Quickest Change Detection Approach to Optimal Control in Markov Decision Processes with Model Changes

TL;DR

This paper introduces a two-threshold switching strategy for quickest change detection in non-stationary Markov decision processes, optimizing long-term rewards and outperforming existing methods in both Bayesian and non-Bayesian scenarios.

Contribution

It proposes a novel two-threshold strategy that balances change detection and reward maximization, improving upon passive detection methods in non-stationary MDPs.

Findings

Outperforms state-of-the-art QCD methods in numerical tests

Significant reward loss occurs when ignoring detection-reward trade-off

Effective in both Bayesian and non-Bayesian change scenarios

Abstract

Optimal control in non-stationary Markov decision processes (MDP) is a challenging problem. The aim in such a control problem is to maximize the long-term discounted reward when the transition dynamics or the reward function can change over time. When a prior knowledge of change statistics is available, the standard Bayesian approach to this problem is to reformulate it as a partially observable MDP (POMDP) and solve it using approximate POMDP solvers, which are typically computationally demanding. In this paper, the problem is analyzed through the viewpoint of quickest change detection (QCD), a set of tools for detecting a change in the distribution of a sequence of random variables. Current methods applying QCD to such problems only passively detect changes by following prescribed policies, without optimizing the choice of actions for long term performance. We demonstrate that ignoring the reward-detection trade-off can cause a significant loss in long term rewards, and propose a two threshold switching strategy to solve the issue. A non-Bayesian problem formulation is also proposed for scenarios where a Bayesian formulation cannot be defined. The performance of the proposed two threshold strategy is examined through numerical analysis on a non-stationary MDP task, and the strategy outperforms the state-of-the-art QCD methods in both Bayesian and non-Bayesian settings.