The cooperative bandit problem is a multi-agent decision problem involving a group of agents that interact simultaneously with a multi-armed bandit, while communicating over a network with delays. The central idea in this problem is to design algorithms that can efficiently leverage communication to obtain improvements over acting in isolation. In this paper, we investigate the stochastic bandit problem under two settings - (a) when the agents wish to make their communication private with respect to the action sequence, and (b) when the agents can be byzantine, i.e., they provide (stochastically) incorrect information. For both these problem settings, we provide upper-confidence bound algorithms that obtain optimal regret while being (a) differentially-private and (b) tolerant to byzantine agents. Our decentralized algorithms require no information about the network of connectivity between agents, making them scalable to large dynamic systems. We test our algorithms on a competitive benchmark of random graphs and demonstrate their superior performance with respect to existing robust algorithms. We hope that our work serves as an important step towards creating distributed decision-making systems that maintain privacy.
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