In Restless-UCB, we present a novel method to construct offline instances,whichonlyrequiresO(N)time-complexity(N isthenumberofarms) and is exponentially better than the complexity of existing learning policy.

In Restless-UCB, we present a novel method to construct offline instances,whichonlyrequiresO(N)time-complexity(N isthenumberofarms) and is exponentially better than the complexity of existing learning policy.

We study the online restless bandit problem, where the state of each arm evolves according to a Markov chain, and the reward of pulling an arm depends on both the pulled arm and the current state of the corresponding Markov chain. In this paper, we propose Restless-UCB, a learning policy that follows the explore-then-commit framework. In Restless-UCB, we present a novel method to construct offline instances, which only requires $O(N)$ time-complexity ($N$ is the number of arms) and is exponentially better than the complexity of existing learning policy. We also prove that Restless-UCB achieves a regret upper bound of $\tilde{O}((N+M^3)T^{2\over 3})$, where $M$ is the Markov chain state space size and $T$ is the time horizon. Compared to existing algorithms, our result eliminates the exponential factor (in $M,N$) in the regret upper bound, due to a novel exploitation of the sparsity in transitions in general restless bandit problems. As a result, our analysis technique can also be adopted to tighten the regret bounds of existing algorithms. Finally, we conduct experiments based on real-world dataset, to compare the Restless-UCB policy with state-of-the-art benchmarks. Our results show that Restless-UCB outperforms existing algorithms in regret, and significantly reduces the running time.

Many sequential decision problems can be modeled as multi-armed bandit problems.

As a result, our analysis technique can also be adopted to tighten the regret bounds of existing algorithms.

As a result, our analysis technique can also be adopted to tighten the regret bounds of existing algorithms.

Online restless bandits extend classic contextual bandits by incorporating state transitions and budget constraints, representing each agent as a Markov Decision Process (MDP). This framework is crucial for finite-horizon strategic resource allocation, optimizing limited costly interventions for long-term benefits. However, learning the underlying MDP for each agent poses a major challenge in finite-horizon settings. To facilitate learning, we reformulate the problem as a scalable budgeted thresholding contextual bandit problem, carefully integrating the state transitions into the reward design and focusing on identifying agents with action benefits exceeding a threshold. We establish the optimality of an oracle greedy solution in a simple two-state setting, and propose an algorithm that achieves minimax optimal constant regret in the online multi-state setting with heterogeneous agents and knowledge of outcomes under no intervention. We numerically show that our algorithm outperforms existing online restless bandit methods, offering significant improvements in finite-horizon performance.