# KLip-PPO: A per-sample KL perspective on PPO-Clip

arXiv: https://arxiv.org/abs/2606.23932 · HTML: https://mlsanity.com/paper/2606.23932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 15 of 15)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Emergence of Locomotion Behaviours in Rich Environments](https://mlsanity.com/paper/1707.02286/) (2017)
- [What Matters In On-Policy Reinforcement Learning? A Large-Scale Empirical Study](https://mlsanity.com/paper/2006.05990/) (2020)
- [Truly Proximal Policy Optimization](https://mlsanity.com/paper/1903.07940/) (2019)
- [Revisiting Design Choices in Proximal Policy Optimization](https://mlsanity.com/paper/2009.10897/) (2020)
- [Trust Region-Guided Proximal Policy Optimization](https://mlsanity.com/paper/1901.10314/) (2019)
- [Simple Policy Optimization](https://mlsanity.com/paper/2401.16025/) (2024)
- [On the Design of KL-Regularized Policy Gradient Algorithms for LLM Reasoning](https://mlsanity.com/paper/2505.17508/) (2025)
- [You May Not Need Ratio Clipping in PPO](https://mlsanity.com/paper/2202.00079/) (2022)
- [Rethinking KL Regularization in RLHF: From Value Estimation to Gradient Optimization](https://mlsanity.com/paper/2510.01555/) (2025)
- [It's Not You, It's Clipping: A Soft Trust-Region via Probability Smoothing for LLM RL](https://mlsanity.com/paper/2509.21282/) (2025)

## Abstract (arXiv)

Proximal Policy Optimization (PPO) is the standard policy-gradient algorithm for on-policy reinforcement learning. The literature presents it in two forms, a clipped surrogate that bounds the importance ratio between successive policies and a Kullback-Leibler penalty between them. These forms are treated as separate algorithms with their own gradients, their own hyperparameters, and their own reference implementations, and a sizeable body of empirical work compares them. We show that the gradient of the clipped surrogate is reproduced exactly by a Kullback-Leibler surrogate whose coefficient varies per sample, with closed-form dependence on the importance ratio and the advantage. The identity holds at every minibatch step and across the entire inner loop, and on five MuJoCo continuous-control benchmarks the two losses produce indistinguishable training curves. The reformulation exposes a structural feature of the clipped surrogate that the min notation hides. PPO-Clip's implicit per-sample penalty is a step function at the boundary of the trust region, and the shape of this coefficient is the natural design axis for generalising the algorithm. We sketch the resulting follow-up directions in the discussion.