We consider the allocation of limited resources to heterogeneous customers who arrive in an online fashion. We would like to allocate the resources "fairly", so that no group of customers is marginalized in terms of their overall service rate. We study whether this is possible to do so in an online fashion, and if so, what a good online allocation policy is.
We model this problem using online bipartite matching under stationary arrivals, a fundamental model in the literature typically studied under the objective of maximizing the total number of customers served. We instead study the objective of maximizing the minimum service rate across all groups, and propose two notions of fairness: long-run and short-run.
For these fairness objectives, we analyze how competitive online algorithms can be, in comparison to offline algorithms which know the sequence of demands in advance. For long-run fairness, we propose two online heuristics (Sampling and Pooling) which establish asymptotic optimality in different regimes (no specialized supplies, no rare demand types, or imbalanced supply/demand). By contrast, outside all of these regimes, we show that the competitive ratio of online algorithms is between 0.632 and 0.732. For short-run fairness, we show for complete bipartite graphs that the competitive ratio of online algorithms is between 0.863 and 0.942; we also derive a probabilistic rejection algorithm which is asymptotically optimal in the total demand.
Depending on the overall scarcity of resources, either our Sampling or Pooling heuristics could be desirable. The most difficult situation for online allocation occurs when the total supply is just enough to serve the total demand.
We simulate our algorithms on a public ride-hailing dataset, which both demonstrates the efficacy of our heuristics and validates our managerial insights.
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；Google Zurich（谷歌苏黎世）；EPFL（洛桑联邦理工学院）；Microsoft Research（微软研究院）
Submodular maximization has become established as the method of choice for the task of selecting representative and diverse summaries of data. However, if datapoints have sensitive attributes such as gender or age, such machine learning algorithms, left unchecked, are known to exhibit bias: under- or over-representation of particular groups. This has made the design of fair machine learning algorithms increasingly important. In this work we address the question: Is it possible to create fair summaries for massive datasets? To this end, we develop the first streaming approximation algorithms fo…
Maximal biclique enumeration is a fundamental problem in bipartite graph data analysis. Existing biclique enumeration methods mainly focus on non-attributed bipartite graphs and also ignore the \emph{fairness} of graph attributes. In this paper, we introduce the concept of fairness into the biclique model for the first time and study the problem of fairness-aware biclique enumeration. Specifically, we propose two fairness-aware biclique models, called \nonesidebc~and \ntwosidebc~respectively. To efficiently enumerate all {\nonesidebc}s, we first present two non-trivial pruning techniques, call…
University of North Texas（北德克萨斯大学）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large dataset. However, data items might have sensitive attributes such as race or gender, in this setting, it is important to design \emph{fairness-aware} algorithms to mitigate potential algorithmic bias that may cause over- or under- representation of particular groups. Motivated by that, we propose and study the classic non-monotone submodular maximization problem…
Streaming Algorithms for Diversity Maximization with Fairness Constraints
East China Normal University（华东师范大学）；Universitat Pompeu Fabra（庞培法布拉大学）；Eurecat – Centre Tecnològic de Catalunya（Eurecat——加泰罗尼亚技术中心）；University of Helsinki（赫尔辛基大学）
Columbia University（哥伦比亚大学）；New Jersey Institute of Technology（新泽西理工学院）；Southeast University（东南大学）
Matching markets involve heterogeneous agents (typically from two parties) who are paired for mutual benefit. During the last decade, matching markets have emerged and grown rapidly through the medium of the Internet. They have evolved into a new format, called Online Matching Markets (OMMs), with examples ranging from crowdsourcing to online recommendations to ridesharing. There are two features distinguishing OMMs from traditional matching markets. One is the dynamic arrival of one side of the market: we refer to these as online agents while the rest are offline agents. Examples of online an…
The influence maximization paradigm has been used by researchers in various fields in order to study how information spreads in social networks. While previously the attention was mostly on efficiency, more recently fairness issues have been taken into account in this scope. In this paper, we propose to use randomization as a mean for achieving fairness. Similar to previous works like Fish et al. (WWW '19) and Tsang et al. (IJCAI '19), we study the maximin criterion for (group) fairness. In contrast to their work however, we model the problem in such a way that, when choosing the seed sets, pr…
Can we efficiently extract useful information from a large user-generated dataset while protecting the privacy of the users and/or ensuring fairness in representation. We cast this problem as an instance of a deletion-robust submodular maximization where part of the data may be deleted due to privacy concerns or fairness criteria. We propose the first memory-efficient centralized, streaming, and distributed methods with constant-factor approximation guarantees against any number of adversarial deletions. We extensively evaluate the performance of our algorithms against prior state-of-the-art o…
Modeling and shaping how information spreads through a network is a major research topic in network analysis. While initially the focus has been mostly on efficiency, recently fairness criteria have been taken into account in this setting. Most work has focused on the maximin criteria however, and thus still different groups can receive very different shares of information. In this work we propose to consider fairness as a notion to be guaranteed by an algorithm rather than as a criterion to be maximized. To this end, we propose three optimization problems that aim at maximizing the overall sp…
