Distributed Projection Sub-gradient Algorithm over General Directed Graphs with Compressed Communication

We consider a distributed convex optimization with the global objective function being distributed over a multi-agent network that can only communicate to their neighbors on a fixed communication digraph with row stochastic weight matrix. As the dimension of local parameter increases, distributed optimization faces a major bottleneck that is the heavy communication load due to each agent transmitting large messages to its neighbors. To tackle this issue, we propose a quantized distributed projection sub-gradient algorithm (Q-DPSG) over general directed graphs. Furthermore, we prove that our algorithm allows us to match the convergence rates of the distributed optimization with perfect-communication for convex objective functions. We also provide numerical simulations that corroborate our main theoretical results and compare the convergence properties of the distributed projection sub-gradient (DPSG) methods with and without quantization.