Convergence rates for distributed stochastic optimization over random networks
- 1. University of Novi Sad Faculty of Sciences
- 2. Carnegie Mellon University
Description
We establish the O(1/k) convergence rate for distributed stochastic gradient methods that operate over strongly convex costs and random networks. The considered class of methods is standard - each node performs a weighted average of its own and its neighbors’ solution estimates (consensus), and takes a negative step with respect to a noisy version of its local function’s gradient (innovation). The underlying communication network is modeled through a sequence of temporally independent identically distributed (i.i.d.) Laplacian matrices such that the underlying graphs are connected on average; the local gradient noises are also i.i.d. in time, have finite second moment, and possibly unbounded support. We show that, after a careful setting of the consensus and innovations potentials (weights), the distributed stochastic gradient method achieves a (order-optimal) O(1/k) convergence rate in the mean square distance from the solution. To the best of our knowledge, this is the first order-optimal convergence rate result on distributed strongly convex stochastic optimization when the network is random and the gradient noises have unbounded support. Simulation examples confirm the theoretical findings.
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Related works
- Is supplemented by
- 10.5281/zenodo.3333685 (DOI)