Distributed saddle-point optimization over time-varying networks with probabilistically quantized information

We consider the problem of optimizing a sum of local objective functions corresponding to multiple agents. We discuss a distributed model where the agents can only exchange quantization data over a time-varying network. For solving this problem, we propose a method that involves agents updating their states by weighted averaging and probabilistically quantized information. The method indicates how the agents converge to a consensus and finds the optimal solution at expected rate O(1/√T), T is the number of iteration. The relationship between the convergence rate and the quantized interval in terms of expectation was also presented.