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.

Trust Region Policy Optimization (TRPO) attractively optimizes the policy while constraining the update of the new policy within a trust region, ensuring the stability and monotonic optimization. Building on the theoretical guarantees of trust region optimization, Proximal Policy Optimization (PPO) successfully enhances the algorithm's sample efficiency and reduces deployment complexity by confining the update of the new and old policies within a surrogate trust region. However, this approach is limited by the fixed setting of surrogate trust region and is not sufficiently adaptive, because there is no theoretical proof that the optimal clipping bound remains consistent throughout the entire training process, truncating the ratio of the new and old policies within surrogate trust region can ensure that the algorithm achieves its best performance, therefore, exploring and researching a dynamic clip bound for improving PPO's performance can be quite beneficial. To design an adaptive clipped trust region and explore the dynamic clip bound's impact on the performance of PPO, we introduce an adaptive PPO-CLIP (Adaptive-PPO) method that dynamically explores and exploits the clip bound using a bandit during the online training process. Furthermore, ample experiments will initially demonstrate that our Adaptive-PPO exhibits sample efficiency and performance compared to PPO-CLIP.

Policy optimization is a fundamental principle for designing reinforcement learning algorithms, and one example is the proximal policy optimization algorithm with a clipped surrogate objective (PPO-Clip), which has been popularly used in deep reinforcement learning due to its simplicity and effectiveness. Despite its superior empirical performance, PPO-Clip has not been justified via theoretical proof up to date. In this paper, we establish the first global convergence rate of PPO-Clip under neural function approximation. We identify the fundamental challenges of analyzing PPO-Clip and address them with the two core ideas: (i) We reinterpret PPO-Clip from the perspective of hinge loss, which connects policy improvement with solving a large-margin classification problem with hinge loss and offers a generalized version of the PPO-Clip objective. (ii) Based on the above viewpoint, we propose a two-step policy improvement scheme, which facilitates the convergence analysis by decoupling policy search from the complex neural policy parameterization with the help of entropic mirror descent and a regression-based policy update scheme. Moreover, our theoretical results provide the first characterization of the effect of the clipping mechanism on the convergence of PPO-Clip. Through experiments, we empirically validate the reinterpretation of PPO-Clip and the generalized objective with various classifiers on various RL benchmark tasks.