[2604.04101] Restless Bandits with Individual Penalty Constraints: A New Near-Optimal Index Policy and How to Learn It

Computer Science > Machine Learning arXiv:2604.04101 (cs) [Submitted on 5 Apr 2026] Title:Restless Bandits with Individual Penalty Constraints: A New Near-Optimal Index Policy and How to Learn It Authors:Nida Zamir, I-Hong Hou View a PDF of the paper titled Restless Bandits with Individual Penalty Constraints: A New Near-Optimal Index Policy and How to Learn It, by Nida Zamir and I-Hong Hou View PDF HTML (experimental) 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 introdu...