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Author: Xue Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 62
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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: Xue Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 62
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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: Sentao Miao
Publisher:
ISBN:
Category :
Languages : en
Pages : 47
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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: Kumar Goutam
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Chapter 1 explores discrete choice models which capture consumer behavior and choices when faced with a set of different alternatives, and the resulting assortment optimization problem along with the different existing algorithms for solving them as well as the existing challenges therein. Chapter 2 models and solves the problem when the sellers have access to a vast array of inventory of products. Chapter 3 models dynamic preferences of consumers and the choice overload phenomenon when the customers are faced with a lot of options, and solves the ensuing optimization problem. Chapter 4 showcases the applicability and effectiveness of such models and approaches on high dimensional data from a field experiment on Flipkart, the largest e-commerce firm in India.
Author: Xi Chen
Publisher: Springer Nature
ISBN: 3031019261
Category : Business & Economics
Languages : en
Pages : 444
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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: Xiao-Yue Gong
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We consider an online assortment optimization problem where we have n substitutable products with fixed reusable capacities c1,...,cn. In each period t, a user with some preferences (potentially adversarially chosen) arrives to the seller's platform who offers a subset of products St, from the set of available products. The user selects product j ∈ St with probability given by the preference model and uses it for a random number of periods, ̃ tj that is distributed i.i.d. according to some distribution that depends only on j generating a revenue rj( ̃ tj) for the seller. The goal of the seller is to find a policy that maximizes the expected cumulative over a finite horizon T. Our main contribution in this paper is to show that a simple myopic policy (where we offer the myopically optimal assortment from the available products to each user) provides a good approximation for the problem. In particular, we show that the myopic policy is 1/2-competitive, i.e., the expected cumulative revenue of the myopic policy is at least 1/2 times the expected revenue of an optimal policy that has full information about the sequence of user preference models and the distribution of random usage times of all the products. In contrast, the myopic policy does not require any information about future arrivals or the distribution of random usage times. The analysis is based on a coupling argument that allows us to bound the expected revenue of the optimal algorithm in terms of the expected revenue of the myopic policy. We also consider the setting where usage time distributions can depend on the type of each user and show that in this more general case there is no online algorithm with a non-trivial competitive ratio guarantee. Finally, we perform numerical experiments to compare the robustness and performance of myopic policy with other natural policies.
Author: Yan Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We analyze the assortment optimization problem faced by a monopolistic firm selling n substitutable products in both store and online channels. In our problem, a subset of products (the assortment) are offered in store while all products are sold online. Compared to purchasing in store, purchasing online would lead to an additional cost to customers in the form of a delivery fee or waiting cost. Interestingly, we find that the introduction of online channel hurts the firm and renders the firm to offer more products in store. However, with capacity constraint in store, the online channel, which enables customers to purchase high profit-margin products that are removed out of the assortment due to capacity limit, might benefit the firm.
Author: Wang Chi Cheung
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
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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: Shukai Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We study a dynamic assortment selection problem where arriving customers make purchase decisions among offered products from a universe of $N$ products under a Markov-chain-based choice (MCBC) model. The retailer observes only the assortment and the customer's single choice per period. Given limited display capacity, resource constraints, and no a priori knowledge of problem parameters, the retailer's objective is to sequentially learn the choice model and optimize cumulative revenues over a selling horizon of length $T$. We develop an explore-then-exploit learning algorithm that balances the trade-off between exploration and exploitation. The algorithm can simultaneously estimate the arrival and transition probabilities in the MCBC model by solving linear equations and determining the near-optimal assortment based on these estimates. Furthermore, compared to existing heuristic estimation methods that suffer from inconsistency and a large computational burden, our consistent estimators enjoy superior computational times.
Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 57
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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: Fransisca Susan
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Digital marketplaces have access to a large amount of user data, which presents new opportunities for learning and data-driven decision-making. However, there are two fundamental challenges associated with the use of data in digital marketplaces. First, many decision-making processes in digital marketplaces involve evaluating and experimenting with a large number of options. While companies may be comfortable with conducting A/B testing when there are only two options, this becomes impractical when there are many more options to consider. Second, machine learning models often rely heavily on data that may not always be accurate or reliable, leading to poor performance when making predictions and later on causing poor decision-making. In addition, real-time decision-making is often required. This motivates the main theme in my thesis, which is to develop effective and efficient online algorithms that take advantage of structures and predictive information in time-varying combinatorial environments, facilitating decision-making in uncertain situations. Examples of such problems include assortment optimization, product ranking, and bid optimization for online advertising. The thesis overall investigates online combinatorial optimization in digital marketplaces with various applications, covering general combinatorial problems, non-parametric choice models, constrained bid optimization in auctions, and fairness-constrained assortment optimization in four parts. In the first chapter, we address the problem of making real-time decisions in a time-varying combinatorial environment where the decision maker needs to balance optimizing their decision and learning about the underlying environment. We propose a unified framework that transforms robust greedy approximation algorithms into their online counterparts, even with non-linear objective functions. This framework is applicable in both full-information and bandit feedback settings, obtaining [square root]T and T3/4 regret respectively. In the second chapter, we focus on the problem of learning non-parametric choice models on digital platforms in an active learning setting. This method involves influencing the data collection process to obtain more favorable data for estimation, in contrast to using only offline data or A/B testing, which might result in limited data sets. In the third and fourth chapters, we incorporate constraints into our optimization problems, which add complexity to the decision space, while still maintaining a large decision space. Specifically, in the third chapter, we propose a bidding strategy for budget-constrained advertisers participating on multiple platforms with different non-IC auction formats. Our proposed non-linear value-pacing-based strategy is optimal in the offline setting and has no-regret in the online setting. Lastly, in the fourth chapter, we incorporate fairness constraints to an assortment optimization problem in digital marketplaces with diverse demographics. We aim to maximize the total market share across groups subject to the condition that the market share of each group meets a predetermined threshold, while also considering legal issues that prevent personalization. We present optimal approximation algorithms for both the offline and online settings.
