38 research outputs found
Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity
In bipartite matching problems, vertices on one side of a bipartite graph are
paired with those on the other. In its online variant, one side of the graph is
available offline, while the vertices on the other side arrive online. When a
vertex arrives, an irrevocable and immediate decision should be made by the
algorithm; either match it to an available vertex or drop it. Examples of such
problems include matching workers to firms, advertisers to keywords, organs to
patients, and so on. Much of the literature focuses on maximizing the total
relevance---modeled via total weight---of the matching. However, in many
real-world problems, it is also important to consider contributions of
diversity: hiring a diverse pool of candidates, displaying a relevant but
diverse set of ads, and so on. In this paper, we propose the Online Submodular
Bipartite Matching (\osbm) problem, where the goal is to maximize a submodular
function over the set of matched edges. This objective is general enough to
capture the notion of both diversity (\emph{e.g.,} a weighted coverage
function) and relevance (\emph{e.g.,} the traditional linear function)---as
well as many other natural objective functions occurring in practice
(\emph{e.g.,} limited total budget in advertising settings). We propose novel
algorithms that have provable guarantees and are essentially optimal when
restricted to various special cases. We also run experiments on real-world and
synthetic datasets to validate our algorithms.Comment: To appear in AAAI 201
Ranking with Slot Constraints
We introduce the problem of ranking with slot constraints, which can be used
to model a wide range of application problems -- from college admission with
limited slots for different majors, to composing a stratified cohort of
eligible participants in a medical trial. We show that the conventional
Probability Ranking Principle (PRP) can be highly sub-optimal for
slot-constrained ranking problems, and we devise a new ranking algorithm,
called MatchRank. The goal of MatchRank is to produce rankings that maximize
the number of filled slots if candidates are evaluated by a human decision
maker in the order of the ranking. In this way, MatchRank generalizes the PRP,
and it subsumes the PRP as a special case when there are no slot constraints.
Our theoretical analysis shows that MatchRank has a strong approximation
guarantee without any independence assumptions between slots or candidates.
Furthermore, we show how MatchRank can be implemented efficiently. Beyond the
theoretical guarantees, empirical evaluations show that MatchRank can provide
substantial improvements over a range of synthetic and real-world tasks
Online Algorithms for Matchings with Proportional Fairness Constraints and Diversity Constraints
Matching problems with group-fairness constraints and diversity constraints
have numerous applications such as in allocation problems, committee selection,
school choice, etc. Moreover, online matching problems have lots of
applications in ad allocations and other e-commerce problems like product
recommendation in digital marketing.
We study two problems involving assigning {\em items} to {\em platforms},
where items belong to various {\em groups} depending on their attributes; the
set of items are available offline and the platforms arrive online. In the
first problem, we study online matchings with {\em proportional fairness
constraints}. Here, each platform on arrival should either be assigned a set of
items in which the fraction of items from each group is within specified bounds
or be assigned no items; the goal is to assign items to platforms in order to
maximize the number of items assigned to platforms.
In the second problem, we study online matchings with {\em diversity
constraints}, i.e. for each platform, absolute lower bounds are specified for
each group. Each platform on arrival should either be assigned a set of items
that satisfy these bounds or be assigned no items; the goal is to maximize the
set of platforms that get matched. We study approximation algorithms and
hardness results for these problems. The technical core of our proofs is a new
connection between these problems and the problem of matchings in hypergraphs.
