Uncertainty Quantification for Demand Prediction in Contextual Dynamic Pricing
Warrington College of Business, University of Florida（佛罗里达大学沃灵顿商学院）；Leonard N. Stern School of Business, New York University（纽约大学伦纳德·N·斯特恩商学院）；School of Management, Xi’an Jiaotong University（西安交通大学管理学院）；Shanghai University of Finance and Economics（上海财经大学）
Data-driven sequential decision has found a wide range of applications in modern operations management, such as dynamic pricing, inventory control, and assortment optimization. Most existing research on data-driven sequential decision focuses on designing an online policy to maximize the revenue. However, the research on uncertainty quantification on the underlying true model function (e.g., demand function), a critical problem for practitioners, has not been well explored. In this paper, using the problem of demand function prediction in dynamic pricing as the motivating example, we study the problem of constructing accurate confidence intervals for the demand function. The main challenge is that sequentially collected data leads to significant distributional bias in the maximum likelihood estimator or the empirical risk minimization estimate, making classical statistics approaches such as the Wald's test no longer valid. We address this challenge by developing a debiased approach and provide the asymptotic normality guarantee of the debiased estimator. Based this the debiased estimator, we provide both point-wise and uniform confidence intervals of the demand function.
The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Purdue University（普渡大学）
Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customer's valuation for the product is a linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customer's true valuation, but instead needs to learn the valuation by leveraging contextual information and historical binary purchase feedbacks. Existing models typically assume full or partial knowledge of the ran…
Minimax Optimality in Contextual Dynamic Pricing with General Valuation Models
School of Management, Xiamen University（厦门大学管理学院）；Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析系）
Sloan School of Management, Massachusetts Institute of Technology（麻省理工学院斯隆管理学院）；University of Southern California（南加州大学）；Google Research（谷歌研究院）
Motivated by pricing in ad exchange markets, we consider the problem of robust learning of reserve prices against strategic buyers in repeated contextual second-price auctions. Buyers' valuations for an item depend on the context that describes the item. However, the seller is not aware of the relationship between the context and buyers' valuations, i.e., buyers' preferences. The seller's goal is to design a learning policy to set reserve prices via observing the past sales data, and her objective is to minimize her regret for revenue, where the regret is computed against a clairvoyant policy …
Delft University of Technology（代尔夫特理工大学）；University of Copenhagen（哥本哈根大学）
Estimating uncertainty of machine learning models is essential to assess the quality of the predictions that these models provide. However, there are several factors that influence the quality of uncertainty estimates, one of which is the amount of model misspecification. Model misspecification always exists as models are mere simplifications or approximations to reality. The question arises whether the estimated uncertainty under model misspecification is reliable or not. In this paper, we argue that model misspecification should receive more attention, by providing thought experiments and co…
Utility Fairness in Contextual Dynamic Pricing with Demand Learning
Leonard N. Stern School of Business, New York University（纽约大学莱昂纳德·N·斯特恩商学院）；Naveen Jindal School of Management, University of Texas at Dallas（德克萨斯大学达拉斯分校纳文·金达尔管理学院）
Darden School of Business, University of Virginia（弗吉尼亚大学达顿商学院）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；IBM Watson（IBM沃森）
We study a pricing setting where each customer is offered a contextualized price based on customer and/or product features. Often only historical sales data are available, so we observe whether a customer purchased a product at the price prescribed rather than the customer's true valuation. Such observational data are influenced by historical pricing policies, which introduce difficulties in evaluating the effectiveness of future policies. The goal of this paper is to formulate loss functions that can be used for evaluating pricing policies directly from observational data, rather than going t…
Darden School of Business, University of Virginia（弗吉尼亚大学达顿商学院）
We study an off-policy contextual pricing problem where the seller has access to samples of prices that customers were previously offered, whether they purchased at that price, and auxiliary features describing the customer and/or item being sold. This is in contrast to the well-studied setting in which samples of the customer's valuation (willingness to pay) are observed. In our setting, the observed data is influenced by the previous pricing policy, and we do not know how customers would have responded to alternative prices. We introduce suitable loss functions for this setting that can be d…
Motivated by the application of real-time pricing in e-commerce platforms, we consider the problem of revenue-maximization in a setting where the seller can leverage contextual information describing the customer's history and the product's type to predict her valuation of the product. However, her true valuation is unobservable to the seller, only binary outcome in the form of success-failure of a transaction is observed. Unlike in usual contextual bandit settings, the optimal price/arm given a covariate in our setting is sensitive to the detailed characteristics of the residual uncertainty d…
