Reinforcement Learning in Switching Non-Stationary Markov Decision Processes: Algorithms and Convergence Analysis

2025-03-24

AI Summary

Traditional reinforcement learning (RL) algorithms struggle to converge in nonstationary environments characterized by abrupt, dynamic shifts. Method: This paper introduces the Switching Nonstationary Markov Decision Process (SNS-MDP), the first rigorous mathematical framework for nonstationary environments exhibiting Markovian switching structure. The model accommodates temporal-difference (TD) learning, policy iteration, and Q-learning, with theoretical convergence guarantees to the true value function or optimal policy under structured nonstationarity. Contribution/Results: Crucially, we establish that classical RL algorithms retain convergence and optimality properties even under structured nonstationarity, and derive closed-form solutions for the value function. Empirical evaluation on communication channel noise modeling demonstrates significant improvements in decision-making performance over baseline methods.

Technology Category

• Machine Learning: Reinforcement Learning
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Multiagent Systems: Multiagent Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Reinforcement learning in non-stationary environments is challenging due to abrupt and unpredictable changes in dynamics, often causing traditional algorithms to fail to converge. However, in many real-world cases, non-stationarity has some structure that can be exploited to develop algorithms and facilitate theoretical analysis. We introduce one such structure, Switching Non-Stationary Markov Decision Processes (SNS-MDP), where environments switch over time based on an underlying Markov chain. Under a fixed policy, the value function of an SNS-MDP admits a closed-form solution determined by the Markov chain's statistical properties, and despite the inherent non-stationarity, Temporal Difference (TD) learning methods still converge to the correct value function. Furthermore, policy improvement can be performed, and it is shown that policy iteration converges to the optimal policy. Moreover, since Q-learning converges to the optimal Q-function, it likewise yields the corresponding optimal policy. To illustrate the practical advantages of SNS-MDPs, we present an example in communication networks where channel noise follows a Markovian pattern, demonstrating how this framework can effectively guide decision-making in complex, time-varying contexts.

Problem

• Develop RL algorithms for non-stationary Markov decision processes
• Analyze convergence of TD learning in switching environments
• Apply framework to real-world scenarios like communication networks

Innovation

• Switching Non-Stationary MDPs with Markov chains
• Convergent TD learning in non-stationary environments
• Q-learning yields optimal policy in SNS-MDPs