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

2026-02-20 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

A new Poisson-MNL model addresses dynamic joint assortment and pricing decisions, where both product assortment and prices influence customer arrival rates, a factor often overlooked by traditional multinomial logit (MNL) models. This model integrates a contextual MNL choice model with a Poisson arrival model, where the arrival rate is explicitly dependent on the offered assortment and prices. Researchers developed an algorithm called PMNL, based on the upper confidence bound (UCB) approach, to optimize cumulative per-period revenue over a horizon T. The PMNL algorithm demonstrates near-optimal performance, achieving a non-asymptotic regret bound of order $\sqrt{T\log{T}}$, which matches the theoretical lower bound up to a $\log T$ factor. Simulation studies confirm that PMNL effectively learns both customer choice and arrival models, outperforming methods that assume fixed arrival rates.

Key takeaway

For retail strategists and e-commerce managers optimizing product offerings, adopting the Poisson-MNL model is crucial. Your current models likely assume fixed customer arrivals, leading to suboptimal revenue. By integrating decision-dependent arrival rates, you can make more informed joint assortment and pricing decisions, potentially increasing cumulative revenue significantly. Consider piloting the PMNL algorithm to validate its performance in your specific market.

Key insights

The Poisson-MNL model optimizes dynamic assortment and pricing by accounting for decision-dependent customer arrival rates.

Principles

• Arrival rates are not fixed but depend on assortment and pricing.
• UCB-based algorithms can achieve near-optimal regret bounds.

Method

The PMNL algorithm couples a contextual MNL choice model with a Poisson arrival model, using an upper confidence bound (UCB) strategy for dynamic assortment and pricing decisions.

In practice

• Implement PMNL for dynamic pricing and product display.
• Use Poisson-MNL to model customer arrivals more accurately.

Topics

• Dynamic Assortment and Pricing
• Poisson-MNL Model
• Multi-armed Bandit
• Regret Bounds
• Customer Arrival Modeling

Best for: AI Researcher, AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.