2025/05/30 by Ofir Schlisselberg, Schlisselberg, Ofir, Tal Lancewicki +5
Computer Science · Decision Sciences · Engineering · #Advanced Bandit Algorithms Research #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Machine Learning (cs.LG) #Smart Grid Energy Management
paper · pdf · doi:10.48550/arxiv.2505.24193
openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the multi-armed bandit problem with adversarially chosen delays in the Best-of-Both-Worlds (BoBW) framework, which aims to achieve near-optimal performance in both stochastic and adversarial environments. While prior work has made progress toward this goal, existing algorithms suffer from significant gaps to the known lower bounds, especially in the stochastic settings. Our main contribution is a new algorithm that, up to logarithmic factors, matches the known lower bounds in each setting individually. In the adversarial case, our algorithm achieves regret of \widetildeO(√(KT) + √(D)), which is optimal up to logarithmic terms, where T is the number of rounds, K is the number of arms, and D is the cumulative delay. In the stochastic case, we provide a regret bound which scale as ∑i:Δi>0(log T/Δi) + (1)/(K)∑ Δi σmax, where Δi is the sub-optimality gap of arm i and σmax is the maximum number of missing observations. To the best of our knowledge, this is the first BoBW algorithm to simultaneously match the lower bounds in both stochastic and adversarial regimes in delayed environment. Moreover, even beyond the BoBW setting, our stochastic regret bound is the first to match the known lower bound under adversarial delays, improving the second term over the best known result by a factor of K.