# CIM-PPO:Proximal Policy Optimization with Liu-Correntropy Induced Metric

arXiv: https://arxiv.org/abs/2110.10522 · HTML: https://mlsanity.com/paper/2110.10522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 20 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Truly Proximal Policy Optimization](https://mlsanity.com/paper/1903.07940/) (2019)
- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [Variational Inference with Tail-adaptive f-Divergence](https://mlsanity.com/paper/1810.11943/) (2018)
- [An Adaptive Clipping Approach for Proximal Policy Optimization](https://mlsanity.com/paper/1804.06461/) (2018)
- [Proximal Policy Optimization with Relative Pearson Divergence](https://mlsanity.com/paper/2010.03290/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Closed-Loop Non-Asymptotic Convergence Analysis of PPO with Learned Critics and Clipping](https://mlsanity.com/paper/2610.10273/) (2026)

## Abstract (arXiv)

As a popular Deep Reinforcement Learning (DRL) algorithm, Proximal Policy Optimization (PPO) has demonstrated remarkable efficacy in numerous complex tasks. According to the penalty mechanism in a surrogate, PPO can be classified into PPO with KL divergence (PPO-KL) and PPO with Clip (PPO-Clip). In this paper, we analyze the impact of asymmetry in KL divergence on PPO-KL and highlight that when this asymmetry is pronounced, it will misguide the improvement of the surrogate. To address this issue, we represent the PPO-KL in inner product form and demonstrate that the KL divergence is a Correntropy Induced Metric (CIM) in Euclidean space. Subsequently, we extend the PPO-KL to the Reproducing Kernel Hilbert Space (RKHS), redefine the inner products with RKHS, and propose the PPO-CIM algorithm. Moreover, this paper states that the PPO-CIM algorithm has a lower computation cost in policy gradient and proves that PPO-CIM can guarantee the new policy is within the trust region while the kernel satisfies some conditions. Finally, we design experiments based on six Mujoco continuous-action tasks to validate the proposed algorithm. The experimental results validate that the asymmetry of KL divergence can affect the policy improvement of PPO-KL and show that the PPO-CIM can perform better than both PPO-KL and PPO-Clip in most tasks.