# Adam on Local Time: Addressing Nonstationarity in RL with Relative Adam Timesteps

arXiv: https://arxiv.org/abs/2412.17113 · HTML: https://mlsanity.com/paper/2412.17113/

## Key facts

- Cited by 11 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 35 of its 50 references that are in the map.
- First posted on arXiv 22 Dec 2024.

## 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, 30 of 35)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [RL2: Fast Reinforcement Learning via Slow Reinforcement Learning](https://mlsanity.com/paper/1611.02779/) (2016)
- [Learning to reinforcement learn](https://mlsanity.com/paper/1611.05763/) (2016)
- [Improving Reproducibility in Machine Learning Research (A Report from the NeurIPS 2019 Reproducibility Program)](https://mlsanity.com/paper/2003.12206/) (2020)
- [The Primacy Bias in Deep Reinforcement Learning](https://mlsanity.com/paper/2205.07802/) (2022)
- [Benchmarking the Spectrum of Agent Capabilities](https://mlsanity.com/paper/2109.06780/) (2021)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [Understanding plasticity in neural networks](https://mlsanity.com/paper/2303.01486/) (2023)
- [What Matters In On-Policy Reinforcement Learning? A Large-Scale Empirical Study](https://mlsanity.com/paper/2006.05990/) (2020)
- [Bigger, Better, Faster: Human-level Atari with human-level efficiency](https://mlsanity.com/paper/2305.19452/) (2023)
- [Understanding and Preventing Capacity Loss in Reinforcement Learning](https://mlsanity.com/paper/2204.09560/) (2022)
- [Dopamine: A Research Framework for Deep Reinforcement Learning](https://mlsanity.com/paper/1812.06110/) (2018)
- [Discovered Policy Optimisation](https://mlsanity.com/paper/2210.05639/) (2022)
- [Evolved Policy Gradients](https://mlsanity.com/paper/1802.04821/) (2018)
- [Craftax: A Lightning-Fast Benchmark for Open-Ended Reinforcement Learning](https://mlsanity.com/paper/2402.16801/) (2024)
- [Discovering Reinforcement Learning Algorithms](https://mlsanity.com/paper/2007.08794/) (2020)
- [Transient Non-Stationarity and Generalisation in Deep Reinforcement Learning](https://mlsanity.com/paper/2006.05826/) (2020)
- [Deep Reinforcement Learning with Plasticity Injection](https://mlsanity.com/paper/2305.15555/) (2023)
- [Meta-Learning via Learned Loss](https://mlsanity.com/paper/1906.05374/) (2019)
- [Atari-5: Distilling the Arcade Learning Environment down to Five Games](https://mlsanity.com/paper/2210.02019/) (2022)
- [Fortuitous Forgetting in Connectionist Networks](https://mlsanity.com/paper/2202.00155/) (2022)
- [Resetting the Optimizer in Deep RL: An Empirical Study](https://mlsanity.com/paper/2306.17833/) (2023)

## Built on by (most cited first, 11 of 11)

- [Stable Gradients for Stable Learning at Scale in Deep Reinforcement Learning](https://mlsanity.com/paper/2506.15544/) (2025)
- [Mitigating Plasticity Loss in Continual Reinforcement Learning by Reducing Churn](https://mlsanity.com/paper/2506.00592/) (2025)
- [Do We Need Adam? Surprisingly Strong and Sparse Reinforcement Learning with SGD in LLMs](https://mlsanity.com/paper/2602.07729/) (2026)
- [How Should We Meta-Learn Reinforcement Learning Algorithms?](https://mlsanity.com/paper/2507.17668/) (2025)
- [The Rank and Gradient Lost in Non-stationarity: Sample Weight Decay for Mitigating Plasticity Loss in Reinforcement Learning](https://mlsanity.com/paper/2604.01913/) (2026)
- [A Physics-Inspired Optimizer: Velocity Regularized Adam](https://mlsanity.com/paper/2505.13196/) (2025)
- [Rethinking the Role of Dynamic Sparse Training for Scalable Deep Reinforcement Learning](https://mlsanity.com/paper/2510.12096/) (2025)
- [Rethinking Adam for Time Series Forecasting: A Simple Heuristic to Improve Optimization under Distribution Shifts](https://mlsanity.com/paper/2603.10095/) (2026)
- [Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization](https://mlsanity.com/paper/2605.04269/) (2026)
- [SingularClip: Preventing Spectral Collapse to Maintain Plasticity in Continual and Reinforcement Learning](https://mlsanity.com/paper/2608.18319/) (2026)
- [The Hidden Ratio in Adam: Stable Structure, Compression, and Sign Dynamics](https://mlsanity.com/paper/2609.35392/) (2026)

## Abstract (arXiv)

In reinforcement learning (RL), it is common to apply techniques used broadly in machine learning such as neural network function approximators and momentum-based optimizers. However, such tools were largely developed for supervised learning rather than nonstationary RL, leading practitioners to adopt target networks, clipped policy updates, and other RL-specific implementation tricks to combat this mismatch, rather than directly adapting this toolchain for use in RL. In this paper, we take a different approach and instead address the effect of nonstationarity by adapting the widely used Adam optimiser. We first analyse the impact of nonstationary gradient magnitude -- such as that caused by a change in target network -- on Adam's update size, demonstrating that such a change can lead to large updates and hence sub-optimal performance. To address this, we introduce Adam-Rel. Rather than using the global timestep in the Adam update, Adam-Rel uses the local timestep within an epoch, essentially resetting Adam's timestep to 0 after target changes. We demonstrate that this avoids large updates and reduces to learning rate annealing in the absence of such increases in gradient magnitude. Evaluating Adam-Rel in both on-policy and off-policy RL, we demonstrate improved performance in both Atari and Craftax. We then show that increases in gradient norm occur in RL in practice, and examine the differences between our theoretical model and the observed data.