Risk-Sensitive Peak-Aware Energy Scheduling: Competitive and Learning-Augmented Algorithms

Risk is a critical consideration in many energy-related problems, where stakeholders are often sensitive to rare but costly events. However, traditional online algorithms typically optimize expected cost and can perform poorly in such risk-sensitive settings. Motivated by this challenge, we study the design of algorithms for peak-aware energy scheduling, where a microgrid operator must decide how much electricity to generate locally vs. purchase from the grid while facing both a spot price and peak charge for grid electricity. Modeling this as an instance of the online Bahncard problem, we obtain three new results: (1) a family of closed-form algorithms with a provable bound on the Conditional Value-at-Risk (CVaR)-competitive ratio, a recently proposed risk-sensitive performance metric for online algorithms; (2) an optimal online algorithm resulting from the solution to a certain delay differential equation, which can be approximated numerically on an instance-by-instance basis; and (3) a learning-augmented algorithm for this problem which, given a hyperparameter λ ∊ (0, 1], achieves 1 + Θ(λ)-consistency while maintaining a risk-sensitive CVaR-robustness of Θ(1/λ).