In this paper, we consider a general observation model for restless multi-armed bandit problems. The operation of the player needs to be based on certain feedback mechanism that is error-prone due to resource constraints or environmental or intrinsic noises. By establishing a general probabilistic model for dynamics of feedback/observation, we formulate the problem as a restless bandit with a countable belief state space starting from an arbitrary initial belief (a priori information). We apply the achievable region method with partial conservation law (PCL) to the infinite-state problem and analyze its indexability and priority index (Whittle index). Finally, we propose an approximation process to transform the problem into which the AG algorithm of Niño-Mora and Bertsimas for finite-state problems can be applied to. Numerical experiments show that our algorithm has an excellent performance.
View on arXiv@article{liu2025_2307.03034,
title={ PCL-Indexability and Whittle Index for Restless Bandits with General Observation Models },
author={ Keqin Liu and Qizhen Jia and Chengzhong Zhang },
journal={arXiv preprint arXiv:2307.03034},
year={ 2025 }
}