{"ID":2827928,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.15205","arxiv_id":"2512.15205","title":"A Regression-Based Prediction-Correction Method for Stochastic Time-Varying Optimization Problems","abstract":"In many real-world applications, optimization problems evolve continuously over time and are often subject to stochastic noise. We consider a stochastic time-varying optimization problem in which the objective function $f(x;t)$ changes continuously and only noisy gradient observations are available. In deterministic settings, the prediction-correction method that exploits the time derivative of the solution is effective for accurately tracking the solution trajectory. However, a straightforward extension to stochastic problems requires an estimate of $\\nabla_{xt} f(x;t)$ and the computation of a Hessian inverse at each step--requirements that are difficult or costly in practice. To address these issues, we propose a prediction-correction algorithm that uses a regression-based prediction step: the prediction is formed as a linear combination of recent iterates, which can be computed efficiently without estimating $\\nabla_{xt}f(x;t)$ or computing Hessian inversions. We prove a tracking-error bound for the proposed method under standard smoothness and stochastic assumptions. Numerical experiments show that the regression-based prediction improves tracking accuracy while reducing computational cost compared with existing methods.","short_abstract":"In many real-world applications, optimization problems evolve continuously over time and are often subject to stochastic noise. We consider a stochastic time-varying optimization problem in which the objective function $f(x;t)$ changes continuously and only noisy gradient observations are available. In deterministic se...","url_abs":"https://arxiv.org/abs/2512.15205","url_pdf":"https://arxiv.org/pdf/2512.15205v1","authors":"[\"Tomoya Kamijima\",\"Naoki Marumo\",\"Akiko Takeda\"]","published":"2025-12-17T08:55:16Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}