Modern HVAC control requires repeatedly solving optimization problems to determine heating and cooling actions under changing weather and building conditions. These problems are dynamic, multi-step, and computationally expensive, making real-time optimization difficult. Amortized optimization offers an alternative: instead of solving a new optimization problem at every time step, a neural network is trained to directly predict near optimal control actions from the current building state and environmental conditions. Training such networks is challenging. Regression-based approaches that learn from optimal solutions are stable but ignore how sensitive the objective function is to control errors. Objective-based approaches directly minimize control cost through rollout simulations, but often suffer from instability and high computational burden, especially for long horizons and nonlinear dynamics. We propose Geometry-Weighted Regression (GWR), a hybrid training method that preserves the stability of regression while incorporating local geometric information from the control objective. The key idea is to weight prediction errors using a context-dependent positive semidefinite matrix that captures the curvature of the HVAC cost function around the optimal solution. To evaluate the method in a realistic setting, we develop a data-driven thermal dynamics model for HVAC control. A finite-horizon, multi-objective cost balancing thermal comfort and grid electricity use is then defined. We compare standard regression, objective-based training, and GWR. GWR improves training stability, mitigates early performance degradation seen in standard regression, and avoids the instability common in objective-based training. These results demonstrate the value of incorporating objective geometry into regression-based learning for stable and efficient amortized HVAC control.

Keywords

Amortized Optimization, Geometry-Weighted Regression, HVAC Control, Building Energy Management