A Robust Accelerated Optimization Algorithm for Strongly Convex Functions

TL;DR

This paper introduces a new accelerated optimization algorithm for strongly convex functions that balances robustness to gradient noise and convergence speed through a tunable parameter, inspired by control theory.

Contribution

It presents the Robust Momentum Method, a novel algorithm with a single parameter allowing a trade-off between robustness and convergence rate, with a simple analytical form.

Findings

Faster than Nesterov's method in noise-free settings

More robust to gradient noise than Nesterov's method

Validated through numerical simulations

Abstract

This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient noise versus worst-case convergence rate. At one extreme, the algorithm is faster than Nesterov's Fast Gradient Method by a constant factor but more fragile to noise. At the other extreme, the algorithm reduces to the Gradient Method and is very robust to noise. The algorithm design technique is inspired by methods from classical control theory and the resulting algorithm has a simple analytical form. Algorithm performance is verified on a series of numerical simulations in both noise-free and relative gradient noise cases.