Robust Learning for Smoothed Online Convex Optimization with Feedback Delay

Abstract

We study a challenging form of Smoothed Online Convex Optimization, a.k.a. SOCO, including multi-step nonlinear switching costs and feedback delay. We propose a novel machine learning (ML) augmented online algorithm, Robustness-Constrained Learning (RCL), which combines untrusted ML predictions with a trusted expert online algorithm via constrained projection to robustify the ML prediction. Specifically,we prove that RCL is able to guarantee$(1+\lambda)$-competitiveness against any given expert for any$\lambda>0$, while also explicitly training the ML model in a robustification-aware manner to improve the average-case performance. Importantly,RCL is the first ML-augmented algorithm with a provable robustness guarantee in the case of multi-step switching cost and feedback delay.We demonstrate the improvement of RCL in both robustness and average performance using battery management for electrifying transportationas a case study.