On Proximal Policy Optimization's Heavy-Tailed Gradients 
Authors: Saurabh Garg, Joshua Zhanson, Emilio Parisotto, Adarsh Prasad, J Zico Kolter, Zachary Chase Lipton, Sivaraman Balakrishnan, Ruslan Salakhutdinov, Pradeep Kumar Ravikumar
Keywords: Heavy-tailed Gradients, Proximal Policy Optimization, Robust Estimation, Deep Reinforcement Learning
Abstract: Modern policy gradient algorithms, notably Proximal Policy Optimization (PPO), rely on an arsenal of heuristics, including loss clipping and gradient clipping, to ensure successful learning. These heuristics are reminiscent of techniques from robust statistics, commonly used for estimation in outlier-rich ("heavy-tailed") regimes. In this paper, we present a detailed empirical study to characterize the heavy-tailed nature of the gradients of the PPO surrogate reward function. 
We demonstrate pronounced heavy-tailedness of the gradients, specifically for the actor network,  which increases as the current policy diverges from the behavioral one (i.e., as the agent goes further off policy).  Further examination implicates the likelihood ratios and advantages in the surrogate reward as the main sources to the observed heavy-tailedness. Subsequently, we study the effects of the standard PPO clipping heuristics, demonstrating how these tricks primarily serve to offset heavy-tailedness in gradients. Motivated by these connections, we propose incorporating GMOM (a high-dimensional robust estimator) into PPO as a substitute for three clipping tricks, achieving performance close to PPO (with all heuristics enabled) on a battery of MuJoCo continuous control tasks.