We consider the problem of PAC learning the most valuable item from a pool of $n$ items using sequential, adaptively chosen plays of subsets of $k$ items, when, upon playing a subset, the learner receives relative feedback sampled according to a general Random Utility Model (RUM) with independent noise perturbations to the latent item utilities. We identify a new property of such a RUM, termed the minimum advantage, that helps in characterizing the complexity of separating pairs of items based on their relative win/loss empirical counts, and can be bounded as a function of the noise distribution alone. We give a learning algorithm for general RUMs, based on pairwise relative counts of items and hierarchical elimination, along with a new PAC sample complexity guarantee of $O(\frac{n}{c^2ε^2} \log \frac{k}δ)$ rounds to identify an $ε$-optimal item with confidence $1-δ$, when the worst case pairwise advantage in the RUM has sensitivity at least $c$ to the parameter gaps of items. Fundamental lower bounds on PAC sample complexity show that this is near-optimal in terms of its dependence on $n,k$ and $c$.
Keep Everyone Happy: Online Fair Division of Numerous Items with Few Copies
Singapore-MIT Alliance for Research and Technology（新加坡-麻省理工联合研究技术联盟）；Faculty of ISEE, Kyushu University（九州大学信息科学与工程学院）；Department of Computer Science, National University of Singapore（新加坡国立大学计算机科学系）
Learning to Select and Rank from Choice-Based Feedback: A Simple Nested Approach
Institute of Operations Research and Analytics, National University of Singapore（新加坡国立大学运营研究与分析研究所）；NUS Business School, National University of Singapore（新加坡国立大学商学院）
The intersection of learning to rank and choice modeling is an active area of research with applications in e-commerce, information retrieval and the social sciences. In some applications such as recommendation systems, the statistician is primarily interested in recovering the set of the top ranked items from a large pool of items as efficiently as possible using passively collected discrete choice data, i.e., the user picks one item from a set of multiple items. Motivated by this practical consideration, we propose the choice-based Borda count algorithm as a fast and accurate ranking algorit…
Yale（耶鲁大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Purdue University（普渡大学）
When tracking user-specific online activities, each user's preference is revealed in the form of choices and comparisons. For example, a user's purchase history is a record of her choices, i.e. which item was chosen among a subset of offerings. A user's preferences can be observed either explicitly as in movie ratings or implicitly as in viewing times of news articles. Given such individualized ordinal data in the form of comparisons and choices, we address the problem of collaboratively learning representations of the users and the items. The learned features can be used to predict a user's p…
In many high-throughput experimental design settings, such as those common in biochemical engineering, batched queries are more cost effective than one-by-one sequential queries. Furthermore, it is often not possible to directly choose items to query. Instead, the experimenter specifies a set of constraints that generates a library of possible items, which are then selected stochastically. Motivated by these considerations, we investigate \emph{Batched Stochastic Bayesian Optimization} (BSBO), a novel Bayesian optimization scheme for choosing the constraints in order to guide exploration towar…
Multinomial logit bandit is a sequential subset selection problem which arises in many applications. In each round, the player selects a $K$-cardinality subset from $N$ candidate items, and receives a reward which is governed by a {\it multinomial logit} (MNL) choice model considering both item utility and substitution property among items. The player's objective is to dynamically learn the parameters of MNL model and maximize cumulative reward over a finite horizon $T$. This problem faces the exploration-exploitation dilemma, and the involved combinatorial nature makes it non-trivial. In rece…
Institute for Basic Science（基础科学研究院）；London School of Economics（伦敦政治经济学院）；KAIST（韩国科学技术院）
Motivated by recent developments in designing algorithms based on individual item scores for solving utility maximization problems, we study the framework of using test scores, defined as a statistic of observed individual item performance data, for solving the budgeted stochastic utility maximization problem. We extend an existing scoring mechanism, namely the replication test scores, to incorporate heterogeneous item costs as well as item values. We show that a natural greedy algorithm that selects items solely based on their replication test scores outputs solutions within a constant factor…
Centre for Pattern Recognition and Data Analytics（模式识别与数据分析中心）；Deakin University（迪肯大学）
We introduce Neural Choice by Elimination, a new framework that integrates deep neural networks into probabilistic sequential choice models for learning to rank. Given a set of items to chose from, the elimination strategy starts with the whole item set and iteratively eliminates the least worthy item in the remaining subset. We prove that the choice by elimination is equivalent to marginalizing out the random Gompertz latent utilities. Coupled with the choice model is the recently introduced Neural Highway Networks for approximating arbitrarily complex rank functions. We evaluate the proposed…
