# Discrete choice prox-functions on the simplex

arXiv: https://arxiv.org/abs/1909.05591 · HTML: https://mlsanity.com/paper/1909.05591/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

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

- [Discrete Choice Multi-Armed Bandits](https://mlsanity.com/paper/2310.00562/) (2023)
- [Beyond Softmax: A New Perspective on Gradient Bandits](https://mlsanity.com/paper/2510.03979/) (2025)

## Abstract (arXiv)

We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to natural probabilistic interpretations of the iteration steps. As illustration we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming naturally adjusts demand within a consumption cycle.