Restless Bandits with Individual Penalty Constraints: Near-Optimal Indices and Deep Reinforcement Learning

TL;DR

This paper introduces a novel index policy for restless bandits with individual constraints, combining theoretical optimality and deep learning for practical resource management in wireless networks.

Contribution

It proposes the Penalty-Optimal Whittle index policy that is computationally efficient, asymptotically optimal, and adaptable via deep reinforcement learning.

Findings

POW index policy is near-optimal in simulations.

The policy satisfies all individual penalty constraints.

Deep RL effectively learns the POW index online.

Abstract

This paper investigates the Restless Multi-Armed Bandit (RMAB) framework under individual penalty constraints to address resource allocation challenges in dynamic wireless networked environments. Unlike conventional RMAB models, our model allows each user (arm) to have distinct and stringent performance constraints, such as energy limits, activation limits, or age of information minimums, enabling the capture of diverse objectives including fairness and efficiency. To find the optimal resource allocation policy, we propose a new Penalty-Optimal Whittle (POW) index policy. The POW index of an user only depends on the user's transition kernel and penalty constraints, and remains invariable to system-wide features such as the number of users present and the amount of resource available. This makes it computationally tractable to calculate the POW indices offline without any need for online adaptation. Moreover, we theoretically prove that the POW index policy is asymptotically optimal while satisfying all individual penalty constraints. We also introduce a deep reinforcement learning algorithm to efficiently learn the POW index on the fly. Simulation results across various applications and system configurations further demonstrate that the POW index policy not only has near-optimal performance but also significantly outperforms other existing policies.