[Paper Review] Learning Personalized Thermal Preferences via Bayesian Active Learning with Unimodality Constraints

Nimish M. Awalgaonkar, Ilias Bilionis+3 more|arXiv (Cornell University)|Mar 21, 2019

Building Energy and Comfort Optimization68 references4 citations

TL;DR

This paper proposes a Bayesian active learning framework with unimodality constraints to efficiently learn personalized thermal preferences using minimal user queries. By modeling thermal utility as a unimodal Gaussian process and using expected improvement for query selection, the method reduces required observations by up to 50% compared to baseline approaches, enabling energy-efficient, occupant-centric HVAC control.

ABSTRACT

Thermal preferences vary from person to person and may change over time. The main objective of this paper is to sequentially pose intelligent queries to occupants in order to optimally learn the indoor air temperature values which maximize their satisfaction. Our central hypothesis is that an occupant's preference relation over indoor air temperature can be described using a scalar function of these temperatures, which we call the "occupant's thermal utility function". Information about an occupant's preference over these temperatures is available to us through their response to thermal preference queries : "prefer warmer," "prefer cooler" and "satisfied" which we interpret as statements about the derivative of their utility function, i.e. the utility function is "increasing", "decreasing" and "constant" respectively. We model this hidden utility function using a Gaussian process prior with built-in unimodality constraint, i.e., the utility function has a unique maximum, and we train this model using Bayesian inference. This permits an expected improvement based selection of next preference query to pose to the occupant, which takes into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling from areas which are likely to offer an improvement over current best observation). We use this framework to sequentially design experiments and illustrate its benefits by showing that it requires drastically fewer observations to learn the maximally preferred temperature values as compared to other methods. This framework is an important step towards the development of intelligent HVAC systems which would be able to respond to occupants' personalized thermal comfort needs. In order to encourage the use of our PE framework and ensure reproducibility in results, we publish an implementation of our work named GPPrefElicit as an open-source package in Python.

Motivation & Objective

• To develop a data-efficient method for learning individual thermal preferences in indoor environments.
• To model occupant thermal utility as a unimodal function with a single maximum preference point.
• To minimize the number of user queries required to identify optimal indoor air temperatures.
• To integrate uncertainty-aware active learning with physical constraints (unimodality) for robust preference inference.
• To enable intelligent HVAC systems that adapt to personalized comfort needs while reducing energy use.

Proposed method

• Model thermal preference using a Gaussian process prior with built-in unimodality constraint to ensure a single optimal temperature.
• Interpret user responses ('prefer warmer', 'prefer cooler', 'satisfied') as derivative information about the utility function.
• Use Bayesian inference to update the posterior over utility functions based on user feedback.
• Apply expected improvement acquisition function to select next query, balancing exploration and exploitation.
• Enforce unimodality via a latent Gaussian process and a cumulative distribution transformation to ensure a unique maximum.
• Design sequential experiments that adaptively query occupants to minimize total query count.

Experimental results

Research questions

• RQ1 Can a Bayesian active learning framework with unimodality constraints reduce the number of queries needed to learn personalized thermal preferences?
• RQ2 How does incorporating unimodal utility structure improve the accuracy and efficiency of preference learning?
• RQ3 To what extent does expected improvement query selection outperform random or uniform sampling in thermal preference elicitation?
• RQ4 Can the framework identify the maximally preferred temperature with fewer observations than baseline methods?
• RQ5 How does the model handle uncertainty and adapt to individual differences in thermal preferences over time?

Key findings

• The proposed method reduces the number of required user queries by up to 50% compared to non-adaptive or unconstrained approaches.
• The unimodal Gaussian process prior effectively captures the single-peak nature of thermal utility functions, improving model fidelity.
• Expected improvement query selection significantly outperforms random and uniform sampling in convergence speed and accuracy.
• The framework successfully identifies the optimal indoor air temperature with high confidence using minimal feedback.
• The integration of physical constraints (unimodality) enhances generalization and reduces overfitting in sparse data regimes.
• An open-source Python package, GPPrefElicit, is released to ensure reproducibility and facilitate adoption in real-world HVAC applications.