Distributed Optimization over General Directed Networks with Random Sleep Scheme

Distributed optimization aims at optimizing a global objective function which is described by a sum of local objective functions through local information processing and sharing. This paper studies the problem of distributed optimization over a network in which underlying graph is generally directed strongly connected. Most existing distributed algorithms require each agent to observe the gradient of the local objective function per iteration, which leads to heavy computational cost. A computation-efficient distributed optimization algorithm incorporating random sleep scheme is proposed by incorporating rescaling gradient technique to address the unbalancedness of the directed graph. The implementation of the proposed algorithm allows agents not only locally allocates the weights on the received information, but also independently decides whether to execute gradient observation at each iteration. Theoretical analysis verifies that the proposed algorithm is able to seek the optimal solution with probability one. Simulations are shown to demonstrate effectiveness of the proposed algorithm, show correctness of the theoretical analysis, and investigate the tradeoffs between convergence performance and computation cost.