Bringing Statistical Thinking in Distributed Optimization. Vignettes from statistical inference over Networks

There is growing interest in solving large-scale statistical machine learning problems over decentralized networks, where data are distributed across the nodes of the network and no centralized coordination is present (we termed these systems “mesh” networks). Modern massive datasets create a fundamental problem at the intersection of the computational and statistical sciences: how to provide guarantees on the quality of statistical inference given bounds on computational resources, such as time and communication efforts. While statistical-computation tradeoffs have been largely explored in the centralized setting, our understanding over mesh networks is limited: (i) distributed schemes, designed and performing well in the classical low-dimensional regime, can break down in the high-dimensional case; and (ii) existing convergence studies may fail to predict algorithmic behaviors; some are in fact confuted by experiments. This is mainly due to the fact that the majority of distributed algorithms have been designed and studied only from the optimization perspective, lacking the statistical dimension. This talk will discuss some vignettes from high-dimensional statistical inference suggesting new analyses aiming at bringing statistical thinking in distributed optimization.