"subagents," one for each subproblem, and then combine their solutions to establish

Restless bandit problems are instances of non-stationary multi-armed bandits.

We consider the online restless bandits with average-reward and multiple actions, where the state of each arm evolves according to a Markov decision process (MDP), and the reward of pulling an arm depends on both the current state of the corresponding MDP and the action taken. Since finding the optimal control is typically intractable for restless bandits, existing learning algorithms are often computationally expensive or with a regret bound that is exponential in the number of arms and states. In this paper, we advocate \textit{index-aware reinforcement learning} (RL) solutions to design RL algorithms operating on a much smaller dimensional subspace by exploiting the inherent structure in restless bandits. Specifically, we first propose novel index policies to address dimensionality concerns, which are provably optimal. We then leverage the indices to develop two low-complexity index-aware RL algorithms, namely, (i) GM-R2MAB, which has access to a generative model; and (ii) UC-R2MAB, which learns the model using an upper confidence style online exploitation method. We prove that both algorithms achieve a sub-linear regret that is only polynomial in the number of arms and states. A key differentiator between our algorithms and existing ones stems from the fact that our RL algorithms contain a novel exploitation that leverages our proposed provably optimal index policies for decision-makings.

Whittle index policy is a powerful tool to obtain asymptotically optimal solutions for the notoriously intractable problem of restless bandits. However, finding the Whittle indices remains a difficult problem for many practical restless bandits with convoluted transition kernels. This paper proposes NeurWIN, a neural Whittle index network that seeks to learn the Whittle indices for any restless bandits by leveraging mathematical properties of the Whittle indices. We show that a neural network that produces the Whittle index is also one that produces the optimal control for a set of Markov decision problems.

Neural Information Processing Systems http://nips.cc/

We study the restless bandit associated with an extremely simple scalar Kalman filter model in discrete time. Under certain assumptions, we prove that the problem is indexable in the sense that the Whittle index is a non-decreasing function of the relevant belief state. In spite of the long history of this problem, this appears to be the first such proof. We use results about Schur-convexity and mechanical words, which are particular binary strings intimately related to palindromes.

Online restless multi-armed bandits (RMABs) typically assume that each arm follows a stationary Markov Decision Process (MDP) with fixed state transitions and rewards. However, in real-world applications like healthcare and recommendation systems, these assumptions often break due to non-stationary dynamics, posing significant challenges for traditional RMAB algorithms. In this work, we specifically consider $N$-armd RMAB with non-stationary transition constrained by bounded variation budgets $B$. Our proposed \rmab\; algorithm integrates sliding window reinforcement learning (RL) with an upper confidence bound (UCB) mechanism to simultaneously learn transition dynamics and their variations. We further establish that \rmab\; achieves $\widetilde{\mathcal{O}}(N^2 B^{\frac{1}{4}} T^{\frac{3}{4}})$ regret bound by leveraging a relaxed definition of regret, providing a foundational theoretical framework for non-stationary RMAB problems for the first time.