Adversarial Semi-Bandits with Moving Arms

This paper studies a novel multi-agent combinatorial bandit problem called moving semi-bandits involving$K$agents and$N$arms, extending the problem of semi-bandits with adversar-ial rewards and stochastic arm availabilities (sleeping semi-bandits). The arms move across agents, making each arm available to at most one agent at a time, and the set of available arms for each agent changes over time. In each round, each agent plays up to$m$arms from their own available arm set simultaneously and observes the random loss for each played arm (i.e., semi-bandit feedback). The loss of each arm has no stochastic assumptions, and different agents may generate different random losses for each arm. The primary goal is to minimize the cumulative loss for all agents through collaboration. This bandit problem is motivated by real-world applications, such as traffic scheduling in wireless networks with multiple access points and task assignment for multiple crowdsourcing platforms. To address this challenge, we propose an efficient framework called Moving-FTPL, which guarantees a regret bound of$O(N\sqrt{NTK\mathrm{I}\mathrm{n}T})$over$T$rounds. Moving-Ftplcan reduce the total regret of all K agents by a factor of$\sqrt{K}$compared to scenarios where agents do not collaborate. Additionally, Moving-FTPL takes a step forward for the long-standing problems of a tighter regret bound for sleeping semi-bandits by significantly improving the state-of-the-art regret bound by a factor of$m\sqrt{N}$and imnroving the bound for sleeping adversarial bandits by a factor of$\sqrt{N}$. Furth ermore, we showcase a crowdsourcing application to demonstrate the effectiveness of our proposed algorithm when compared with others.