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

arXiv: https://arxiv.org/abs/2312.12065 · HTML: https://mlsanity.com/paper/2312.12065/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 33 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 18 of 18)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift](https://mlsanity.com/paper/1908.00261/) (2019)
- [Mastering Complex Control in MOBA Games with Deep Reinforcement Learning](https://mlsanity.com/paper/1912.09729/) (2019)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Global Optimality Guarantees For Policy Gradient Methods](https://mlsanity.com/paper/1906.01786/) (2019)
- [Adaptive Trust Region Policy Optimization: Global Convergence and Faster Rates for Regularized MDPs](https://mlsanity.com/paper/1909.02769/) (2019)
- [Revisiting Rainbow: Promoting more Insightful and Inclusive Deep Reinforcement Learning Research](https://mlsanity.com/paper/2011.14826/) (2020)
- [Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programming](https://mlsanity.com/paper/1310.3787/) (2013)
- [An Improved Analysis of (Variance-Reduced) Policy Gradient and Natural Policy Gradient Methods](https://mlsanity.com/paper/2211.07937/) (2022)
- [Convergence Rate of Frank-Wolfe for Non-Convex Objectives](https://mlsanity.com/paper/1607.00345/) (2016)
- [Global Convergence of Policy Gradient for Linear-Quadratic Mean-Field Control/Game in Continuous Time](https://mlsanity.com/paper/2008.06845/) (2020)
- [An Adaptive Clipping Approach for Proximal Policy Optimization](https://mlsanity.com/paper/1804.06461/) (2018)
- [Proximal Policy Gradient: PPO with Policy Gradient](https://mlsanity.com/paper/2010.09933/) (2020)

## Built on by (most cited first, 17 of 17)

- [Process-Supervised Reinforcement Learning for Code Generation](https://mlsanity.com/paper/2502.01715/) (2025)
- [Improving Discrete Diffusion Unmasking Policies Beyond Explicit Reference Policies](https://mlsanity.com/paper/2510.05725/) (2025)
- [HM3: Hierarchical Multi-Objective Model Merging for Pretrained Models](https://mlsanity.com/paper/2409.18893/) (2024)
- [Reward Score Matching: Unifying Reward-based Fine-tuning for Flow and Diffusion Models](https://mlsanity.com/paper/2604.17415/) (2026)
- [PPO in the Fisher-Rao geometry](https://mlsanity.com/paper/2506.03757/) (2025)
- [PCPO: Proportionate Credit Policy Optimization for Aligning Image Generation Models](https://mlsanity.com/paper/2509.25774/) (2025)
- [Test-Time Alignment for Large Language Models via Textual Model Predictive Control](https://mlsanity.com/paper/2502.20795/) (2025)
- [Optimizing Navigation And Chemical Application in Precision Agriculture With Deep Reinforcement Learning And Conditional Action Tree](https://mlsanity.com/paper/2503.17985/) (2025)
- [Non-Asymptotic Global Convergence of PPO-Clip](https://mlsanity.com/paper/2512.16565/) (2025)
- [Bridging MARL to SARL: An Order-Independent Multi-Agent Transformer via Latent Consensus](https://mlsanity.com/paper/2604.13472/) (2026)
- [SPARTA: Evaluating Reasoning Segmentation Robustness through Black-Box Adversarial Paraphrasing in Text Autoencoder Latent Space](https://mlsanity.com/paper/2510.24446/) (2025)
- [ReLA: Representation Learning and Aggregation for Job Scheduling with Reinforcement Learning](https://mlsanity.com/paper/2601.03646/) (2026)
- [From Reward-Free Representations to Preferences: Rethinking Offline Preference-Based Reinforcement Learning](https://mlsanity.com/paper/2606.01123/) (2026)
- [Beyond Fixed Morphologies: Learning Graph Policies with Trust Region Compensation in Variable Action Spaces](https://mlsanity.com/paper/2508.14102/) (2025)
- [Directional-Clamp PPO](https://mlsanity.com/paper/2511.02577/) (2025)
- [Plan2Cleanse: Test-Time Backdoor Defense via Monte-Carlo Planning in Deep Reinforcement Learning](https://mlsanity.com/paper/2605.09638/) (2026)
- [COOPO: Cyclic Offline-Online Policy Optimization Algorithm](https://mlsanity.com/paper/2605.18675/) (2026)

## Abstract (arXiv)

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/√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.