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

Risk is a critical consideration in many energy-related problems, as stakeholders like energy resource operators and consumers are often sensitive to rare but costly events. However, traditional online algorithms typically optimize expected cost, and thus can perform poorly in such risk-sensitive settings. Motivated by this challenge, we study the design of risk-sensitive algorithms for the problem of 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 first propose a family of closed-form algorithms that obtain a provable bound on the Conditional Value-at-Risk (\(\operatorname{\mathrm{CVaR}}\))-competitive ratio, a recently proposed risk-sensitive performance metric for online algorithms. We then characterize an optimal online algorithm for this problem, which results from the solution to a certain delay differential equation which can be approximated numerically on an instance-by-instance basis. We then consider the design of learning-augmented algorithms in this risk-sensitive setting, where the decision-maker receives a potentially inaccurate prediction about the problem instance. We specifically propose an algorithm that, given a hyperparameter λ ∈ (0, 1], achieves 1 + Θ(λ)-consistency—thus ensuring good performance if the prediction is accurate—while maintaining a risk-sensitive robustness of Θ(1/λ), ensuring strong worst-case guarantees. We empirically evaluate our algorithms in a case study on peak-aware energy scheduling for a datacenter on a microgrid with varying renewable electricity generation. Our results highlight the advantages of risk-sensitive algorithm design in energy problems, where it can mitigate poor tail costs while maintaining strong average-case performance.