Poisson-MNL Bandit: Nearly Optimal Dynamic Joint Assortment and Pricing with Decision-Dependent Customer Arrivals

TL;DR

This paper introduces a Poisson-MNL model for dynamic joint assortment and pricing, accounting for decision-dependent customer arrivals, and proposes an algorithm with near-optimal regret bounds that outperforms traditional fixed-arrival models.

Contribution

The paper develops a novel Poisson-MNL model coupling customer choice with decision-dependent arrivals and provides an efficient UCB-based algorithm with provable near-optimal regret bounds.

Findings

PMNL effectively learns customer choice and arrival models.

Joint assortment-pricing decisions outperform fixed-arrival models.

Regret bound of order √T log T established for the algorithm.

Abstract

We study dynamic joint assortment and pricing where a seller updates decisions at regular accounting/operating intervals to maximize the cumulative per-period revenue over a horizon $T$. In many settings, assortment and prices affect not only what an arriving customer buys but also how many customers arrive within the period, whereas classical multinomial logit (MNL) models assume arrivals as fixed, potentially leading to suboptimal decisions. We propose a Poisson-MNL model that couples a contextual MNL choice model with a Poisson arrival model whose rate depends on the offered assortment and prices. Building on this model, we develop an efficient algorithm PMNL based on the idea of upper confidence bound (UCB). We establish its (near) optimality by proving a non-asymptotic regret bound of order $\sqrt{T\log{T}}$ and a matching lower bound (up to $\log T$). Simulation studies underscore the importance of accounting for the dependency of arrival rates on assortment and pricing: PMNL effectively learns customer choice and arrival models and provides joint assortment-pricing decisions that outperform others that assume fixed arrival rates.