Distributed online bandit optimization under random quantization

This paper considers the problem of solving distributed online optimization over a network that consists of multiple interacting nodes. Each node in the network is endowed with a sequence of loss functions, each of which is revealed to the node after a decision has been committed. The goal of the network is to minimize the cumulative loss functions of nodes in a distributed fashion, while subject to two types of information constraints, namely, message quantization and bandit feedback. To this end, a quantized distributed online bandit optimization algorithm is proposed by adopting random quantization operation and one-point gradient estimator. We show the convergence of the algorithm by establishing an O(dT^3/4) regret bound, where d is the dimension of states and T is the total number of rounds. Finally, an online distributed quadratic programming problem is investigated to validate the theoretical findings of the paper.