# The Rank and Gradient Lost in Non-stationarity: Sample Weight Decay for Mitigating Plasticity Loss in Reinforcement Learning

arXiv: https://arxiv.org/abs/2604.01913 · HTML: https://mlsanity.com/paper/2604.01913/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 29 of its 36 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 29 of 29)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [The Primacy Bias in Deep Reinforcement Learning](https://mlsanity.com/paper/2205.07802/) (2022)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learning](https://mlsanity.com/paper/2410.09754/) (2024)
- [Deep Reinforcement Learning with Plasticity Injection](https://mlsanity.com/paper/2305.15555/) (2023)
- [Addressing Loss of Plasticity and Catastrophic Forgetting in Continual Learning](https://mlsanity.com/paper/2404.00781/) (2024)
- [In value-based deep reinforcement learning, a pruned network is a good network](https://mlsanity.com/paper/2402.12479/) (2024)
- [Continual Learning as Computationally Constrained Reinforcement Learning](https://mlsanity.com/paper/2307.04345/) (2023)
- [Small batch deep reinforcement learning](https://mlsanity.com/paper/2310.03882/) (2023)
- [No Representation, No Trust: Connecting Representation, Collapse, and Trust Issues in PPO](https://mlsanity.com/paper/2405.00662/) (2024)
- [Resetting the Optimizer in Deep RL: An Empirical Study](https://mlsanity.com/paper/2306.17833/) (2023)
- [Directions of Curvature as an Explanation for Loss of Plasticity](https://mlsanity.com/paper/2312.00246/) (2023)
- [Parseval Regularization for Continual Reinforcement Learning](https://mlsanity.com/paper/2412.07224/) (2024)
- [Improving Deep Reinforcement Learning by Reducing the Chain Effect of Value and Policy Churn](https://mlsanity.com/paper/2409.04792/) (2024)
- [Measure gradients, not activations! Enhancing neuronal activity in deep reinforcement learning](https://mlsanity.com/paper/2505.24061/) (2025)
- [Adam on Local Time: Addressing Nonstationarity in RL with Relative Adam Timesteps](https://mlsanity.com/paper/2412.17113/) (2024)
- [A Forget-and-Grow Strategy for Deep Reinforcement Learning Scaling in Continuous Control](https://mlsanity.com/paper/2507.02712/) (2025)
- [Reset It and Forget It: Relearning Last-Layer Weights Improves Continual and Transfer Learning](https://mlsanity.com/paper/2310.07996/) (2023)
- [Exit Time Analysis for Approximations of Gradient Descent Trajectories Around Saddle Points](https://mlsanity.com/paper/2006.01106/) (2020)

## Built on by (most cited first, 2 of 2)

- [The Mirage of Optimizing Training Policies: Monotonic Inference Policies as the Real Objective for LLM Reinforcement Learning](https://mlsanity.com/paper/2606.29526/) (2026)
- [WarpSAC: Towards the Pinnacle of Scalable Off-policy RL by Rethinking Exploration and Exploitation](https://mlsanity.com/paper/2608.24479/) (2026)

## Abstract (arXiv)

Deep reinforcement learning (RL) suffers from plasticity loss severely due to the nature of non-stationarity, which impairs the ability to adapt to new data and learn continually. Unfortunately, our understanding of how plasticity loss arises, dissipates, and can be dissolved remains limited to empirical findings, leaving the theoretical end underexplored.To address this gap, we study the plasticity loss problem from the theoretical perspective of network optimization. By formally characterizing the two culprit factors in online RL process: the non-stationarity of data distributions and the non-stationarity of targets induced by bootstrapping, our theory attributes the loss of plasticity to two mechanisms: the rank collapse of the Neural Tangent Kernel (NTK) Gram matrix and the Theta(frac1k) decay of gradient magnitude. The first mechanism echoes prior empirical findings from the theoretical perspective and sheds light on the effects of existing methods, e.g., network reset, neuron recycle, and noise injection. Against this backdrop, we focus primarily on the second mechanism and aim to alleviate plasticity loss by addressing the gradient attenuation issue, which is orthogonal to existing methods. We propose Sample Weight Decay -- a lightweight method to restore gradient magnitude, as a general remedy to plasticity loss for deep RL methods based on experience replay. In experiments, we evaluate the efficacy of methodName upon TD3, myaddedDouble DQN and SAC with SimBa architecture in MuJoCo, myaddedALE and DeepMind Control Suite tasks. The results demonstrate that methodName effectively alleviates plasticity loss and consistently improves learning performance across various configurations of deep RL algorithms, UTD, network architectures, and environments, achieving SOTA performance on challenging DMC Humanoid tasks.