Combinatorial Bandits under Strategic Manipulations.

We study the problem of combinatorial multi-armed bandits (CMAB) under strategic manipulations of rewards, where each arm can modify the emitted reward signals for its own interest. Our setting elaborates a more realistic model of adaptive arms that imposes relaxed assumptions compared to adversarial corruptions and adversarial attacks. Algorithms designed under strategic arms gain robustness in real applications while avoiding being overcautious and hampering the performance. We bridge the gap between strategic manipulations and adversarial attacks by investigating the optimal colluding strategy among arms under the MAB problem. We then propose a strategic variant of the combinatorial UCB algorithm, which has a regret of at most $O(m\log T + m B_{max})$ under strategic manipulations, where $T$ is the time horizon, $m$ is the number of arms, and $B_{max}$ is the maximum budget. We further provide lower bounds on the strategic budgets for attackers to incur certain regret of the bandit algorithm. Extensive experiments corroborate our theoretical findings on robustness and regret bounds, in a variety of regimes of manipulation budgets.