  We study online convex optimization with switching costs, a practically
important but also extremely challenging problem due to the lack of complete
offline information. By tapping into the power of machine learning (ML) based
optimizers, ML-augmented online algorithms (also referred to as expert
calibration in this paper) have been emerging as state of the art, with
provable worst-case performance guarantees. Nonetheless, by using the standard
practice of training an ML model as a standalone optimizer and plugging it into
an ML-augmented algorithm, the average cost performance can be highly
unsatisfactory. In order to address the "how to learn" challenge, we propose
EC-L2O (expert-calibrated learning to optimize), which trains an ML-based
optimizer by explicitly taking into account the downstream expert calibrator.
To accomplish this, we propose a new differentiable expert calibrator that
generalizes regularized online balanced descent and offers a provably better
competitive ratio than pure ML predictions when the prediction error is large.
For training, our loss function is a weighted sum of two different losses --
one minimizing the average ML prediction error for better robustness, and the
other one minimizing the post-calibration average cost. We also provide
theoretical analysis for EC-L2O, highlighting that expert calibration can be
even beneficial for the average cost performance and that the high-percentile
tail ratio of the cost achieved by EC-L2O to that of the offline optimal oracle
(i.e., tail cost ratio) can be bounded. Finally, we test EC-L2O by running
simulations for sustainable datacenter demand response. Our results demonstrate
that EC-L2O can empirically achieve a lower average cost as well as a lower
competitive ratio than the existing baseline algorithms.

Machine Learning;Optimization and Control