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

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