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

2026-02-18

AI Summary

This study addresses a key limitation in existing dynamic joint assortment and pricing methods, which typically assume a fixed customer arrival rate and neglect the impact of assortment and pricing decisions on that rate, leading to suboptimal revenue. To overcome this, the paper introduces the Poisson-MNL model, which explicitly models the customer arrival rate as a function of both assortment and price by coupling a contextual multinomial logit (MNL) choice model with a Poisson arrival process. Building on a multi-armed bandit framework, the authors propose an efficient UCB-type algorithm, PMNL. Theoretical analysis establishes a non-asymptotic regret bound of order √(T log T), which is shown to be minimax optimal. Extensive simulations demonstrate that the proposed approach significantly outperforms benchmark methods that assume a fixed arrival rate.

Technology Category

• Machine Learning: Online Learning & Bandits
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

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.

Problem

• dynamic assortment and pricing
• customer arrivals
• multinomial logit model
• decision-dependent arrivals
• revenue maximization

Innovation

• Poisson-MNL
• dynamic assortment and pricing
• decision-dependent arrivals
• upper confidence bound
• regret bound