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Nonstationary Reinforcement Learning with Linear Function Approximation

arXiv 2010.04244 ↗First posted 8 Oct 2020cs.LG stat.MLcited by 23

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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.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Oct 2020.

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Citing papers per year: 2021: 2; 2022: 6; 2023: 7; 2024: 4; 2025: 3; 2026: 1.

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  1. 2021Non-stationary Reinforcement Learning without Prior Knowledge: An Optimal Black-box Approachcited by 98
  2. 2023Provably Efficient Model-Free Algorithms for Non-stationary CMDPscited by 21
  3. 2021Optimistic Policy Optimization is Provably Efficient in Non-stationary MDPscited by 16
  4. 2022Dynamic Regret of Online Markov Decision Processescited by 13
  5. 2022Provably Efficient Primal-Dual Reinforcement Learning for CMDPs with Non-stationary Objectives and Constraintscited by 10
  6. 2023Tracking Most Significant Shifts in Nonparametric Contextual Banditscited by 10
  7. 2023The complexity of non-stationary reinforcement learningcited by 7
  8. 2022Near-Optimal Goal-Oriented Reinforcement Learning in Non-Stationary Environmentscited by 6
  9. 2022Learning Dynamic Mechanisms in Unknown Environments: A Reinforcement Learning Approachcited by 5
  10. 2023Non-stationary Reinforcement Learning under General Function Approximationcited by 5
  11. 2024Pessimism Meets Risk: Risk-Sensitive Offline Reinforcement Learningcited by 5
  12. 2024Near-Optimal Dynamic Regret for Adversarial Linear Mixture MDPscited by 5
11 more
  1. 2022Non-stationary Risk-sensitive Reinforcement Learning: Near-optimal Dynamic Regret, Adaptive Detection, and Separation Designcited by 4
  2. 2024Sample Complexity Characterization for Linear Contextual MDPscited by 4
  3. 2023Off-Policy Evaluation for Action-Dependent Non-Stationary Environmentscited by 2
  4. 2023Provably Efficient Algorithm for Nonstationary Low-Rank MDPscited by 2
  5. 2025Reinforcement Learning in Switching Non-Stationary Markov Decision Processes: Algorithms and Convergence Analysiscited by 2
  6. 2022Online Reinforcement Learning for Periodic MDPcited by 0
  7. 2023Online Reinforcement Learning in Periodic MDPcited by 0
  8. 2024Efficient, Low-Regret, Online Reinforcement Learning for Linear MDPscited by 0
  9. 2025Natural Policy Gradient for Average Reward Non-Stationary RLcited by 0
  10. 2025Efficient Restarts in Non-Stationary Model-Free Reinforcement Learningcited by 0
  11. 2026DARLING: Detection Augmented Reinforcement Learning with Non-Stationary Guaranteescited by 0