Impact of quantized inter-agent communications on game-theoretic and distributed optimization algorithms

Abstract

Quantized inter-agent communications in game-theoretic and distributed optimization algorithms generate uncertainty that affects the asymptotic and transient behavior of such algorithms. This chapter uses the information-theoretic notion of differential entropy power to establish universal bounds on the maximum exponential convergence rates of primal-dual and gradient-based Nash seeking algorithms under quantized communications. These bounds depend on the inter-agent data rate and the local behavior of the agents’ objective functions, and are independent of the quantizer structure. The presented results provide trade-offs between the speed of exponential convergence, the agents’ objective fu..