We consider a dynamic assortment selection problem where in every round the retailer offers a subset (assortment) of N substitutable products to a consumer, who selects one of these products according to a multinomial logit (MNL) choice model. The retailer observes this choice, and the objective is to dynamically learn the model parameters while optimizing cumulative revenues over a selling horizon of length T. We refer to this exploration–exploitation formulation as the MNL-Bandit problem. Existing methods for this problem follow an explore-then-exploit approach, which estimates parameters to a desired accuracy and then, treating these estimates as if they are the correct parameter values, offers the optimal assortment based on these estimates. These approaches require certain a priori knowledge of “separability,” determined by the true parameters of the underlying MNL model, and this in turn is critical in determining the length of the exploration period. (Separability refers to the distinguishability of the true optimal assortment from the other suboptimal alternatives.) In this paper, we give an efficient algorithm that simultaneously explores and exploits, without a priori knowledge of any problem parameters. Furthermore, the algorithm is adaptive in the sense that its performance is near optimal in the “well-separated” case as well as the general parameter setting where this separation need not hold.

No abstract

We consider a dynamic assortment selection problem, where in every round the retailer offers a subset (assortment) of N substitutable products to a consumer, who selects one of these products according to a multinomial logit (MNL) choice model. The retailer observes this choice and the objective is to dynamically learn the model parameters, while optimizing cumulative revenues over a selling horizon of length T . We refer to this exploration-exploitation formulation as the MNL-Bandit problem. Existing methods for this problem follow an explore-then-exploit approach, which estimate parameters to a desired accuracy and then, treating these estimates as if they are the correct parameter values, offers the optimal assortment based on these estimates. These approaches require certain a priori knowledge of "separability," determined by the true parameters of the underlying MNL model, and this in turn is critical in determining the length of the exploration period. (Separability refers to the distinguishability of the true optimal assortment from the other sub-optimal alternatives.) In this paper, we give an efficient algorithm that simultaneously explores and exploits, without a priori knowledge of any problem parameters. Furthermore, the algorithm is adaptive in the sense that its performance is near-optimal in both the "well separated" case, as well as the general parameter setting where this separation need not hold.

We consider a sequential subset selection problem under parameter uncertainty, where at each time step, the decision maker selects a subset of cardinality K from N possible items (arms), and observes a (bandit) feedback in the form of the index of one of the items in said subset, or none. Each item in the index set is ascribed a certain value (reward), and the feedback is governed by a Multinomial Logit (MNL) choice model whose parameters are a priori unknown. The objective of the decision maker is to maximize the expected cumulative rewards over a finite horizon T , or alternatively, minimize the regret relative to an oracle that knows the MNL parameters. We refer to this as the MNL-Bandit problem. This problem is representative of a larger family of exploration-exploitation problems that involve a combinatorial objective, and arise in several important application domains. We present an approach to adapt Thompson Sampling to this problem and show that it achieves near-optimal regret as well as attractive numerical performance.

No abstract