PPO-Clip Attains Global Optimality: Towards Deeper Understandings of Clipping

TL;DR

This paper addresses the lack of theoretical guarantees for PPO-Clip by introducing a hinge-loss–based generalization of the PPO-Clip objective and proving global convergence in both tabular and neural-function settings. It develops EMDA-based methods: (i) a tabular, direct-parameterization analysis yielding asymptotic convergence to the optimal policy, and (ii) a neural two-step policy search that decouples policy improvement from neural parameterization and proves a $O(1/\sqrt{T})$ min-iterate convergence rate under suitable conditions. A key finding is that the clipping range affects only the pre-constant of the convergence rate, while the overall asymptotic behavior is governed by the EMDA step-size and objective structure; this provides a theoretical lens on PPO-Clip’s empirical robustness. Empirically, Neural PPO-Clip variants with different hinge-based classifiers achieve competitive results across standard RL benchmarks, underscoring the practicality of the hinge-loss reinterpretation and offering guidance for classifier choices in deployment.

Abstract

Proximal Policy Optimization algorithm employing a clipped surrogate objective (PPO-Clip) is a prominent exemplar of the policy optimization methods. However, despite its remarkable empirical success, PPO-Clip lacks theoretical substantiation to date. In this paper, we contribute to the field by establishing the first global convergence results of a PPO-Clip variant in both tabular and neural function approximation settings. Our findings highlight the $O(1/\sqrt{T})$ min-iterate convergence rate specifically in the context of neural function approximation. We tackle the inherent challenges in analyzing PPO-Clip through three central concepts: (i) We introduce a generalized version of the PPO-Clip objective, illuminated by its connection with the hinge loss. (ii) Employing entropic mirror descent, we establish asymptotic convergence for tabular PPO-Clip with direct policy parameterization. (iii) Inspired by the tabular analysis, we streamline convergence analysis by introducing a two-step policy improvement approach. This decouples policy search from complex neural policy parameterization using a regression-based update scheme. Furthermore, we gain deeper insights into the efficacy of PPO-Clip by interpreting these generalized objectives. Our theoretical findings also mark the first characterization of the influence of the clipping mechanism on PPO-Clip convergence. Importantly, the clipping range affects only the pre-constant of the convergence rate.

Figures (1)

• Figure 1: Evaluation of PPO-Clip with different classifiers and popular benchmark methods in MinAtar and OpenAI Gym.

Theorems & Definitions (46)

• Theorem 1: Global Convergence of PPO-Clip
• Proposition 1: EMDA Target Policy
• Theorem 2: General Convergence Rate of Neural PPO-Clip
• Corollary 1: Global Convergence of Neural PPO-Clip, Informal
• Remark A.1
• Proposition : EMDA Target Policy
• proof : Proof of Proposition \ref{['pp:PI']}
• Lemma 1: Policy Evaluation Error
• Lemma 2: Theorem 4.6 in liu2019neural
• proof : Proof of Lemma \ref{['lm:PE_error']}