriction; violating these conditions does not establish divergence. For finite layered MDPs with tabular critics, a uniform bound on the actual clipped-gradient class replaces complete-trajectory counting. A verified growing-horizon family has polynomial sample complexity, and a two-time-scale schedule gives $O(T^{-2/5})$ stationarity and critic-tracking bounds with explicit fresh-rollout accounting. These results together advance our understanding about PPO and provide theoretical guidance in tuning.

Problem

• Proximal Policy Optimization
• PPO-Clip
• non-asymptotic convergence
• closed-loop actor-critic
• clipping

Innovation

• Non-asymptotic convergence
• Closed-loop actor-critic
• PPO-Clip
• Coupling condition
• Two-time-scale schedule