DIMIX: Diminishing Mixing for Sloppy Agents
针对时变网络中智能体只能获取邻居粗略信息的问题，提出一种双时间尺度分布式算法，通过抑制不完美信息并操作局部梯度，实现非凸优化问题的收敛。
.We study nonconvex distributed optimization problems where a set of agents collaboratively solve a separable optimization problem that is distributed over a time-varying network. The existing methods to solve these problems rely on (at most) one-time-scale algorithms, where each agent performs a diminishing or constant step-size gradient descent at the average estimate of the agents in the network. However, if possible at all, exchanging exact information, which is required to evaluate these average estimates, potentially introduces a massive communication overhead. Therefore, a reasonable practical assumption to be made is that agents only receive a rough approximation of the neighboring agents' information. To address this, we introduce and study a two-time-scale decentralized algorithm with a broad class of lossy information sharing methods (which includes noisy, quantized, and/or compressed information sharing) over time-varying networks. In our method, one time-scale suppresses the (imperfect) incoming information from the neighboring agents, and one time-scale operates on local cost functions' gradients. We show that with a proper choices for the step-sizes' parameters, the algorithm achieves a convergence rate of \(\mathcal{O}(T^{-1/3 + \epsilon })\) for nonconvex distributed optimization problems over time-varying networks for any \(\epsilon \gt 0\).Keywordsnonconvex optimizationtime-varying graphsdistributed multiagent systemdistributed optimizationgradient descent algorithmsMSC codes90Cxx