Federated Bandit: A Gossiping Approach
This addresses privacy-preserving decentralized decision-making for agents in networked systems, with incremental improvements in federated learning and bandit algorithms.
The paper tackles the Federated Bandit problem, where decentralized agents with local, biased feedback must select optimal arms while only sharing information with neighbors, proposing Gossip_UCB and Fed_UCB algorithms that achieve regret bounds of O(max{poly(N,M) log T, poly(N,M) log_{λ_2^{-1}} N}) and O(max{poly(N,M)/ε log^{2.5} T, poly(N,M) (log_{λ_2^{-1}} N + log T)}) respectively.
In this paper, we study \emph{Federated Bandit}, a decentralized Multi-Armed Bandit problem with a set of $N$ agents, who can only communicate their local data with neighbors described by a connected graph $G$. Each agent makes a sequence of decisions on selecting an arm from $M$ candidates, yet they only have access to local and potentially biased feedback/evaluation of the true reward for each action taken. Learning only locally will lead agents to sub-optimal actions while converging to a no-regret strategy requires a collection of distributed data. Motivated by the proposal of federated learning, we aim for a solution with which agents will never share their local observations with a central entity, and will be allowed to only share a private copy of his/her own information with their neighbors. We first propose a decentralized bandit algorithm Gossip_UCB, which is a coupling of variants of both the classical gossiping algorithm and the celebrated Upper Confidence Bound (UCB) bandit algorithm. We show that Gossip_UCB successfully adapts local bandit learning into a global gossiping process for sharing information among connected agents, and achieves guaranteed regret at the order of $O(\max\{ \texttt{poly}(N,M) \log T, \texttt{poly}(N,M)\log_{λ_2^{-1}} N\})$ for all $N$ agents, where $λ_2\in(0,1)$ is the second largest eigenvalue of the expected gossip matrix, which is a function of $G$. We then propose Fed_UCB, a differentially private version of Gossip_UCB, in which the agents preserve $ε$-differential privacy of their local data while achieving $O(\max \{\frac{\texttt{poly}(N,M)}ε\log^{2.5} T, \texttt{poly}(N,M) (\log_{λ_2^{-1}} N + \log T) \})$ regret.