Distributed Linear Bandits under Communication Constraints

We consider distributed linear bandits where $M$ agents learn collaboratively to minimize the overall cumulative regret incurred by all agents. Information exchange is facilitated by a central server, and both the uplink and downlink communications are carried over channels with fixed capacity, which limits the amount of information that can be transmitted in each use of the channels. We investigate the regret-communication trade-off by (i) establishing information-theoretic lower bounds on the required communications (in terms of bits) for achieving a sublinear regret order; (ii) developing an efficient algorithm that achieves the minimum sublinear regret order offered by centralized learning using the minimum order of communications dictated by the information-theoretic lower bounds. For sparse linear bandits, we show a variant of the proposed algorithm offers better regret-communication trade-off by leveraging the sparsity of the problem

Random Exploration in Bayesian Optimization: Order-Optimal Regret and Computational Efficiency

We consider Bayesian optimization using Gaussian Process models, also referred to as kernel-based bandit optimization. We study the methodology of exploring the domain using random samples drawn from a distribution. We show that this random exploration approach achieves the optimal error rates. Our analysis is based on novel concentration bounds in an infinite dimensional Hilbert space established in this work, which may be of independent interest. We further develop an algorithm based on random exploration with domain shrinking and establish its order-optimal regret guarantees under both noise-free and noisy settings. In the noise-free setting, our analysis closes the existing gap in regret performance and thereby resolves a COLT open problem. The proposed algorithm also enjoys a computational advantage over prevailing methods due to the random exploration that obviates the expensive optimization of a non-convex acquisition function for choosing the query points at each iteration

A Communication-Efficient Adaptive Algorithm for Federated Learning under Cumulative Regret

We consider the problem of online stochastic optimization in a distributed setting with $M$ clients connected through a central server. We develop a distributed online learning algorithm that achieves order-optimal cumulative regret with low communication cost measured in the total number of bits transmitted over the entire learning horizon. This is in contrast to existing studies which focus on the offline measure of simple regret for learning efficiency. The holistic measure for communication cost also departs from the prevailing approach that \emph{separately} tackles the communication frequency and the number of bits in each communication round