Cost-Informed Learning for Aggregating Building HVAC Flexibility

This research develops a cost-informed learning framework to aggregate building HVAC flexibility by jointly learning surrogate parameters and an inner-approximation objective from downstream utilization costs, which addresses the limitation that existing methods fail to preserve flexibility most valuable for reducing dispatch costs.

Problem Formulation and Motivation

The core challenge addressed is that existing aggregation methods rely on volume-oriented objectives, which may fail to preserve the flexibility most valuable for reducing downstream dispatch costs because they treat flexibility aggregation and downstream utilization as separate stages. The paper motivates a cost-informed framework by noting that geometric size is not the final performance metric, as different price trajectories activate different dispatch points, meaning two inner approximations with similar volumes can lead to substantially different operating costs. The goal is to learn an aggregate set that preserves flexibility in cost-relevant regions rather than just relying on geometric volume.

Framework Components

The proposed framework consists of three main components:

1. A parameterized storage surrogate, denoted as the storage-form surrogate, which is parameterized by a vector of parameters θ (Equation 9). This surrogate is designed to be physically interpretable and compatible with market requirements.

2. A parameterized inner approximation, denoted as Ue(θ), which is constructed as an affine image of the storage surrogate using building-specific parameters γb and a diagonal linear transformation matrix Γb (Equation 11). This ensures disaggregation feasibility by construction.

3. A risk- and ambiguity-aware flexibility utilization task formulated using a distributionally robust conditional value-at-risk (DR-CVaR) objective, denoted as J(θ, w) (Equation 18). This task captures both distributional ambiguity and tail risk by considering price trajectories from a set S.

Closed-Loop Learning Procedure

The framework operates in a closed-loop learning formulation where the surrogate parameters θ and the inner-approximation objective weight vector w are jointly learned. The optimization problem seeks to:

min θ,w J (θ, w) s.t. Ue (θ, w) = X b∈B γ⋆ b! + Φ X b∈B Γ⋆ b! U0 (θ), (γ⋆ b,Γ⋆ b, Λ⋆b) ∈ omegab (θ, w), ∀b ∈ B.

This coupling ensures that the utilization cost can provide cost-informed feedback for learning both the surrogate parameters θ and the objective weight w. The learning is performed via gradient descent on a smoothed objective derived from randomized smoothing to estimate gradients efficiently without differentiating through large-scale building-level LPs.

Tractable Solution Procedure

To ensure computational tractability, the framework employs a tailored solution procedure:

1. The DR-CVaR evaluation in the forward pass is reformulated as a tractable second-order cone program (SOCP) using Wasserstein-CVaR duality, resulting in Equation (22).

2. Gradient estimation utilizes randomized smoothing and a score-function estimator to avoid differentiation through building-level optimization problems.

3. The parallel structure allows for the independent solution of building-level LPs across all buildings, while the subsequent DR-CVaR SOCP depends only on the aggregate affine surrogate, ensuring that the computational burden of the utilization layer does not grow with the number of buildings.

Key Findings and Contributions

Case studies comparing Oracle (non-aggregation benchmark), Volume-Maximization Aggregation (VMA), and the Proposed method demonstrate significant economic benefits. The proposed cost-informed learning method achieves a lower dispatch cost gap relative to VMA, showing that it reallocates representation capacity toward the regions activated by the cost-minimizing dispatch. Furthermore, under unseen price-distribution shifts (e.g., July testing data), the risk- and ambiguity-aware modeling component improves generalization, with the DR-CVaR formulation helping to avoid high-cost tail outcomes. The framework successfully links physically feasible HVAC flexibility aggregation and economically effective flexibility utilization.

Future Directions

Future work will focus on systematic calibration of the DRCVaR parameters to better balance economic performance and out-of-sample robustness. The current results show that the method improves downstream economic performance while preserving computational tractability and disaggregation feasibility. The framework provides a principled link between physically feasible HVAC flexibility aggregation and economically effective flexibility utilization.

The gist: This research develops a cost-informed learning framework to aggregate building HVAC flexibility by jointly learning surrogate parameters and an inner-approximation objective from downstream utilization costs, which addresses the limitation that existing methods fail to preserve flexibility most valuable for reducing dispatch costs.

How it works

1. A parameterized storage surrogate U0(θ) is introduced, structured to be physically interpretable and compatible with market requirements. This surrogate is updated using cost-informed feedback from downstream utilization costs.

As a fastidious researcher, I have analyzed this paper, Cost-Informed Learning for Aggregating Building HVAC Flexibility. The proposed framework represents a significant advancement in how artificial intelligence can manage and optimize complex, distributed physical systems (HVAC fleets) by bridging the gap between abstract mathematical representations and tangible economic outcomes.

Here are the specific improvements to AI systems that can be derived from this research, focusing on what the improved system can achieve:

The core improvement is moving AI from merely predicting what will happen (prediction-based learning) to learning how to optimize a complex physical system's structure for a desired economic outcome (decision-focused, feedback-driven learning).

Specifically, the improved AI systems can perform the following capabilities:

A. Optimized Flexibility Set Construction for Downstream Utility:

In current AI methods (like volume-based aggregation), the system learns an aggregate set based purely on geometric size or simple volume metrics. The improved system learns a representation that is explicitly tailored to the downstream economic objective (dispatch cost). It can identify and prioritize flexibility directions that are most valuable for reducing operational costs, even if those directions occupy a smaller geometric volume.

B. Risk-Aware, Uncertainty-Robust Aggregation:

The system moves beyond nominal forecasts by incorporating explicit distributional ambiguity (using the Wasserstein distance) and tail risk (using CVaR). The improved AI system can generate an aggregate flexibility set that is robust not just to a single predicted price path, but to entire families of plausible future price distributions. This means the resulting aggregated schedule will perform well even when electricity prices shift significantly or experience unexpected high-cost events (like peak demand spikes).

C. Adaptive Representation Capacity Allocation:

The AI system learns how to allocate its limited representation capacity efficiently. Instead of treating all parts of the aggregate set equally, it concentrates its memory on the specific regions of flexibility that are most cost-relevant under various price trajectories. This allows the system to make high-quality dispatch decisions by focusing its learned structure where it matters most economically.

D. Efficient and Scalable Learning via Gradient Estimation:

The framework solves a massive optimization problem (learning parameters for thousands of buildings) by breaking it down into tractable building-level problems and using randomized smoothing/score-function estimators to calculate gradients efficiently. The improved AI system can be trained on very large, real-world HVAC fleets (thousands of buildings) in a computationally feasible manner, avoiding the need to differentiate through high-dimensional building models directly.

E. Closed-Loop System Improvement:

The entire process is a closed loop: the AI learns an aggregate set → the system operator uses it for dispatch → realized costs provide feedback to refine the learned set parameters (surrogate and objective). This enables continuous, self-improving optimization of the aggregation strategy over time, leading to a system that gets progressively better at minimizing dispatch costs as more data is collected.

In summary, the improved AI system transforms HVAC flexibility management from a static geometric approximation into a dynamic, economically informed engine capable of making robust dispatch decisions under uncertainty.