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November 810, 2015
ROBUST OPTIMIZATION in applied probability
SUMMARY The aim of this workshop is to bring together leaders whose expertise
spans two areas of research: robust optimization & applied probability. ORGANISERS
CONFIRMED SPEAKERS
MONDAY November 9
TUESDAY November 10
*************************************************************************************************************************************** Chaitanya Bandi Tractable SimulationOptimization: A Robust Optimization Approach To understand and optimize the performance of a system under uncertainty, the traditional approach consists of positing a probability distribution over the uncertain parameters, and derive information on the system performance and optimize it. When the system’s dynamics are complex, computing the above expression analytically becomes challenging, and simulation becomes the only resort. However, simulation models may take a considerable amount of time for the results to be statistically significant and can often be complex, making it difficult to understand and further optimize key qualitative insights. Motivated by these challenges, we propose a robust optimization approach to analyzing and optimizing the expected performance of stochastic systems characterized by linear dynamics, based on a robust optimization framework. Our approach consists of the following steps: (1) We model uncertainty via polyhedral sets inspired by the limit laws of probability. The size of these sets is characterized by few variability parameters, which controls the degree of conservatism of the model. (2) We then cast the performance analysis problem as a optimization problem, for instance maximizing a given performance measure subject to the system’s dynamics and the parametric uncertainty sets. The output of this optimization can be thought of as a worst case performance measure function of the variability parameters. (3) Instead of computing the expected performance of the system via averaging simulation outputs, we assume the variability parameters follow limiting distributions (derivatives of the normal distribution for lighttailed systems and the stable distribution for heavytailed systems) and average the worst case outputs from the optimization over a discretized space over the variability parameters. (4) To optimize the stochastic system, we propose to cast the problem of finding the optimal design input via a robust optimization problem, e.g., minimizing the average or conditional valueatrisk of the worst case performance outputs. This framework allows a significant reduction in the dimension of uncertainty which provides grounds for tractable analyses. We illustrate the tractability and accuracy of our approach by (a) simulating the transient behavior of multiserver feedforward queueing networks, and (b) determining optimal base stock policies of generalized supply chain networks. This is joint work with Dimitris Bertsimas and Nataly Youssef. Aharon BenTal Robust Solutions of Uncertain Optimization Problems under Ambiguous Stochastic Data We show how robust optimization can provide tractable safe approximations to probabilistic constrains (chance constraints) even under partial information (ambiguity) on the random parameters. In particular we address the case where the only available information is on means and dispersion measures. Unlike previous attempts, using the variance as the dispersion measure, here we derive tight approximations using the MAD (mean absolute deviation). The theory is applied to problems in portfolio selection, inventory control and antenna array design. Erick Delage The Value of Distribution Information in Distributionally Robust Optimization Decisions often need to be made with incomplete knowledge about some parameters of the problem. While formulating a stochastic model that captures accurately this knowledge can be a costly task, solving a distributionally robust optimization model that makes use of historical data can provide useful guidance. Unfortunately, one might worry of being misled by distributionally robust solutions and be tempted to invest in the acquisition of more data before committing to a decision. In this work, we propose tractable methods for bounding the value of additional (or more accurate) distribution information in a twostage linear program with objective uncertainty. David Goldberg Distributionally robust inventory control when demand is a martingale Demand forecasting plays an
important role in many inventory control problems. To mitigate the
potential harms of model misspecification, various forms of
distributionally robust optimization have been applied. Although many of
these methodologies suffer from the problem of timeinconsistency, the
work of Klabjan et al. established a general timeconsistent framework
for such problems by connecting to the literature on robust Markov
decision processes. Varun Gupta Online stochastic bin packing In online bin packing, a sequence of items is revealed oneatatime and must be packed in a feasible bin (from a collection of infinite bins). The goal is to minimize the number of bins used at the end of the packing horizon, the usual measure of performance being regret against the offlineoptimal packing. In the stochastic version of the problem one further assumes that item sizes are i.i.d. samples from an unknown distribution. We will first propose an algorithm that is the first asymptotically optimal algorithm while being truly distribution oblivious. In addition, we present three flavors of robustness guarantees for noni.i.d. sequences. Bernd Heidergott (short talk) Statistics, Applied Probability and the Human Factor In the past decades we have witnessed a paradigmshift from scarcity of data to abundance of data. How to deal with this datarevolution that is driven mainly by computer science and statistics? In my opinion the most challenging question is how to marry data science with the wealth of knowledge on models in applied probability. Rather than discarding analytical models and the analysis thereof, I advocate to build a shell around these models to allow for data dependency in a controlled way. Here, the word ``model'' refers to stochastic models describing a phenomenon such as, for example, the stationary throughput in a queuing system. An instance of a stochastic model is obtained by choosing the actual values of parameters defining the underlying dynamics of the model. Parameter insecurity refers to subjective probabilities (inferred by data) and I will argue that behavioral techniques should be incorporated into the analysis, thus bringing the human decision taker into the picture. For an example from queuing theory I will show how the density of the model outcome under parameter insecurity can be evaluated using the technique of nested derivatives and how this allows to jointly address the epistemological and aleatoric insecurity. Dick den Hertog Tutorial on robust optimization This tutorial will provide you a basic understanding of practical robust optimization. Optimization problems in practice often contain parameters that are uncertain, due to e.g. estimation or rounding. The idea of robust optimization is to find a solution that is immune against these uncertainties. The last two decades efficient methods have been developed to find such robust solutions. The underlying idea is to formulate an uncertainty region for the uncertain parameters, and then require that the