Discrete Choice Models Based on Random Walks

Berbeglia, Gerardo

doi:10.2139/ssrn.2605666

Cited by 6 publications

(8 citation statements)

References 17 publications

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“…Recently, Berbeglia [9] showed that every choice model based on Markov chains models belongs to the class of choice models based on random utility. Jagabathula [25] introduced a local search heuristic for the assortment problem under an arbitrary discrete choice model.…”

Section: Introductionmentioning

confidence: 99%

Assortment Optimisation Under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Berbeglia

Joret

2015

SSRN Journal

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The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue π and then choosing all products with revenue at least π. This is known as the revenue-ordered assortments strategy. In this paper we study the approximation guarantees provided by revenue-ordered assortments when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the set is enlarged. This rationality assumption, known as regularity, is satisfied by almost all discrete choice models considered in the revenue management and choice theory literature, and in particular by random utility models. The bounds we obtain are tight and improve on recent results in that direction, such as for the Mixed Multinomial Logit model by Rusmevichientong et al. [42]. An appealing feature of our analysis is its simplicity, as it relies only on the regularity condition.We also draw a connection between assortment optimisation and two pricing problems called unit demand envy-free pricing and Stackelberg minimum spanning tree: These problems can be restated as assortment problems under discrete choice models satisfying the regularity condition, and moreover revenue-ordered assortments correspond then to the well-studied uniform pricing heuristic. When specialised to that setting, the general bounds we establish for revenue-ordered assortments match and unify the best known results on uniform pricing.(

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Section: Introductionmentioning

confidence: 99%

Assortment Optimisation Under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Berbeglia

Joret

2015

SSRN Journal

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“…This paper contributes to the existing literature in four main aspects. First, although our choice model can be seen as a special case of the more general Markov-chain and random-walk based models of Blanchet et al (2016) and Berbeglia (2016), respectively, and the general ranking-based models of Mahajan and Van Ryzin (2001) and Farias et al (2013), our approach explicitly incorporates the cumulative effect that the number of unavailable products attempted (i.e., number of substitution attempts) has on the customers' leaving probability. Moreover, the sequential process in our choice model allows us to include those cases where the customer is determined to make a purchase in the current store.…”

Section: Solution Methodsmentioning

confidence: 99%

“…These probabilities only depend on the last visited product due to the Markovian memoryless property, which implies that the cumulative effect of finding multiple products unavailable is limited to one product. Berbeglia (2016) generalizes the Markov chainbased model by proposing a random walk-based model that solves the memoryless limitation by considering that the substitution probability depends on the whole sequence of previously visited products.…”

Section: Choice Modelsmentioning

confidence: 99%

Robust Assortment Optimization under a Ranking-based Choice Model with Product Unavailability Effect

Mehrani,

Sefair

2020

Preprint

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The assortment planning problem is a central piece in the revenue management strategy of any company in the retail industry. In this paper, we study a robust assortment optimization problem for substitutable products under a sequential ranking-based choice model. Our modeling approach incorporates the cumulative effect of finding multiple unavailable products on the customers' purchase decisions. To model the highly uncertain order in which a customer explores the products to buy, we present a bi-level optimization approach to maximize the expected revenue under the worst-case order of products in the preference lists of customers.We provide a polynomial-time algorithm that optimally solves a special case of the unconstrained assortment planning problem under our choice model. For the general constrained version of the problem, we devise a solution procedure that includes a single-level reformulation and a cutting-plane approach to iteratively tighten the solution space. We also provide a greedy algorithm that can quickly solve large instances with small optimality gaps.

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“…Désir et al [2015], Blanchet et al [2016] approximate the user's choice as a random walk on a Markov chain. Berbeglia [2016] shows that the discrete choice model and the Markov chain model can be viewed as instances of a "random utility model" (RUM), which also assumes a total order of all the arms. We will show in Section 3.3 that MNL and RUM are both special cases of Assumption 1.…”

Section: Motivation and Related Workmentioning

confidence: 99%

Combinatorial Bandits without Total Order for Arms

Yang,

Ren,

Dhillon

et al. 2021

Preprint

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We consider the combinatorial bandits problem, where at each time step, the online learner selects a size-k subset s from the arms set A, where |A| = n, and observes a stochastic reward of each arm in the selected set s. The goal of the online learner is to minimize the regret, induced by not selecting s * which maximizes the expected total reward. Specifically, we focus on a challenging setting where 1) the reward distribution of an arm depends on the set s it is part of, and crucially 2) there is no total order for the arms in A.In this paper, we formally present a reward model that captures set-dependent reward distribution and assumes no total order for arms. Correspondingly, we propose an Upper Confidence Bound (UCB) algorithm that maintains UCB for each individual arm and selects the arms with top-k UCB. We develop a novel regret analysis and show an O k 2 n log T gap-dependent regret bound as well as an O k 2 √ nT log T gap-independent regret bound. We also provide a lower bound for the proposed reward model, which shows our proposed algorithm is near-optimal for any constant k. Empirical results on various reward models demonstrate the broad applicability of our algorithm.

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Discrete Choice Models Based on Random Walks

Cited by 6 publications

References 17 publications

Assortment Optimisation Under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Assortment Optimisation Under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Robust Assortment Optimization under a Ranking-based Choice Model with Product Unavailability Effect

Combinatorial Bandits without Total Order for Arms

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