# General Formulation and PCL-Analysis for Restless Bandits with Limited Observability

arXiv: https://arxiv.org/abs/2307.03034 · HTML: https://mlsanity.com/paper/2307.03034/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 6 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Dynamic priority allocation via restless bandit marginal productivity indices](https://mlsanity.com/paper/2304.06115/) (2023)
- [A verification theorem for threshold-indexability of real-state discounted restless bandits](https://mlsanity.com/paper/1902.09318/) (2019)
- [Dynamic allocation indices for restless projects and queueing admission control: a polyhedral approach](https://mlsanity.com/paper/2304.01946/) (2023)
- [Low-Complexity Algorithm for Restless Bandits with Imperfect Observations](https://mlsanity.com/paper/2108.03812/) (2021)
- [Relaxed Indexability and Index Policy for Partially Observable Restless Bandits](https://mlsanity.com/paper/2107.11939/) (2021)
- [A Restless Bandit Model for Dynamic Ride Matching with Reneging Travelers](https://mlsanity.com/paper/2111.12431/) (2021)

## Built on by (most cited first, 1 of 1)

- [From Relaxed Indexability to Exact Indexability: A t-Step Approach for Partially Observable Restless Bandits](https://mlsanity.com/paper/2608.24167/) (2026)

## Abstract (arXiv)

In this paper, we consider a general observation model for restless multi-armed bandit problems. The operation of the player is based on the past observation history that is limited (partial) and error-prone due to resource constraints or environmental or intrinsic noises. By establishing a general probabilistic model for dynamics of the observation process, we formulate the problem as a restless bandit with an infinite high-dimensional belief state space. 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 Ni~no-Mora (2001) for finite-state problems can be applied. Numerical experiments show that our algorithm has excellent performance.