Fully Gap-Dependent Bounds for Multinomial Logit Bandit
Jiaqi Yang
Abstract:We study the multinomial logit (MNL) bandit problem, where at each time step, the seller offers an assortment of size at most K from a pool of N items, and the buyer purchases an item from the assortment according to a MNL choice model. The objective is to learn the model parameters and maximize the expected revenue. We present (i) an algorithm that identifies the optimal assortment S * within O( N i=1 ∆ −2 i ) time steps with high probability, and (ii) an algorithm that incurs O( i / ∈S * K∆ −1 i log T ) regr… Show more
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