Our experimental evaluation shows the performance of our algorithms on
real-world and synthetic datasets exceeds our theoretical guarantees.Comment: 16 pages, Full version of a paper accepted in ECAI 202
Two-Sided Capacitated Submodular Maximization in Gig Platforms
In this paper, we propose three generic models of capacitated coverage and,
more generally, submodular maximization to study task-worker assignment
problems that arise in a wide range of gig economy platforms. Our models
incorporate the following features: (1) Each task and worker can have an
arbitrary matching capacity, which captures the limited number of copies or
finite budget for the task and the working capacity of the worker; (2) Each
task is associated with a coverage or, more generally, a monotone submodular
utility function. Our objective is to design an allocation policy that
maximizes the sum of all tasks' utilities, subject to capacity constraints on
tasks and workers. We consider two settings: offline, where all tasks and
workers are static, and online, where tasks are static while workers arrive
dynamically. We present three LP-based rounding algorithms that achieve optimal
approximation ratios of for offline coverage
maximization, competitive ratios of and
for online coverage and online monotone submodular maximization,
respectively.Comment: This paper was accepted to the 19th Conference on Web and Internet
Economics (WINE), 202
A Bilevel Formalism for the Peer-Reviewing Problem
Due to the large number of submissions that more and more conferences
experience, finding an automatized way to well distribute the submitted papers
among reviewers has become necessary. We model the peer-reviewing matching
problem as a {\it bilevel programming (BP)} formulation. Our model consists of
a lower-level problem describing the reviewers' perspective and an upper-level
problem describing the editors'. Every reviewer is interested in minimizing
their overall effort, while the editors are interested in finding an allocation
that maximizes the quality of the reviews and follows the reviewers'
preferences the most. To the best of our knowledge, the proposed model is the
first one that formulates the peer-reviewing matching problem by considering
two objective functions, one to describe the reviewers' viewpoint and the other
to describe the editors' viewpoint. We demonstrate that both the upper-level
and lower-level problems are feasible and that our BP model admits a solution
under mild assumptions. After studying the properties of the solutions, we
propose a heuristic to solve our model and compare its performance with the
relevant state-of-the-art methods. Extensive numerical results show that our
approach can find fairer solutions with competitive quality and less effort
from the reviewers.Comment: 14 pages, 7 figure
Online Dependent Rounding Schemes
We study the abstract problem of rounding fractional bipartite -matchings
online. The input to the problem is an unknown fractional bipartite
-matching, exposed node-by-node on one side. The objective is to maximize
the \emph{rounding ratio} of the output matching , which is the
minimum over all fractional -matchings , and edges , of the
ratio . In offline settings, many dependent rounding
schemes achieving a ratio of one and strong negative correlation properties are
known (e.g., Gandhi et al., J.ACM'06 and Chekuri et al., FOCS'10), and have
found numerous applications. Motivated by online applications, we present
\emph{online dependent-rounding schemes} (ODRSes) for -matching.
For the special case of uniform matroids (single offline node), we present a
simple online algorithm with a rounding ratio of one. Interestingly, we show
that our algorithm yields \emph{the same distribution} as its classic offline
counterpart, pivotal sampling (Srinivasan, FOCS'01), and so inherits the
latter's strong correlation properties. In arbitrary bipartite graphs, an
online rounding ratio of one is impossible, and we show that a combination of
our uniform matroid ODRS with repeated invocations of \emph{offline} contention
resolution schemes (CRSes) yields a rounding ratio of . Our
main technical contribution is an ODRS breaking this pervasive bound, yielding
rounding ratios of and for -matchings and simple matchings,
respectively. We obtain these results by grouping nodes and using CRSes for
negatively-correlated distributions, together with a new method we call
\emph{group discount and individual markup}, analyzed using the theory of
negative association. We present a number of applications of our ODRSes to
online edge coloring, several stochastic optimization problems, and algorithmic
fairness
Learning for Edge-Weighted Online Bipartite Matching with Robustness Guarantees
Many problems, such as online ad display, can be formulated as online
bipartite matching. The crucial challenge lies in the nature of
sequentially-revealed online item information, based on which we make
irreversible matching decisions at each step. While numerous expert online
algorithms have been proposed with bounded worst-case competitive ratios, they
may not offer satisfactory performance in average cases. On the other hand,
reinforcement learning (RL) has been applied to improve the average
performance, but it lacks robustness and can perform arbitrarily poorly. In
this paper, we propose a novel RL-based approach to edge-weighted online
bipartite matching with robustness guarantees (LOMAR), achieving both good
average-case and worst-case performance. The key novelty of LOMAR is a new
online switching operation which, based on a judicious condition to hedge
against future uncertainties, decides whether to follow the expert's decision
or the RL decision for each online item. We prove that for any ,
LOMAR is -competitive against any given expert online algorithm. To
improve the average performance, we train the RL policy by explicitly
considering the online switching operation. Finally, we run empirical
experiments to demonstrate the advantages of LOMAR compared to existing
baselines. Our code is available at: https://github.com/Ren-Research/LOMARComment: Accepted by ICML 202