Decision-Focused Learning for Neural Network-Constrained Optimization: Application to HVAC Management System

Abstract: Heating, Ventilation, and Air Conditioning (HVAC) is a major electricity end-use with a substantial potential for grid services such as demand response. Harnessing this flexibility requires accurate modeling of the thermal dynamics of buildings, which is challenging due to their nonlinear and repetitive behavior (e.g., daily pattern), which reduce the value of historical data. To address this issue, this paper presents an HVAC management system formulated as a Mixed Integer Quadratic Program (MIQP), where Neural Network (NN) models of thermal dynamics are embedded as exact mixed-integer linear constraints. We employ Decision-Focused Learning (DFL) which tunes the NN parameters to improve the HVAC performance rather than prediction metrics. However, the discrete nature of the MIQP poses challenges for this approach, as it leads to gradients that are undefined or discontinuous, thus impeding standard gradient-based training. Here, we employ Stochastic Smoothing (SS), which enables efficient gradient computation without the need to differentiate through the MIQP. Experiments on a realistic five-zone building using a high-fidelity building simulator demonstrate that the proposed SS-DFL approach outperforms conventional two-stage and relaxed DFL methods in both cost savings and grid service performance, highlighting its potential for scalable, grid-interactive building control.