We consider a dynamic pricing problem for repeated contextual second-price auctions with multiple strategic buyers who aim to maximize their long-term time discounted utility. The seller has limited information on buyers' overall demand curves which depends on a non-parametric market-noise distribution, and buyers may potentially submit corrupted bids (relative to true valuations) to manipulate the seller's pricing policy for more favorable reserve prices in the future. We focus on designing the seller's learning policy to set contextual reserve prices where the seller's goal is to minimize re…
In this paper, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to Javanmard and Nazerzadeh [2019] except that we expand the demand curve to a semiparametric model and need to learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision-making policy that combines semiparametric estimation from a generali…
Prompt-Dependent Ranking of Large Language Models with Uncertainty Quantification
Department of Statistics and Data Science, UCLA（统计与数据科学系，加州大学洛杉矶分校）；Department of Statistics, University of Michigan（统计系，密歇根大学）；Department of Statistics and Data Science, and of Biostatistics, UCLA（统计与数据科学系及生物统计学系，加州大学洛杉矶分校）
Mitchell E. Daniels, Jr. School of Business, Purdue University（普渡大学米切尔·E·丹尼尔斯 Jr.商学院）；Department of Statistics and Data Science, Yale University（耶鲁大学统计与数据科学系）；Department of Industrial Engineering and Management Sciences, Northwestern University（西北大学工业工程与管理科学系）
University of Illinois（伊利诺伊大学）；Deepair LLC（Deepair有限责任公司）；University of Notre Dame（圣母大学）
Traditional AI approaches in customized (personalized) contextual pricing applications assume that the data distribution at the time of online pricing is similar to that observed during training. However, this assumption may be violated in practice because of the dynamic nature of customer buying patterns, particularly due to unanticipated system shocks such as COVID-19. We study the changes in customer behavior for a major airline during the COVID-19 pandemic by framing it as a covariate shift and concept drift detection problem. We identify which customers changed their travel and purchase b…
University of Science and Technology of China（中国科学技术大学）；Beijing Institute of Control Engineering（北京控制工程研究所）
The high dynamics and heterogeneous interactions in the complicated urban systems have raised the issue of uncertainty quantification in spatiotemporal human mobility, to support critical decision-makings in risk-aware web applications such as urban event prediction where fluctuations are of significant interests. Given the fact that uncertainty quantifies the potential variations around prediction results, traditional learning schemes always lack uncertainty labels, and conventional uncertainty quantification approaches mostly rely upon statistical estimations with Bayesian Neural Networks or…
We study off-policy evaluation and learning from sequential data in a structured class of Markov decision processes that arise from repeated interactions with an exogenous sequence of arrivals with contexts, which generate unknown individual-level responses to agent actions. This model can be thought of as an offline generalization of contextual bandits with resource constraints. We formalize the relevant causal structure of problems such as dynamic personalized pricing and other operations management problems in the presence of potentially high-dimensional user types. The key insight is that …
We present Bayesian Spillover Graphs (BSG), a novel method for learning temporal relationships, identifying critical nodes, and quantifying uncertainty for multi-horizon spillover effects in a dynamic system. BSG leverages both an interpretable framework via forecast error variance decompositions (FEVD) and comprehensive uncertainty quantification via Bayesian time series models to contextualize temporal relationships in terms of systemic risk and prediction variability. Forecast horizon hyperparameter $h$ allows for learning both short-term and equilibrium state network behaviors. Experiments…
We consider the problem of multi-product dynamic pricing, in a contextual setting, for a seller of differentiated products. In this environment, the customers arrive over time and products are described by high-dimensional feature vectors. Each customer chooses a product according to the widely used Multinomial Logit (MNL) choice model and her utility depends on the product features as well as the prices offered. The seller a-priori does not know the parameters of the choice model but can learn them through interactions with customers. The seller's goal is to design a pricing policy that maxim…
In this paper, we propose deep learning algorithms for ranking response surfaces, with applications to optimal stopping problems in financial mathematics. The problem of ranking response surfaces is motivated by estimating optimal feedback policy maps in stochastic control problems, aiming to efficiently find the index associated to the minimal response across the entire continuous input space $\mathcal{X} \subseteq \mathbb{R}^d$. By considering points in $\mathcal{X}$ as pixels and indices of the minimal surfaces as labels, we recast the problem as an image segmentation problem, which assigns…
