Individual Regret in Cooperative Nonstochastic Multi-Armed Bandits

We study a network of agents communicating with each other and optimizing their performance in a common nonstochastic multi-armed bandit problem. We derive regret minimization algorithms that guarantee for each agent $v$ an individual expected regret of \[ \widetilde{O}\left(\sqrt{\left(1+\frac{K}{\left|\mathcal{N}\left(v\right)\right|}\right)T}\right), \] where $T$ is the number of time steps, $K$ is the number of actions and $\mathcal{N}\left(v\right)$ is the set of neighbors of agent $v$ in the communication graph. We present algorithms both for the case that the communication graph is known to all the agents, and for the case that the graph is unknown. When the communication graph is unknown, each agent knows only the set of its neighbors and a bound on the total number of agents. The individual regret between the models differ only by a logarithmic factor. Our work resolves an open problem from (\citet{cesa2019delay}).

• Machine Intelligence