MNL-Bandits under Inventory and Limited Switches Constraints

TL;DR

This paper addresses the challenge of optimizing product assortments under inventory and limited switching constraints using a UCB-like algorithm, demonstrating sub-linear regret bounds and superior empirical performance.

Contribution

It introduces a novel algorithm for assortment optimization under practical constraints, with proven regret bounds and improved empirical results.

Findings

The proposed algorithm achieves sub-linear regret bounds.

It outperforms baseline methods in numerical experiments.

The regret bound is nearly optimal with respect to the time horizon.

Abstract

Optimizing the assortment of products to display to customers is a key to increasing revenue for both offline and online retailers. To trade-off between exploring customers' preference and exploiting customers' choices learned from data, in this paper, by adopting the Multi-Nomial Logit (MNL) choice model to capture customers' choices over products, we study the problem of optimizing assortments over a planning horizon $T$ for maximizing the profit of the retailer. To make the problem setting more practical, we consider both the inventory constraint and the limited switches constraint, where the retailer cannot use up the resource inventory before time $T$ and is forbidden to switch the assortment shown to customers too many times. Such a setting suits the case when an online retailer wants to dynamically optimize the assortment selection for a population of customers. We develop an efficient UCB-like algorithm to optimize the assortments while learning customers' choices from data. We prove that our algorithm can achieve a sub-linear regret bound $\tilde{O}\left(T^{1-\alpha/2}\right)$ if $O(T^\alpha)$ switches are allowed. %, and our regret bound is optimal with respect to $T$. Extensive numerical experiments show that our algorithm outperforms baselines and the gap between our algorithm's performance and the theoretical upper bound is small.