# Learning in Position-Aware Multinomial Logit Bandits: From Multiplicative to General Position Effects

arXiv: https://arxiv.org/abs/2605.17238 · HTML: https://mlsanity.com/paper/2605.17238/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 38 references that are in the map.
- First posted on arXiv 17 May 2026.

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

- [Stop Relying on No-Choice and Do not Repeat the Moves: Optimal, Efficient and Practical Algorithms for Assortment Optimization](https://mlsanity.com/paper/2402.18917/) (2024)
- [Learning an Optimal Assortment Policy under Observational Data](https://mlsanity.com/paper/2502.06777/) (2025)
- [PASTA: A Unified Framework for Offline Assortment Learning](https://mlsanity.com/paper/2510.01693/) (2025)

## Abstract (arXiv)

We study the dynamic joint assortment selection and positioning problem, where the attraction of each product depends on both its intrinsic appeal and its display position under a Multinomial Logit (MNL) choice framework. Our study ranges from the multiplicative position effects model, in which each product's attraction is scaled by a position-specific factor, to a general position effects model assigning independent attraction parameters to every product--position pair to capture heterogeneous synergies. For both models, we design round-based learning algorithms that update decisions after every single feedback, and establish the first regret-optimal characterization. Besides, our round-based algorithms provide the prompt operations needed by modern platforms. For the multiplicative model, we develop a cross-position pairwise maximum likelihood estimator with a clipping mechanism, and prove that our algorithm P2MLE-UCB attains a regret of tildeO(√NT), matching the lower bound and closing the √K gap left by prior epoch-based analyses. For the general model, we establish a minimax lower bound and propose GP2-UCB with a matching upper bound. Moreover, we design an efficient subroutine for the per-round joint assortment and positioning optimization based on Dinkelbach's method and maximum-weight bipartite matching. Numerical experiments on synthetic data and the Expedia dataset show that our algorithms consistently outperform state-of-the-art benchmarks.