# On Pareto Optimality for Parametric Choice Bandits

arXiv: https://arxiv.org/abs/2501.19277 · HTML: https://mlsanity.com/paper/2501.19277/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 31 Jan 2025.

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

- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Thompson Sampling for the MNL-Bandit](https://mlsanity.com/paper/1706.00977/) (2017)
- [Semiparametric Efficient Inference in Adaptive Experiments](https://mlsanity.com/paper/2311.18274/) (2023)
- [Multinomial Logit Contextual Bandits: Provable Optimality and Practicality](https://mlsanity.com/paper/2103.13929/) (2021)
- [Dynamic pricing and assortment under a contextual MNL demand](https://mlsanity.com/paper/2110.10018/) (2021)
- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Achieving the Pareto Frontier of Regret Minimization and Best Arm Identification in Multi-Armed Bandits](https://mlsanity.com/paper/2110.08627/) (2021)
- [Optimizing Adaptive Experiments: A Unified Approach to Regret Minimization and Best-Arm Identification](https://mlsanity.com/paper/2402.10592/) (2024)

## Abstract (arXiv)

We study online assortment optimization under stochastic choice when a decision maker simultaneously values cumulative revenue performance and the quality of post-hoc inference on revenue contrasts. We analyze a forced-exploration optimism-in-the-face-of-uncertainty (OFU) scheme that combines two regularized maximum-likelihood estimators: one based on all observations for sequential decision making, and one based only on exploration rounds for inference. Our general theory is developed under predictable score proxies and per-round action-dependent curvature domination. Under these conditions we establish a self-normalized concentration inequality, a likelihood-based ellipsoidal confidence-set theorem, and a regret bound for approximate optimistic actions that explicitly accounts for optimization error. For the multinomial logit (MNL) model we derive explicit score and curvature proxies and show that a balanced spaced singleton-exploration schedule yields realized coordinate coverage, implying regret Otilde(nT + T/√nT) and revenue-contrast error Otilde(1/√nT) up to fixed problem-dependent factors. A hard two-assortment subclass yields a matching lower bound at the product level. Consequently, within the polynomial exploration family nT asymp Tα, the regret and inference rates become Otilde(T^maxα,1-α/2) and Otilde(T-α/2), respectively; hence α∈[2/3,1) is the rate-wise Pareto-undominated interval and α=2/3 is the unique balancing point that minimizes the regret exponent. Finally, for the Exponomial Choice and Nested Logit models we state verifiable sufficient conditions that would instantiate the general framework.