2024/05/28 by Yige Hong, Hong, Yige, Qiaomin Xie +5 · 1 citation
Decision Sciences · Neuroscience · #90C40 #Advanced Bandit Algorithms Research #Decision-Making and Behavioral Economics #FOS: Computer and information sciences #FOS: Mathematics #G.3 #I.6 #Machine Learning (cs.LG) #Mind wandering and attention #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2405.17882
openalex publication_date 2024/05/28 · openalex created_date 2024/05/30 · openalex updated_date 2026/07/28
We consider the infinite-horizon average-reward restless bandit problem. We propose a novel two-set policy that maintains two dynamic subsets of arms: one subset of arms has a nearly optimal state distribution and takes actions according to an Optimal Local Control routine; the other subset of arms is driven towards the optimal state distribution and gradually merged into the first subset. We show that our two-set policy is asymptotically optimal with an O(exp(-C N)) optimality gap for an N-armed problem, under the mild assumptions of aperiodic-unichain, non-degeneracy, and local stability. Our policy is the first to achieve exponential asymptotic optimality under the above set of easy-to-verify assumptions, whereas prior work either requires a strong global attractor assumption or only achieves an O(1/√(N)) optimality gap. We further discuss obstacles in weakening the assumptions by demonstrating examples where exponential asymptotic optimality is not achievable when any of the three assumptions is violated. Notably, we prove a lower bound for a large class of locally unstable restless bandits, showing that local stability is particularly fundamental for exponential asymptotic optimality. Finally, we use simulations to demonstrate that the two-set policy outperforms previous policies on certain RB problems and performs competitively overall.