Convex Synthesis of First-Order Methods for Time-Varying Smooth Strongly Convex Optimization

TL;DR

This paper introduces a control synthesis framework for designing first-order optimization algorithms that adapt to time-varying smooth strongly convex problems, improving decision-making in dynamic environments.

Contribution

It combines convex robust control synthesis and the internal model principle to systematically create algorithms that handle evolving objectives.

Findings

Developed a systematic design method for time-varying optimization algorithms.

Embedded models of problem variability directly into the algorithm design.

Enhanced decision-making accuracy in dynamic environments.

Abstract

Time-varying optimization is fundamental to decision-making in dynamic environments, where objectives evolve over time due to exogenous signals or data streams. However, algorithms designed for static problems yield suboptimal decisions in dynamic scenarios, even asymptotically. In this paper, we develop a robust control synthesis framework to systematically design first-order methods for smooth strongly convex problems that vary in time. Our approach leverages both convex robust control synthesis in the static setting and the internal model principle by directly embedding a model of the underlying variability into the designed algorithm.