Decision-Focused Learning for Complex System Identification: HVAC Management System Application

TL;DR

This work tackles day-ahead HVAC scheduling by learning the parameters of a grey-box RC building model through Decision-Focused Learning (DFL) that integrates a convex optimization policy. It introduces a non-differentiable-friendly loss L_DFL based on system response and a hierarchical loss to reflect building, floor, and zone contributions, enabling backpropagation through the optimization with conic-program differentiation via Cvxpylayers. The key contributions are: end-to-end simultaneous system identification and control, a robust loss formulation with constraint relaxation and pre-training, and a demonstration on a 15-zone Denver building showing substantial reductions in ex-post cost and improved bill forecasting compared with a traditional Identify-Then-Optimize approach. The approach offers practical impact for real-world building management by aligning parameter learning with control performance, and shows robustness to ambient-temperature distribution shifts, albeit with increased computational demands that motivate future software and surrogate-model refinements.

Abstract

As opposed to conventional training methods tailored to minimize a given statistical metric or task-agnostic loss (e.g., mean squared error), Decision-Focused Learning (DFL) trains machine learning models for optimal performance in downstream decision-making tools. We argue that DFL can be leveraged to learn the parameters of system dynamics, expressed as constraint of the convex optimization control policy, while the system control signal is being optimized, thus creating an end-to-end learning framework. This is particularly relevant for systems in which behavior changes once the control policy is applied, hence rendering historical data less applicable. The proposed approach can perform system identification - i.e., determine appropriate parameters for the system analytical model - and control simultaneously to ensure that the model's accuracy is focused on areas most relevant to control. Furthermore, because black-box systems are non-differentiable, we design a loss function that requires solely to measure the system response. We propose pre-training on historical data and constraint relaxation to stabilize the DFL and deal with potential infeasibilities in learning. We demonstrate the usefulness of the method on a building Heating, Ventilation, and Air Conditioning day-ahead management system for a realistic 15-zone building located in Denver, US. The results show that the conventional RC building model, with the parameters obtained from historical data using supervised learning, underestimates HVAC electrical power consumption. For our case study, the ex-post cost is on average six times higher than the expected one. Meanwhile, the same RC model with parameters obtained via DFL underestimates the ex-post cost only by 3%.

Figures (9)

• Figure 1: The proposed framework starts by pre-training the system dynamics model on historical data. Then, the pre-trained model parameters are fed into the convex optimization control policy where they keep being updated on representative scenarios to minimize the loss metric evaluating the mismatch between the expected and observed system states.
• Figure 2: The building is made of three similar floors. Each floor is equipped with its own variable air volume air handling unit responsible for the thermal comfort of the five zones.
• Figure 3: Ambient temperature profiles of the ten medoids. The three first labels are extreme scenarios.
• Figure 4: Mean and standard deviation of the medoids. They are ordered to form a smooth cycle.
• Figure 5: The building rc model is pre-trained on one year of historical data before a small noise is applied on the parameters. They are then updated to perform the best day-ahead hvac scheduling over 10 representative days with respect to the task-aware MAE loss.