On the Necessity of Collaboration in Online Model Selection with Decentralized Data

We consider online model selection with decentralized data over $M$ clients, and study the necessity of collaboration among clients. Previous work omitted the problem and proposed various federated algorithms, while we provide a comprehensive answer from the perspective of computational constraints. We propose a federated algorithm and analyze the upper and lower bounds on the regret that show (i) collaboration is unnecessary in the absence of additional constraints on the problem; (ii) collaboration is necessary if the computational cost on each client is limited to $o(K)$, where $K$ is the number of candidate hypothesis spaces. We clarify the unnecessary nature of collaboration in previous federated algorithms, and improve the regret bounds of algorithms for distributed online multi-kernel learning at a smaller computational and communication cost. Our algorithm relies on three new techniques including an improved Bernstein's inequality for martingale, a federated online mirror descent framework, and decoupling model selection and predictions, which might be of independent interest.