Stochastic Gradient Descent with Strategic Querying

TL;DR

This paper explores how strategic querying of gradients can improve stochastic gradient methods, introducing practical algorithms that outperform standard SGD in transient states and reduce variance under certain conditions.

Contribution

It proposes the SGQ algorithm for practical strategic gradient querying, improving transient performance over SGD and demonstrating benefits under the Polyak-Lojasiewicz condition.

Findings

SGQ outperforms SGD in transient-state performance.

OGQ improves steady-state variance under EI heterogeneity.

Numerical experiments validate theoretical advantages.

Abstract

This paper considers a finite-sum optimization problem under first-order queries and investigates the benefits of strategic querying on stochastic gradient-based methods compared to uniform querying strategy. We first introduce Oracle Gradient Querying (OGQ), an idealized algorithm that selects one user's gradient yielding the largest possible expected improvement (EI) at each step. However, OGQ assumes oracle access to the gradients of all users to make such a selection, which is impractical in real-world scenarios. To address this limitation, we propose Strategic Gradient Querying (SGQ), a practical algorithm that has better transient-state performance than SGD while making only one query per iteration. For smooth objective functions satisfying the Polyak-Lojasiewicz condition, we show that under the assumption of EI heterogeneity, OGQ enhances transient-state performance and reduces steady-state variance, while SGQ improves transient-state performance over SGD. Our numerical experiments validate our theoretical findings.