820 research outputs found
Non-Smooth, H\"older-Smooth, and Robust Submodular Maximization
We study the problem of maximizing a continuous DR-submodular function that
is not necessarily smooth. We prove that the continuous greedy algorithm
achieves an [(1-1/e)\OPT-\epsilon] guarantee when the function is monotone
and H\"older-smooth, meaning that it admits a H\"older-continuous gradient. For
functions that are non-differentiable or non-smooth, we propose a variant of
the mirror-prox algorithm that attains an [(1/2)\OPT-\epsilon] guarantee. We
apply our algorithmic frameworks to robust submodular maximization and
distributionally robust submodular maximization under Wasserstein ambiguity. In
particular, the mirror-prox method applies to robust submodular maximization to
obtain a single feasible solution whose value is at least (1/2)\OPT-\epsilon.
For distributionally robust maximization under Wasserstein ambiguity, we deduce
and work over a submodular-convex maximin reformulation whose objective
function is H\"older-smooth, for which we may apply both the continuous greedy
and the mirror-prox algorithms
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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