An Adaptive Convex Combination between Prediction and Correction in Online Quadratic optimization

Abstract

We study a particular class of online quadratic optimization problems, where the objective function linearly depends on some time-varying parameters. In the context of prediction-correction algorithms, that is, algorithms that combine a prediction of the future cost function and a correction on the observation of the past one, we explore the effect of a stochastic disturbance in the prediction. We then propose an algorithm that leverages the information on the prediction uncertainty and on the problem structure to approximate the optimal combination between prediction and correction.