Technical University of Denmark (DTU)（丹麦技术大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Specifying utility functions is a key step towards applying the discrete choice framework for understanding the behaviour processes that govern user choices. However, identifying the utility function specifications that best model and explain the observed choices can be a very challenging and time-consuming task. This paper seeks to help modellers by leveraging the Bayesian framework and the concept of automatic relevance determination (ARD), in order to automatically determine an optimal utility function specification from an exponentially large set of possible specifications in a purely data…
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received significant attention is the Plackett-Luce model, for which fast inference methods for maximum likelihood estimators are available. This paper develops conditions on general random utility models that enable fast inference within a Bayesian framework through MC-EM, providing concave loglikelihood functions and bounded sets of glob…
ETH Zurich（苏黎世联邦理工学院）；Amadeus IT Group SA（艾玛迪斯信息技术集团股份公司）
Suppose there is a large collection of items, each with an associated cost and an inherent utility that is revealed only once we commit to selecting it. Given a budget on the cumulative cost of the selected items, how can we pick a subset of maximal value? This task generalizes several important problems such as multi-arm bandits, active search and the knapsack problem. We present an algorithm, GP-Select, which utilizes prior knowledge about similarity be- tween items, expressed as a kernel function. GP-Select uses Gaussian process prediction to balance exploration (estimating the unknown valu…
Towards Efficient Pareto-optimal Utility-Fairness between Groups in Repeated Rankings
College of Engineering & Computer Science, VinUniversity（VinUniversity工程与计算机科学学院）；University of Engineering and Technology, Vietnam National University（越南国家大学工程技术大学）
Massachusetts Institute of Technology（麻省理工学院）；Amazon Search（亚马逊搜索）；Amazon Music（亚马逊音乐）；UT Austin（德克萨斯大学奥斯汀分校）
Conventional methods for query autocompletion aim to predict which completed query a user will select from a list. A shortcoming of this approach is that users often do not know which query will provide the best retrieval performance on the current information retrieval system, meaning that any query autocompletion methods trained to mimic user behavior can lead to suboptimal query suggestions. To overcome this limitation, we propose a new approach that explicitly optimizes the query suggestions for downstream retrieval performance. We formulate this as a problem of ranking a set of rankings, …
Whereas deep neural network (DNN) is increasingly applied to choice analysis, it is challenging to reconcile domain-specific behavioral knowledge with generic-purpose DNN, to improve DNN's interpretability and predictive power, and to identify effective regularization methods for specific tasks. This study designs a particular DNN architecture with alternative-specific utility functions (ASU-DNN) by using prior behavioral knowledge. Unlike a fully connected DNN (F-DNN), which computes the utility value of an alternative k by using the attributes of all the alternatives, ASU-DNN computes it by …
The fair-ranking problem, which asks to rank a given set of items to maximize utility subject to group fairness constraints, has received attention in the fairness, information retrieval, and machine learning literature. Recent works, however, observe that errors in socially-salient (including protected) attributes of items can significantly undermine fairness guarantees of existing fair-ranking algorithms and raise the problem of mitigating the effect of such errors. We study the fair-ranking problem under a model where socially-salient attributes of items are randomly and independently pertu…
There is a growing need for discrete choice models that account for the complex nature of human choices, escaping traditional behavioral assumptions such as the transitivity of pairwise preferences. Recently, several parametric models of intransitive comparisons have been proposed, but in all cases the maximum likelihood problem is non-concave, making inference difficult. In this work we generalize this trend, showing that there cannot exist any parametric model with a concave log-likelihood function that can exhibit intransitive preferences. Given this result, we motivate a new model for anal…
We consider the problem of computing a sequence of rankings that maximizes consumer-side utility while minimizing producer-side individual unfairness of exposure. While prior work has addressed this problem using linear or quadratic programs on bistochastic matrices, such approaches, relying on Birkhoff-von Neumann (BvN) decompositions, are too slow to be implemented at large scale. In this paper we introduce a geometrical object, a polytope that we call expohedron, whose points represent all achievable exposures of items for a Position Based Model (PBM). We exhibit some of its properties and …
Tencent AI Lab（腾讯人工智能实验室）；AI Foundations Lab, IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心人工智能基础实验室）；University of California, Davis（加州大学戴维斯分校）；IBM Research AI（IBM人工智能研究院）；National Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）
Recommendation for e-commerce with a mix of durable and nondurable goods has characteristics that distinguish it from the well-studied media recommendation problem. The demand for items is a combined effect of form utility and time utility, i.e., a product must both be intrinsically appealing to a consumer and the time must be right for purchase. In particular for durable goods, time utility is a function of inter-purchase duration within product category because consumers are unlikely to purchase two items in the same category in close temporal succession. Moreover, purchase data, in contrast…
