Online Optimization with Predictions and Switching Costs: Fast Algorithms and Fundamental Limits

This paper studies an online optimization problem with switching costs and a finite prediction window. We propose a computationally efficient algorithm, Receding Horizon Gradient Descent (RHGD), which only requires a finite number of gradient evaluations at each time. We show that both the dynamic regret and the competitive ratio of the algorithm decay exponentially fast with the length of the prediction window. Moreover, we provide a fundamental lower bound on dynamic regret for general online algorithms with a finite prediction window. The lower bound matches the dynamic regret of our RHGD, meaning that the performance can not improve significantly even with more computation. Lastly, we present simulation results to test our algorithm numerically.