# Nonstationary Reinforcement Learning with Linear Function Approximation

arXiv: https://arxiv.org/abs/2010.04244 · HTML: https://mlsanity.com/paper/2010.04244/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2020.

## Built on by (most cited first, 23 of 23)

- [Non-stationary Reinforcement Learning without Prior Knowledge: An Optimal Black-box Approach](https://mlsanity.com/paper/2102.05406/) (2021)
- [Provably Efficient Model-Free Algorithms for Non-stationary CMDPs](https://mlsanity.com/paper/2303.05733/) (2023)
- [Optimistic Policy Optimization is Provably Efficient in Non-stationary MDPs](https://mlsanity.com/paper/2110.08984/) (2021)
- [Dynamic Regret of Online Markov Decision Processes](https://mlsanity.com/paper/2208.12483/) (2022)
- [Provably Efficient Primal-Dual Reinforcement Learning for CMDPs with Non-stationary Objectives and Constraints](https://mlsanity.com/paper/2201.11965/) (2022)
- [Tracking Most Significant Shifts in Nonparametric Contextual Bandits](https://mlsanity.com/paper/2307.05341/) (2023)
- [The complexity of non-stationary reinforcement learning](https://mlsanity.com/paper/2307.06877/) (2023)
- [Near-Optimal Goal-Oriented Reinforcement Learning in Non-Stationary Environments](https://mlsanity.com/paper/2205.13044/) (2022)
- [Non-stationary Reinforcement Learning under General Function Approximation](https://mlsanity.com/paper/2306.00861/) (2023)
- [Pessimism Meets Risk: Risk-Sensitive Offline Reinforcement Learning](https://mlsanity.com/paper/2407.07631/) (2024)
- [Learning Dynamic Mechanisms in Unknown Environments: A Reinforcement Learning Approach](https://mlsanity.com/paper/2202.12797/) (2022)
- [Sample Complexity Characterization for Linear Contextual MDPs](https://mlsanity.com/paper/2402.02700/) (2024)
- [Near-Optimal Dynamic Regret for Adversarial Linear Mixture MDPs](https://mlsanity.com/paper/2411.03107/) (2024)
- [Non-stationary Risk-sensitive Reinforcement Learning: Near-optimal Dynamic Regret, Adaptive Detection, and Separation Design](https://mlsanity.com/paper/2211.10815/) (2022)
- [Reinforcement Learning in Switching Non-Stationary Markov Decision Processes: Algorithms and Convergence Analysis](https://mlsanity.com/paper/2503.18607/) (2025)
- [Off-Policy Evaluation for Action-Dependent Non-Stationary Environments](https://mlsanity.com/paper/2301.10330/) (2023)
- [Provably Efficient Algorithm for Nonstationary Low-Rank MDPs](https://mlsanity.com/paper/2308.05471/) (2023)
- [Online Reinforcement Learning in Periodic MDP](https://mlsanity.com/paper/2303.09629/) (2023)
- [Online Reinforcement Learning for Periodic MDP](https://mlsanity.com/paper/2207.12045/) (2022)
- [Efficient, Low-Regret, Online Reinforcement Learning for Linear MDPs](https://mlsanity.com/paper/2411.10906/) (2024)
- [Natural Policy Gradient for Average Reward Non-Stationary RL](https://mlsanity.com/paper/2504.16415/) (2025)
- [Efficient Restarts in Non-Stationary Model-Free Reinforcement Learning](https://mlsanity.com/paper/2510.11933/) (2025)
- [DARLING: Detection Augmented Reinforcement Learning with Non-Stationary Guarantees](https://mlsanity.com/paper/2604.16684/) (2026)

## Abstract (arXiv)

We consider reinforcement learning (RL) in episodic Markov decision processes (MDPs) with linear function approximation under drifting environment. Specifically, both the reward and state transition functions can evolve over time but their total variations do not exceed a textitvariation budget. We first develop textttLSVI-UCB-Restart algorithm, an optimistic modification of least-squares value iteration with periodic restart, and bound its dynamic regret when variation budgets are known. Then we propose a parameter-free algorithm textttAda-LSVI-UCB-Restart that extends to unknown variation budgets. We also derive the first minimax dynamic regret lower bound for nonstationary linear MDPs and as a byproduct establish a minimax regret lower bound for linear MDPs unsolved by Jin et al. (2020). Finally, we provide numerical experiments to demonstrate the effectiveness of our proposed algorithms.