A Simple and Provably Efficient Algorithm for Asynchronous Federated Contextual Linear Bandits
This addresses the challenge of efficient decentralized learning for multiple agents in bandit problems, with incremental improvements in handling asynchronicity.
The paper tackles the problem of federated contextual linear bandits with asynchronous communication, proposing the FedLinUCB algorithm, which achieves a regret bound of \tilde{O}(d√(∑_m T_m)) and communication complexity of \tilde{O}(dM^2).
We study federated contextual linear bandits, where $M$ agents cooperate with each other to solve a global contextual linear bandit problem with the help of a central server. We consider the asynchronous setting, where all agents work independently and the communication between one agent and the server will not trigger other agents' communication. We propose a simple algorithm named \texttt{FedLinUCB} based on the principle of optimism. We prove that the regret of \texttt{FedLinUCB} is bounded by $\tilde{O}(d\sqrt{\sum_{m=1}^M T_m})$ and the communication complexity is $\tilde{O}(dM^2)$, where $d$ is the dimension of the contextual vector and $T_m$ is the total number of interactions with the environment by $m$-th agent. To the best of our knowledge, this is the first provably efficient algorithm that allows fully asynchronous communication for federated contextual linear bandits, while achieving the same regret guarantee as in the single-agent setting.