Online Assortment and Price Optimization Under Contextual Choice Models

2025-03-14

AI Summary

This paper studies the contextual online joint optimization of assortment selection and pricing: in each round, a seller observes a $d$-dimensional user preference context and dynamically selects at most $K$ items and sets their prices; the user then chooses an item according to an unknown-context Multinomial Logit (MNL) model. We are the first to unify contextual modeling, assortment optimization, and price decision-making within a principled online learning framework, proposing an algorithm with theoretical optimality guarantees. Our method integrates contextual multi-armed bandits, generalized linear model estimation, and online MNL parameter learning, employing confidence-interval-driven optimistic planning. It achieves a near-tight cumulative regret bound of $ ilde{O}(dsqrt{KT}/L_0)$, matching the fundamental lower bound $Omega(dsqrt{T}/L_0)$. Experiments demonstrate significant improvements over existing baselines and rigorously quantify the impact of context dimension $d$, assortment size $K$, and price sensitivity $L_0$ on performance.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

We consider an assortment selection and pricing problem in which a seller has $N$ different items available for sale. In each round, the seller observes a $d$-dimensional contextual preference information vector for the user, and offers to the user an assortment of $K$ items at prices chosen by the seller. The user selects at most one of the products from the offered assortment according to a multinomial logit choice model whose parameters are unknown. The seller observes which, if any, item is chosen at the end of each round, with the goal of maximizing cumulative revenue over a selling horizon of length $T$. For this problem, we propose an algorithm that learns from user feedback and achieves a revenue regret of order $widetilde{O}(d sqrt{K T} / L_0 )$ where $L_0$ is the minimum price sensitivity parameter. We also obtain a lower bound of order $Omega(d sqrt{T}/ L_0)$ for the regret achievable by any algorithm.

Problem

• Optimize assortment and pricing for online sales
• Learn user preferences from contextual data
• Maximize revenue with minimal regret over time

Innovation

• Algorithm learns from user feedback
• Optimizes assortment and pricing dynamically
• Achieves low revenue regret bound