Online Assortment Optimization with High-Dimensional Data
In this research, we consider an online assortment optimization problem, where a decision-maker needs to sequentially offer assortments to users instantaneously upon their arrivals and users select products from offered assortments according to the contextual multinomial logit choice model. We propose a computationally efficient Lasso-RP-MNL algorithm for the online assortment optimization problem under the cardinality constraint in high-dimensional settings. The Lasso-RP-MNL algorithm combines the Lasso and random projection as dimension reduction techniques to alleviate the computational complexity and improve the learning and estimation accuracy under high-dimensional data with limited samples. For each arriving user, the Lasso-RP-MNL algorithm constructs an upper-confidence bound for each individual product's attraction parameter, based on which the optimistic assortment can be identified by solving a reformulated linear programming problem. We demonstrate that for the feature dimension $d$ and the sample size dimension $T$, the expected cumulative regret under the Lasso-RP-MNL algorithm is upper bounded by $\tilde{\mathcal{O}}(\sqrt{T}\log d)$ asymptotically, where $\tilde{\mathcal{O}}$ suppresses the logarithmic dependence on $T$. Furthermore, we show that even when available samples are extremely limited, the Lasso-RP-MNL algorithm continues to perform well with a regret upper bound of $\tilde{\mathcal{O}}( T^{\frac{2}{3}}\log d)$. Finally, through synthetic-data-based experiments and a high-dimensional XianYu assortment recommendation experiment, we show that the Lasso-RP-MNL algorithm is computationally efficient and outperforms other benchmarks in terms of the expected cumulative regret
Year of publication: |
2020
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Authors: | Wang, Xue |
Other Persons: | Wei, Mike Mingcheng (contributor) ; Yao, Tao (contributor) |
Publisher: |
[2020]: [S.l.] : SSRN |
Saved in:
freely available
Extent: | 1 Online-Ressource (62 p) |
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Type of publication: | Book / Working Paper |
Language: | English |
Notes: | Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments November 15, 2019 erstellt |
Other identifiers: | 10.2139/ssrn.3521843 [DOI] |
Source: | ECONIS - Online Catalogue of the ZBW |
Persistent link: https://www.econbiz.de/10012843675
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