  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.
