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arXiv · 2411.19056

Stochastic models for online optimization

Umberto Casti·Sandro Zampieri
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Abstract

In this paper, we propose control-theoretic methods as tools for the design of online optimization algorithms that are able to address dynamic, noisy, and partially uncertain time-varying quadratic objective functions. Our approach introduces two algorithms specifically tailored for scenarios where the cost function follows a stochastic linear model. The first algorithm is based on a Kalman filter-inspired approach, leveraging state estimation techniques to account for the presence of noise in the evolution of the objective function. The second algorithm applies $\mathcal{H}_\infty$-robust control strategies to enhance performance under uncertainty, particularly in cases in which model parameters are characterized by a high variability. Through numerical experiments, we demonstrate that our algorithms offer significant performance advantages over the traditional gradient-based method and also over the optimization strategy proposed in arXiv:2205.13932 based on deterministic models.

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Umberto Casti, Sandro Zampieri. 2024-11-28. Stochastic models for online optimization. https://arxiv.org/abs/2411.19056

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