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arXiv Machine Learning By Joongkyu Lee, Min-hwan Oh

Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification

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The paper presents a computationally efficient optimal design framework for multinomial logit (MNL) bandits, addressing the combinatorial action space that makes traditional methods infeasible. It introduces two approaches: an exact or certified-approximate mixed-integer linear program with solver‑certified early stopping, and a fully polynomial‑time lifted design using a tractable surrogate objective. Leveraging the Kiefer‑Wolfowitz equivalence theorem, the authors provide near G‑optimality guarantees and apply the framework to develop a best assortment identification algorithm with an instance‑dependent sample complexity of τO((d log N)/Δ²).

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