338 research outputs found
Balancing Utility and Fairness in Submodular Maximization (Technical Report)
Submodular function maximization is central in numerous data science
applications, including data summarization, influence maximization, and
recommendation. In many of these problems, our goal is to find a solution that
maximizes the \emph{average} of the utilities for all users, each measured by a
monotone submodular function. When the population of users is composed of
several demographic groups, another critical problem is whether the utility is
fairly distributed across groups. In the context of submodular optimization, we
seek to improve the welfare of the \emph{least well-off} group, i.e., to
maximize the minimum utility for any group, to ensure fairness. Although the
\emph{utility} and \emph{fairness} objectives are both desirable, they might
contradict each other, and, to our knowledge, little attention has been paid to
optimizing them jointly. In this paper, we propose a novel problem called
\emph{Bicriteria Submodular Maximization} (BSM) to strike a balance between
utility and fairness. Specifically, it requires finding a fixed-size solution
to maximize the utility function, subject to the value of the fairness function
not being below a threshold. Since BSM is inapproximable within any constant
factor in general, we propose efficient data-dependent approximation algorithms
for BSM by converting it into other submodular optimization problems and
utilizing existing algorithms for the converted problems to obtain solutions to
BSM. Using real-world and synthetic datasets, we showcase applications of our
framework in three submodular maximization problems, namely maximum coverage,
influence maximization, and facility location.Comment: 13 pages, 7 figures, under revie
Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization
Creating impact in real-world settings requires artificial intelligence
techniques to span the full pipeline from data, to predictive models, to
decisions. These components are typically approached separately: a machine
learning model is first trained via a measure of predictive accuracy, and then
its predictions are used as input into an optimization algorithm which produces
a decision. However, the loss function used to train the model may easily be
misaligned with the end goal, which is to make the best decisions possible.
Hand-tuning the loss function to align with optimization is a difficult and
error-prone process (which is often skipped entirely).
We focus on combinatorial optimization problems and introduce a general
framework for decision-focused learning, where the machine learning model is
directly trained in conjunction with the optimization algorithm to produce
high-quality decisions. Technically, our contribution is a means of integrating
common classes of discrete optimization problems into deep learning or other
predictive models, which are typically trained via gradient descent. The main
idea is to use a continuous relaxation of the discrete problem to propagate
gradients through the optimization procedure. We instantiate this framework for
two broad classes of combinatorial problems: linear programs and submodular
maximization. Experimental results across a variety of domains show that
decision-focused learning often leads to improved optimization performance
compared to traditional methods. We find that standard measures of accuracy are
not a reliable proxy for a predictive model's utility in optimization, and our
method's ability to specify the true goal as the model's training objective
yields substantial dividends across a range of decision problems.Comment: Full version of paper accepted at AAAI 201
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