# Decision-Making under Combinatorial Risk

arXiv: https://arxiv.org/abs/2606.10092 · HTML: https://mlsanity.com/paper/2606.10092/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [Deep Generative Symbolic Regression](https://mlsanity.com/paper/2401.00282/) (2023)
- [Complexity Measures for Multi-objective Symbolic Regression](https://mlsanity.com/paper/2109.00238/) (2021)
- [A Neural Symbolic Model for Space Physics](https://mlsanity.com/paper/2503.07994/) (2025)
- [Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics](https://mlsanity.com/paper/2102.08351/) (2021)

## Abstract (arXiv)

Decision-making under risk is typically studied through single-shot lottery choices. Yet many real decisions involve combinatorial risk, where risk arises from multiple risky components, so the lottery over outcomes is induced rather than given outright and can be costly to evaluate exactly. We introduce an investment-allocation task to study decision under combinatorial risk, where investing in a component raises its success probability and thereby reshapes the outcome distribution. Participants favor the option with the larger probability increment, and, when increments are equal, the option with the higher initial success probability. Revealing the induced probability mass function (PMF) substantially changes behavior, making participants less responsive to combinatorial-risk features and reducing choice variance. To explain these patterns, we move beyond standard benchmarks and hand-crafted hypotheses with symbolic regression to discover compact descriptive models. The discovered models rely mainly on combinatorial-risk features, such as the after-investment success probability, rather than exact evaluation of the full induced distribution. Behavior under the displayed PMF is then well explained by augmenting this model with a prospect-theoretic residual model. The results show that people navigate combinatorial risk primarily through its core features, shifting toward lottery valuation only when the induced PMF is displayed.