# Dynamic Learning with Frequent New Product Launches: A Sequential Multinomial Logit Bandit Problem

## TL;DR

This paper introduces a sequential multinomial logit bandit model for online learning in dynamic markets with frequent new product launches, providing algorithms with regret bounds and strategies to mitigate risks in learning new products.

## Contribution

It develops a novel SMNL model for tiered recommendations, proposes polynomial-time algorithms for offline and online learning, and extends the model to include learning accuracy constraints for new products.

## Key findings

- Proposed a polynomial-time algorithm for offline preference learning.
- Designed an online learning algorithm with quantifiable regret bounds.
- Extended the model to ensure learning accuracy for new products.

## Abstract

Motivated by the phenomenon that companies introduce new products to keep abreast with customers' rapidly changing tastes, we consider a novel online learning setting where a profit-maximizing seller needs to learn customers' preferences through offering recommendations, which may contain existing products and new products that are launched in the middle of a selling period. We propose a sequential multinomial logit (SMNL) model to characterize customers' behavior when product recommendations are presented in tiers. For the offline version with known customers' preferences, we propose a polynomial-time algorithm and characterize the properties of the optimal tiered product recommendation. For the online problem, we propose a learning algorithm and quantify its regret bound. Moreover, we extend the setting to incorporate a constraint which ensures every new product is learned to a given accuracy. Our results demonstrate the tier structure can be used to mitigate the risks associated with learning new products.