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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 evenmore »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.« less

In addition to ocean acidification, a significant recent warming trend in Chinese coastal waters has received much attention. However, studies of the combined effects of warming and acidification on natural coastal phytoplankton assemblages here are scarce. We conducted a continuous incubation experiment with a natural spring phytoplankton assemblage collected from the Bohai Sea near Tianjin. Experimental treatments used a full factorial combination of temperature (7 and 11°C) and pCO 2 (400 and 800 ppm) treatments. Results suggest that changes in pCO 2 and temperature had both individual and interactive effects on phytoplankton species composition and elemental stoichiometry. Warming mainly favored the accumulation of picoplankton and dinoflagellate biomass. Increased pCO 2 significantly increased particulate organic carbon to particulate organic phosphorus (C:P) and particulate organic carbon to biogenic silica (C:BSi) ratios, and decreased total diatom abundance; in the meanwhile, higher pCO 2 significantly increased the ratio of centric to pennate diatom abundance. Warming and increased pCO 2 both greatly decreased the proportion of diatoms to dinoflagellates. The highest chlorophyll a biomass was observed in the high pCO 2 , high temperature phytoplankton assemblage, which also had the slowest sinking rate of all treatments. Overall, there were significant interactive effects of increased pCOmore »2 and warming on dinoflagellate abundance, pennate diatom abundance, diatom vs. dinoflagellates ratio and the centric vs. pennate ratio. These findings suggest that future ocean acidification and warming trends may individually and cumulatively affect coastal biogeochemistry and carbon fluxes through shifts in phytoplankton species composition and sinking rates.« less