Submodular Maximization over Bipartite Perfect Matchings and Matroid Intersection Bases
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Southern Denmark（南丹麦大学）；EPFL Lausanne（洛桑联邦理工学院）；Stanford University（斯坦福大学）；ETH Zürich（苏黎世联邦理工学院）
Group Equality in Adaptive Submodular Maximization
Naveen Jindal School of Management, The University of Texas at Dallas（德克萨斯大学达拉斯分校纳文·金德尔管理学院）；Department of Computer Science and Engineering, The University of North Texas（北德克萨斯大学计算机科学与工程系）
Matching algorithms are used routinely to match donors to recipients for solid organs transplantation, for the assignment of medical residents to hospitals, record linkage in databases, scheduling jobs on machines, network switching, online advertising, and image recognition, among others. Although many optimal solutions may exist to a given matching problem, when the elements that shall or not be included in a solution correspond to individuals, it becomes of paramount importance that the solution be selected fairly. In this paper we study individual fairness in matching problems. Given that …
Bipartite matching, where agents on one side of a market are matched to agents or items on the other, is a classical problem in computer science and economics, with widespread application in healthcare, education, advertising, and general resource allocation. A practitioner's goal is typically to maximize a matching market's economic efficiency, possibly subject to some fairness requirements that promote equal access to resources. A natural balancing act exists between fairness and efficiency in matching markets, and has been the subject of much research. In this paper, we study a complementar…
Most recent papers addressing the algorithmic problem of allocating advertisement space for keywords in sponsored search auctions assume that pricing is done via a first-price auction, which does not realistically model the Generalized Second Price (GSP) auction used in practice. Towards the goal of more realistically modeling these auctions, we introduce the Second-Price Ad Auctions problem, in which bidders' payments are determined by the GSP mechanism. We show that the complexity of the Second-Price Ad Auctions problem is quite different than that of the more studied First-Price Ad Auctions…
The surprising results of Karp, Vazirani and Vazirani and (respectively) Buchbinder et al are examples where rather simple randomizations provide provably better approximations than the corresponding deterministic counterparts for online bipartite matching and (respectively) unconstrained non-monotone submodular maximization. We show that seemingly strong extensions of the deterministic online computation model can at best match the performance of naive randomization. More specifically, for bipartite matching, we show that in the priority model (allowing very general ways to order the input st…
Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes round a fractional point by first rounding each coordinate independently, and then dropping some elements to reach a feasible set. Also the second step, where elements are dropped, is typically randomized. This leads to an additional source of randomization within the procedure, which can complicate the analysis. We suggest a different, polyhedral viewpoint t…
In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions over integer lattice have been defined submodular property that is similar to submodularity of set functions. DR-submodular is a further extended submodular concept for functions over the integer lattice, which captures the diminishing return property. Such functions find many applications in machine learning, social networks, wireless networks, etc. The techniques for submodular set function maximization can be applied to DR-submodular function maximization, e.g., the double greedy alg…
Online matching and its variants are some of the most fundamental problems in the online algorithms literature. In this paper, we study the online weighted bipartite matching problem. Karp et al. (STOC 1990) gave an elegant algorithm in the unweighted case that achieves a tight competitive ratio of $1-1/e$. In the weighted case, however, we can easily show that no competitive ratio is obtainable without the commonly accepted free disposal assumption. Under this assumption, it is not hard to prove that the greedy algorithm is $1/2$ competitive, and that this is tight for deterministic algorithm…
In Bipartite Correlation Clustering (BCC) we are given a complete bipartite graph $G$ with `+' and `-' edges, and we seek a vertex clustering that maximizes the number of agreements: the number of all `+' edges within clusters plus all `-' edges cut across clusters. BCC is known to be NP-hard. We present a novel approximation algorithm for $k$-BCC, a variant of BCC with an upper bound $k$ on the number of clusters. Our algorithm outputs a $k$-clustering that provably achieves a number of agreements within a multiplicative ${(1-δ)}$-factor from the optimal, for any desired accuracy $δ$. It reli…
MIT（麻省理工学院）；TTIC（丰田理工学院）；University of Washington（华盛顿大学）
``Composable core-sets'' are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also be cast as the MAP inference task for determinantal point processes, that have recently gained a lot of interest for modeling diversity and fairness. The problem was recently studied in [IMOR'18], where they designed composable core-sets with the optimal approximation bound of $\tilde O(k)^k$. On the other hand, the more practical Greedy algorithm has been pr…
Fairness in influence maximization has been a very active research topic recently. Most works in this context study the question of how to find seeding strategies (deterministic or probabilistic) such that nodes or communities in the network get their fair share of coverage. Different fairness criteria have been used in this context. All these works assume that the entity that is spreading the information has an inherent interest in spreading the information fairly, otherwise why would they want to use the developed fair algorithms? This assumption may however be flawed in reality -- the sprea…
