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.

我们研究了一种具有多步非线性切换成本和反馈延迟的挑战性平滑在线凸优化（SOCO）形式，提出了一种新颖的机器学习（ML）增强的在线算法，名为 Robustness-Constrained Learning（RCL），它通过受限投影将不受信任的 ML 预测与可信的专家在线算法结合起来，以增强 ML 预测的鲁棒性。具体而言，我们证明了 RCL 能够对于任何给定的专家保证（1+λ）竞争力，其中 λ>0，同时以鲁棒性感知的方式明确地训练 ML 模型以提高平均性能。重要的是，RCL 是第一个在多步切换成本和反馈延迟情况下具有可证明的鲁棒性保证的 ML 增强算法。我们以电动交通的电池管理为案例研究，展示了 RCL 在鲁棒性和平均性能方面的改进。