# Investigating the Edge of Stability Phenomenon in Reinforcement Learning

arXiv: https://arxiv.org/abs/2307.04210 · HTML: https://mlsanity.com/paper/2307.04210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 9 Jul 2023.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Overcoming Exploration in Reinforcement Learning with Demonstrations](https://mlsanity.com/paper/1709.10089/) (2017)
- [Noisy Networks for Exploration](https://mlsanity.com/paper/1706.10295/) (2017)
- [The large learning rate phase of deep learning: the catapult mechanism](https://mlsanity.com/paper/2003.02218/) (2020)
- [Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability](https://mlsanity.com/paper/2209.15594/) (2022)
- [Adaptive Gradient Methods at the Edge of Stability](https://mlsanity.com/paper/2207.14484/) (2022)
- [An Optimistic Perspective on Offline Reinforcement Learning](https://mlsanity.com/paper/1907.04543/) (2019)
- [MinAtar: An Atari-Inspired Testbed for Thorough and Reproducible Reinforcement Learning Experiments](https://mlsanity.com/paper/1903.03176/) (2019)
- [Efficient Evaluation of Natural Stochastic Policies in Offline Reinforcement Learning](https://mlsanity.com/paper/2006.03886/) (2020)

## Abstract (arXiv)

Recent progress has been made in understanding optimisation dynamics in neural networks trained with full-batch gradient descent with momentum with the uncovering of the edge of stability phenomenon in supervised learning. The edge of stability phenomenon occurs as the leading eigenvalue of the Hessian reaches the divergence threshold of the underlying optimisation algorithm for a quadratic loss, after which it starts oscillating around the threshold, and the loss starts to exhibit local instability but decreases over long time frames. In this work, we explore the edge of stability phenomenon in reinforcement learning (RL), specifically off-policy Q-learning algorithms across a variety of data regimes, from offline to online RL. Our experiments reveal that, despite significant differences to supervised learning, such as non-stationarity of the data distribution and the use of bootstrapping, the edge of stability phenomenon can be present in off-policy deep RL. Unlike supervised learning, however, we observe strong differences depending on the underlying loss, with DQN -- using a Huber loss -- showing a strong edge of stability effect that we do not observe with C51 -- using a cross entropy loss. Our results suggest that, while neural network structure can lead to optimisation dynamics that transfer between problem domains, certain aspects of deep RL optimisation can differentiate it from domains such as supervised learning.