Thompson Sampling for Online Personalized Assortment Optimization Problems with Multinomial Logit Choice Models PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Thompson Sampling for Online Personalized Assortment Optimization Problems with Multinomial Logit Choice Models PDF full book. Access full book title Thompson Sampling for Online Personalized Assortment Optimization Problems with Multinomial Logit Choice Models by Wang Chi Cheung. Download full books in PDF and EPUB format.
Author: Wang Chi Cheung
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
Get Book Here
Book Description
Motivated by online retail applications, we study the online personalized assortment optimization problem. A seller conducts sales by offering assortments of products to a stream of arriving customers. The customers' purchase behavior follows their respective personalized Multinomial Logit choice models, which vary according to their individual attributes. The seller aims to maximize his revenue by offering personalized assortments to the customers, notwithstanding his uncertainty about the customers' choice models. We propose a Thompson Sampling based policy, policy Pao-Ts, where surrogate models for the latent choice models are constructed using samples from a progressively updated posterior distribution. We derive bounds on the revenue loss, namely Bayesian regret, incurred by policy Pao-Ts, in comparison to the optimal policy which is provided with the latent models. The regret bounds hold even when the customers' attributes vary arbitrarily, but not independently and identically distributed.
Author: Wang Chi Cheung
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
Get Book Here
Book Description
Motivated by online retail applications, we study the online personalized assortment optimization problem. A seller conducts sales by offering assortments of products to a stream of arriving customers. The customers' purchase behavior follows their respective personalized Multinomial Logit choice models, which vary according to their individual attributes. The seller aims to maximize his revenue by offering personalized assortments to the customers, notwithstanding his uncertainty about the customers' choice models. We propose a Thompson Sampling based policy, policy Pao-Ts, where surrogate models for the latent choice models are constructed using samples from a progressively updated posterior distribution. We derive bounds on the revenue loss, namely Bayesian regret, incurred by policy Pao-Ts, in comparison to the optimal policy which is provided with the latent models. The regret bounds hold even when the customers' attributes vary arbitrarily, but not independently and identically distributed.
Author: Jens Vygen
Publisher: Springer Nature
ISBN: 3031598350
Category :
Languages : en
Pages : 474
Get Book Here
Book Description
Author: Xi Chen
Publisher: Springer Nature
ISBN: 3031019261
Category : Business & Economics
Languages : en
Pages : 444
Get Book Here
Book Description
This book examines recent developments in Operations Management, and focuses on four major application areas: dynamic pricing, assortment optimization, supply chain and inventory management, and healthcare operations. Data-driven optimization in which real-time input of data is being used to simultaneously learn the (true) underlying model of a system and optimize its performance, is becoming increasingly important in the last few years, especially with the rise of Big Data.
Author: Sentao Miao
Publisher:
ISBN:
Category :
Languages : en
Pages : 47
Get Book Here
Book Description
We consider an online personalized assortment optimization problem where customers arrive sequentially and make their choices (e.g., click an ad, purchase a product) following the multinomial logit (MNL) model with unknown parameters. Utilizing customer's personal information, the firm makes an assortment decision tailored for the individual customer's preference. We develop two algorithms which make assortment recommendations to maximize expected total revenue while concurrently learning the demand. The first algorithm constructs upper-confidence bounds (UCB) of product utilities using estimated demand parameters and personalized data to balance exploration and exploitation. The second algorithm incorporates a fast online convex optimization procedure in the first algorithm, which significantly reduces the computational effort; thus it is particularly useful when solving online personalized assortment optimization problem in a big data regime. We show that the algorithms can be modified to solve high dimensional problem (i.e., when the dimension of customer's personal information data is high) through a dimension reduction method known as random projection. The theoretical performance for our algorithms in terms of regret are derived, and numerical experiments using synthetic and real data demonstrate that they perform very well in both low and high dimensional settings compared with several benchmarks.
Author: Qingwei Jin
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
We study assortment optimization problems under multinomial logit choice model with two tree structured consideration set models, i.e., the subtree model and the induced paths model. In each model, there are multiple customer types and each customer type has a different consideration set. A customer of a particular type only purchases product within his consideration set. The tree structure means all products form a tree with each node representing one product and all consideration sets are induced from this tree. In the subtree model, each consideration set consists of products in a subtree and in the induced paths model, each consideration set consists of products on the path from one node to the root. All customers make purchase decisions following the same multinomial logit choice model except that different customer types have different consideration sets. The goal of the assortment optimization is to determine a set of products offered to customers such that the expected revenue is maximized. We consider both unconstrained problem and capacitated problem. We show that these problems are all NP-hard problems and propose a unified framework, which captures the tree structure in both models, to design fully polynomial time approximation schemes (FPTAS) for all these problems. Besides, we identify a special case under the induced paths model, showing that it can be solved in $O(n)$ operations.
