Continuous Assortment Optimization with Logit Choice Probabilities and Incomplete Information

• 成果类型: Article; Early Access
• 署名作者: Peeters, Yannik; den Boer, Arnoud V.; Mandjes, Michel
• 署名单位: University of Amsterdam; University of Amsterdam
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2235
• 发表日期: 2022
• 关键词: assortment optimization; learning; multiarmed bandit; continuous assortment

摘要

We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the relation between assortment and customer choice, we propose a probabilistic choice model that forms the continuous counterpart of the widely studied discrete multinomial logit model. We consider the seller's problem under incomplete information, propose a stochastic approximation type of policy, and show that its regret, its performance loss compared with the optimal policy, is only logarithmic in the time horizon. We complement this result by showing a matching lower bound on the regret of any policy, implying that our policy is asymptotically optimal. We then show that adding a capacity constraint significantly changes the structure of the problem: we construct a policy and show that its regret after T time periods is bounded above by a constant times T-2/3 (up to a logarithmic term); in addition, we show that the regret of any policy is bounded from below by a positive constant times T-2/3, so that also in the capacitated case, we obtain asymptotic optimality. Numerical illustrations show that our policies outperform or are on par with alternatives.