Leveraging Predictions in Smoothed Online Convex Optimization via Gradient-based Algorithms

Understand

We consider online convex optimization with time-varying stage costs and additional switching costs.

• Since the switching costs introduce coupling across all stages, multi-step-ahead (long-term) predictions are incorporated to improve the online performance.
• However, longer-term predictions tend to suffer from lower quality.
• Thus, a critical question is: how to reduce the impact of long-term prediction errors on the online performance? To address this question, we introduce a gradient-based online algorithm, Receding Horizon Inexact Gradient (RHIG), and analyze its performance by dynamic regrets in terms of the temporal variation of the environment and the prediction errors.