Author: Antoine Désir
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Assortment optimization is an important problem that arises in many practical applications such as retailing and online advertising. In this problem, the goal is to select a subset of items that maximizes the expected revenue in the presence of (1) the substitution behavior of consumers specified by a choice model, and (2) a potential capacity constraint bounding the total weight of items in the assortment. The latter is a natural constraint arising in many applications. We begin by showing how challenging these two aspects are from an optimization perspective. First, we show that adding a general capacity constraint makes the problem NP-hard even for the simplest choice model, namely the multinomial logit model. Second, we show that even the unconstrained assortment optimization for the mixture of multinomial logit model is hard to approximate within any reasonable factor when the number of mixtures is not constant.In view of these hardness results, we present near-optimal algorithms for the capacity constrained assort- ment optimization problem under a large class of parametric choice models including the mixture of multinomial logit, Markov chain, nested logit and d-level nested logit choice models. In fact, we develop near-optimal algorithms for a general class of capacity constrained optimization problems whose objective function depends on a small number of linear functions. For the mixture of multinomial logit model (resp. Markov chain model), the running time of our algorithm depends exponentially on the number of segments (resp. rank of the transition matrix). Therefore, we get efficient algorithms only for the case of constant number of segments (resp. constant rank). However, in light of our hardness result, any near-optimal algorithm will have a super polynomial dependence on the number of mixtures for the mixture of multinomial logit choice model.
Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 57
Get Book Here
Book Description
In this paper, we consider the yet-uncharted assortment optimization problem under the Exponomial choice model, where the objective is to determine the revenue maximizing set of products that should be offered to customers. Our main algorithmic contribution comes in the form of a fully polynomial-time approximation scheme (FPTAS), showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. This result is obtained through a synthesis of ideas related to approximate dynamic programming, that enable us to derive a compact discretization of the continuous state space by keeping track of several key statistics in "rounded" form throughout the overall computation. Consequently, we obtain the first provably-good algorithm for assortment optimization under the Exponomial choice model, which is complemented by a number of hardness results for natural extensions. We show in computational experiments that our solution method admits an efficient implementation, based on additional pruning criteria.Furthermore, we conduct empirical evaluations of the Exponomial choice model. We present a number of case studies using real-world data sets, spanning retail, online platforms, and transportation. We focus on a comparison with the popular Multinomial Logit choice model (MNL), which is largely dominant in the choice modeling practice, as both models share a simple parametric structure with desirable statistical and computational properties. We identify several settings where the Exponomial choice model has better predictive accuracy than MNL and leads to more profitable assortment decisions. We provide implementation guidelines and insights about the performance of the Exponomial choice model relative to MNL.
Author: Jacob Feldman
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
We study assortment optimization problems under a natural variant of the multinomial logit model where the customers are willing to focus only on a certain number of products that provide the largest utilities. In particular, each customer has a rank cutoff, characterizing the number of products that she will focus on during the course of her choice process. Given that we offer a certain assortment of products, the choice process of a customer with rank cutoff k proceeds as follows. The customer associates random utilities with all of the products as well as the no-purchase option. She ignores all alternatives whose utilities are not within the k largest utilities. Among the remaining alternatives, the customer chooses the available alternative that provides the largest utility. Under the assumption that the~utilities follow Gumbel distributions with the same scale parameter, we provide a recursion to compute the choice probabilities. Considering the assortment optimization problem to find the revenue-maximizing assortment of products to offer, we show that the problem is NP-hard and give a polynomial-time approximation scheme. Since the customers ignore the products below their rank cutoffs in our variant of the multinomial logit model, intuitively speaking, our variant captures choosier choice behavior than the standard multinomial logit model. Accordingly, we show that the revenue-maximizing assortment under our variant includes the revenue-maximizing assortment under the standard multinomial logit model, so choosier behavior leads to larger assortments offered to maximize the expected revenue. We conduct computational experiments on both synthetic and real datasets to demonstrate that incorporating rank cutoffs can yield better predictions of customer choices and yield more profitable assortment recommendations.
Author: Xue Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 62
Get Book Here
Book Description
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.
Author: Ruxian Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
This paper incorporates heterogeneous threshold effects into the classical multinomial logit (MNL) model, and studies the associated operations problems such as estimation and assortment optimization. The derived model is referred to as the threshold multinomial logit (TMNL) model and incorporates the recently proposed threshold Luce (T-Luce) model as a limiting case. Under the TMNL model, consumers first form their (heterogeneous) consideration set: If an alternative with significantly low utility is dominated by another one, it will not be included in the consideration set. The TMNL model can alleviate the restricted substitution patterns of MNL due to the independence of irrelevant alternatives (IIA) property, and therefore can model more flexible choice behavior. We develop a maximum likelihood based estimation to calibrate the proposed threshold model and further establish its statistical properties such as consistency and asymptotic normality under mild conditions. An efficient EM algorithm is also developed to handle the scenario with incomplete sales data. Our extensive numerical studies on synthetic and real datasets show that the new model can improve the goodness of fit and prediction accuracy of consumer choice behavior. In addition, we characterize the optimal strategies and provide efficient solutions for the associated assortment optimization problems under the TMNL model. Our theoretical and empirical results suggest that the threshold effects should be taken into account in firms' decision making such as demand estimation and operations management, and ignoring these effects could lead to sub-optimal solutions or even substantial losses for firms.
