Stochastic Decision-Focused Learning for Thermal Energy Scheduling in Multi-Zone Buildings

This paper aims to optimize the day-ahead energy scheduling within a multi-zone building, wherein the internal thermal dynamics are unknown. These dynamics are learned end-to-end using decision-focused learning where the building model is parameterized based on the ex-post quality of the decision of the optimization model. Yet, in practice, the building's simulator is non-differentiable (e.g., such as a true building) and the optimization is non-convex (e.g., due to mixed-integer decisions from reversible heat pump), which makes conventional gradient-based learning impractical.We address these challenges through a stochastic, context-aware modeling framework where thermal dynamics follow a probabilistic, grey-box resistance-capacitance (RC) structure with parameters conditioned on exogenous context (weather, calendar data, thermal history). These context-dependent parameter distributions serve dual purposes: they enable score-function (REINFORCE-type) gradient estimation through the non-differentiable pipeline, and generate scenarios for a mixed-integer, scenario-based HVAC optimization enforcing comfort and equipment constraints under uncertainty. Preliminary results on a realistic multi-zone office building demonstrate that the proposed stochastic decision-focused learning does work.