Efficient Reinforcement Learning in Nonstationary Environments with Linear Function Approximation

Core Concepts

The authors propose efficient reinforcement learning algorithms, LSVI-UCB-Restart and Ada-LSVI-UCB-Restart, that can adapt to nonstationary environments with linear function approximation. They derive minimax dynamic regret lower bounds and provide matching upper bounds for their proposed algorithms.

Abstract

The paper considers reinforcement learning (RL) in episodic Markov decision processes (MDPs) with linear function approximation under a drifting environment. Specifically, both the reward and state transition functions can evolve over time, but their total variations are bounded.
The key contributions are:

The authors derive minimax dynamic regret lower bounds for nonstationary linear MDPs, showing that it is impossible for any algorithm to achieve sublinear regret on any nonstationary linear MDP with total variation linear in the time horizon T. They also establish a minimax regret lower bound for stationary linear MDPs.

They propose the LSVI-UCB-Restart algorithm, which is an optimistic modification of least-squares value iteration with periodic restart. They analyze its dynamic regret bounds for the cases when local variations are known or unknown.

They introduce a parameter-free algorithm called Ada-LSVI-UCB-Restart, which extends LSVI-UCB-Restart to handle unknown variation budgets. They prove that it can achieve near-optimal dynamic regret without knowing the total variations.

Numerical experiments on synthetic nonstationary linear MDPs demonstrate the effectiveness of the proposed algorithms.

Stats

The paper does not provide any specific numerical data or statistics to support the key claims. The analysis is primarily theoretical, focusing on deriving regret bounds.

Quotes

None.

Key Insights Distilled From

Nonstationary Reinforcement Learning with Linear Function Approximation

by Huozhi Zhou,... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2010.04244.pdf

Deeper Inquiries

How can the proposed algorithms be extended to handle more general function approximation schemes beyond linear MDPs

The proposed algorithms can be extended to handle more general function approximation schemes beyond linear MDPs by incorporating more complex feature maps and non-linear function approximators. One approach could be to use deep neural networks as function approximators, allowing for more flexibility in capturing the underlying dynamics of the environment. By replacing the linear feature map with a neural network architecture, the algorithms can learn more intricate patterns and relationships in the state-action space. This extension would require modifications in the algorithm design to accommodate the non-linearities introduced by the neural network function approximators. Additionally, techniques such as experience replay and target networks commonly used in deep reinforcement learning could be integrated to stabilize the learning process and improve sample efficiency.

What are the practical implications of the derived regret lower bounds

The derived regret lower bounds have significant practical implications for the design and analysis of reinforcement learning algorithms in nonstationary environments. By establishing minimax regret lower bounds for nonstationary linear MDPs, the research provides a theoretical foundation for understanding the inherent challenges and limitations of learning in dynamic environments. These lower bounds can serve as benchmarks for evaluating the performance of new algorithms and can guide the development of more efficient and robust algorithms for broader classes of nonstationary MDPs. The insights gained from the lower bounds can inspire the design of adaptive algorithms that can dynamically adjust to changing environments, leading to more effective decision-making in real-world applications.

Can they inspire the design of new algorithms for broader classes of nonstationary MDPs

The proposed nonstationary RL algorithms can be particularly useful in real-world applications where the environment is subject to changes over time, such as autonomous driving, financial trading, and healthcare management. In autonomous driving, for example, the dynamics of traffic patterns and road conditions can vary unpredictably, requiring adaptive decision-making strategies. The nonstationary RL algorithms can help autonomous vehicles learn to navigate complex and changing environments more effectively. However, deploying these algorithms in practice may pose challenges related to computational complexity, data efficiency, and robustness to noisy or incomplete information. Ensuring the stability and reliability of the algorithms in real-world scenarios would be crucial for their successful deployment.