15,498 research outputs found
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Overcommitment in Cloud Services -- Bin packing with Chance Constraints
This paper considers a traditional problem of resource allocation, scheduling
jobs on machines. One such recent application is cloud computing, where jobs
arrive in an online fashion with capacity requirements and need to be
immediately scheduled on physical machines in data centers. It is often
observed that the requested capacities are not fully utilized, hence offering
an opportunity to employ an overcommitment policy, i.e., selling resources
beyond capacity. Setting the right overcommitment level can induce a
significant cost reduction for the cloud provider, while only inducing a very
low risk of violating capacity constraints. We introduce and study a model that
quantifies the value of overcommitment by modeling the problem as a bin packing
with chance constraints. We then propose an alternative formulation that
transforms each chance constraint into a submodular function. We show that our
model captures the risk pooling effect and can guide scheduling and
overcommitment decisions. We also develop a family of online algorithms that
are intuitive, easy to implement and provide a constant factor guarantee from
optimal. Finally, we calibrate our model using realistic workload data, and
test our approach in a practical setting. Our analysis and experiments
illustrate the benefit of overcommitment in cloud services, and suggest a cost
reduction of 1.5% to 17% depending on the provider's risk tolerance
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
Outlier detection using distributionally robust optimization under the Wasserstein metric
We present a Distributionally Robust Optimization (DRO) approach to outlier detection in a linear regression setting, where the closeness of probability distributions is measured using the Wasserstein metric. Training samples contaminated with outliers skew the regression plane computed by least squares and thus impede outlier detection. Classical approaches, such as robust regression, remedy this problem by downweighting the contribution of atypical data points. In contrast, our Wasserstein DRO approach hedges against a family of distributions that are close to the empirical distribution. We show that the resulting formulation encompasses a class of models, which include the regularized Least Absolute Deviation (LAD) as a special case. We provide new insights into the regularization term and give guidance on the selection of the regularization coefficient from the standpoint of a confidence region. We establish two types of performance guarantees for the solution to our formulation under mild conditions. One is related to its out-of-sample behavior, and the other concerns the discrepancy between the estimated and true regression planes. Extensive numerical results demonstrate the superiority of our approach to both robust regression and the regularized LAD in terms of estimation accuracy and outlier detection rates
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