# Uncovering Utility Functions from Observed Outcomes

arXiv: https://arxiv.org/abs/2503.13432 · HTML: https://mlsanity.com/paper/2503.13432/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 52 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 3 of 3)

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Maximum Entropy Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/1507.04888/) (2015)
- [Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences](https://mlsanity.com/paper/1912.00331/) (2019)

## Built on by (most cited first, 2 of 2)

- [Solving Heterogeneous Agent Models with Physics-informed Neural Networks](https://mlsanity.com/paper/2511.20283/) (2025)
- [Neural Demand Estimation with Habit Formation and Rationality Constraints](https://mlsanity.com/paper/2603.02331/) (2026)

## Abstract (arXiv)

Determining consumer preferences and utility is a foundational challenge in economics. They are central in determining consumer behaviour through the utility-maximising consumer decision-making process. However, preferences and utilities are not observable and may not even be known to the individual making the choice; only the outcome is observed in the form of demand. Without the ability to observe the decision-making mechanism, demand estimation becomes a challenging task and current methods fall short due to lack of scalability or ability to identify causal effects. Estimating these effects is critical when considering changes in policy, such as pricing, the impact of taxes and subsidies, and the effect of a tariff. To address the shortcomings of existing methods, we combine revealed preference theory and inverse reinforcement learning to present a novel algorithm, Preference Extraction and Reward Learning (PEARL) which, to the best of our knowledge, is the only algorithm that can uncover a representation of the utility function that best rationalises observed consumer choice data given a specified functional form. We introduce a flexible utility function, the Input-Concave Neural Network which captures complex relationships across goods, including cross-price elasticities. Results show PEARL outperforms the benchmark on both noise-free and noisy synthetic data.