Stochastic models for online optimization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916591602499584 |
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| author | Casti, Umberto Zampieri, Sandro |
| author_facet | Casti, Umberto Zampieri, Sandro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic models for online optimization Casti, Umberto Zampieri, Sandro Optimization and Control Systems and Control 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. |
| title | Stochastic models for online optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2411.19056 |