Distributed stochastic optimization with large delays

TL;DR

This paper analyzes the convergence of distributed asynchronous stochastic gradient descent (DASGD) in large delay scenarios, providing theoretical guarantees for convergence under certain conditions and insights for algorithm design.

Contribution

It demonstrates that DASGD can still converge with unbounded polynomial delays by tuning step-size and establishes global convergence in structured problems.

Findings

Convergence to the critical set in mean square with large delays.

Global convergence in variationally coherent problems.

Step-size tuning is crucial for handling delays.

Abstract

One of the most widely used methods for solving large-scale stochastic optimization problems is distributed asynchronous stochastic gradient descent (DASGD), a family of algorithms that result from parallelizing stochastic gradient descent on distributed computing architectures (possibly) asychronously. However, a key obstacle in the efficient implementation of DASGD is the issue of delays: when a computing node contributes a gradient update, the global model parameter may have already been updated by other nodes several times over, thereby rendering this gradient information stale. These delays can quickly add up if the computational throughput of a node is saturated, so the convergence of DASGD may be compromised in the presence of large delays. Our first contribution is that, by carefully tuning the algorithm's step-size, convergence to the critical set is still achieved in mean square, even if the delays grow unbounded at a polynomial rate. We also establish finer results in a broad class of structured optimization problems (called variationally coherent), where we show that DASGD converges to a global optimum with probability $1$ under the same delay assumptions. Together, these results contribute to the broad landscape of large-scale non-convex stochastic optimization by offering state-of-the-art theoretical guarantees and providing insights for algorithm design.