constraints should hold for all parameter values in this uncertainty region. It can be shown that e.g. for linear programming, for the most important choices of the uncertainty region, the robust optimization problem can be reformulated as linear programming or conic quadratic programming problems, for which very efficient solvers are available nowadays. In this tutorial we restrict ourselves to linear programming; extensions to nonlinear programming are briefly sketched. We will treat the basics of robust linear optimization, and also show the huge value of robust optimization in (dynamic) multistage problems. Attention will also be given to important modelling issues in robust optimization. We also shortly introduce distributionally robust optimization, since several talks in this workshop deal with this topic. Different applications of (adjustable) robust optimization will be given in the tutorial. Robust optimization has already shown its high practical value in many fields: logistics, engineering, finance, medicine, etc. Some stateoftheart modelling packages have already implemented robust optimization technology. Sandeep Juneja (short talk) Selecting the best population using large deviations and multiarmed bandit methods Consider the problem of finding a population amongst many with the smallest mean when these means are unknown but population samples can be generated. Typically, by selecting a population with the smallest sample mean, it can be shown that the false selection probability decays at an exponential rate. Lately researchers have sought algorithms that guarantee that this probability is restricted to a small d in order log(1/d) computational time by estimating the associated large deviations rate function via simulation. We show that such guarantees are misleading. Enroute, we identify the large deviations principle followed by the empirically estimated large deviations rate function that may also be of independent interest. Further, we show a negative result that when populations have unbounded support, any policy that asymptotically identifies the correct population with probability at least 1d for each problem instance requires more than O(log(1/d)) samples in making such a determination in any problem instance. This suggests that some restrictions are essential on populations to devise O(log(1/d)) algorithms with 1d correctness guarantees. We note that under restriction on population moments, such methods are easily designed. Further, under similar restrictions, sequential methods from multiarmed bandit literature can also be adapted to devise such algorithms. Nathan Kallus Robust SAA and the Statistics of DRO The sample average approximation (SAA) is the standard approach to datadriven optimization. While it enjoys computational tractability and asymptotic convergence guarantees, it is known to produce unstable results and to lack strong, general finitesample guarantees. We study a robustification of SAA via distributionally robust optimization (DRO) with respect to confidence regions of goodnessoffit (GoF) tests and explore its computational and statistical properties. We develop theory that intimately links guarantees and convergence of datadriven DRO to newly developed statistical properties of GoF tests. This, along with considerations of computational tractability, guides our choice of tests in formulating DRO depending on the problem case and leads us to develop a novel test for multivariate distributions that, when used in DRO, offers tractable optimization with both finitesample and asymptotic guarantees. Our theory also allows us to analyze existing datadriven DRO approaches and our statistical testing perspective suggests ways these can be improved in practice via applied statistical tools like the bootstrap. Examples from inventory management and portfolio allocation demonstrate that this approach produces solutions that are stable and perform well even with little data, while at the same time converging as more data becomes available. Ton de Kok t.b.a. Ger Koole Robust optimization for integrated call center planning We consider a multiperiod staffing problem in a singleshift call center. The call center handles inbound calls, as well as some alternative backoffice jobs. The call arrival process is assumed to follow a doubly nonstationary stochastic process with a random mean arrival rate. The inbound calls have to be handled as quickly as possible, while the backoffice jobs, such as answering emails, may be delayed to some extent. The staffing problem is modeled as a generalized newsboytype model under an expected cost criterion. Two different solution approaches are considered. First, by discretization of the underlying probability distribution, we explicitly formulate the expected cost newsboytype formulation as a stochastic program. Second, we develop a robust programming formulation. Daniel Kuhn DataDriven Distributionally Robust Optimization Using the Wasserstein Metric We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and nondiscrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worstcase distribution within this Wasserstein ball. The stateoftheart methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques, which quickly become computationally excruciating. In this paper we demonstrate that, under mild assumptions, the distributionally robust optimization problems over Wasserstein balls can in fact be reformulated as finite convex programs  in many interesting cases even as tractable linear programs. Leveraging recent measure concentration results, we also show that their solutions enjoy powerful finitesample performance guarantees. Our theoretical results are exemplified in meanrisk portfolio optimization, uncertainty quantification and machine learning. Henry Lam (short talk) t.b.a. Melvyn Sim A Practically Efficient Framework for Distributionally Robust Optimization with Recourse We develop a modular and tractable framework to obtain approximate and possibly exact solutions to a distributionally robust optimization problem with recourse, where we minimize the worstcase expected cost over an ambiguity set of probability distributions. Such a framework has numerous management inspired applications including, among other things, improving healthcare services and reducing inventory costs. In characterizing uncertainty, we adopt the ambiguity set proposed by Wiesemann et al. (2014) and show that by restricting the recourse decision functions to those with affine dependency on the actual and auxiliary random variables, we can improve the solutions of distributionally robust optimization problems with recourse. Using an algebraic modeling package we have developed, we illustrate how our approach can be used to obtain high quality solutions to a class of appointment scheduling problems. This is a joint work with Dimitris Bertsimas and Meilin Zhang. Gideon Weiss (short talk) Transient control of queueing networks, using continuous linear programs Optimal control of a queueing network over a finite time horizon is an intractable task and can only be achieved approximately. We will survey two approaches: Controlling the fluid approximation of the network and using a stochastic maximum pressure policy to track the fluid solution (following results of NazarathyWeiss), and formulation the problem as a robust optimization problem (following results of BertsimasNasarabaldiPaschallidis). In either case this involves a centralized solution of a separated continuous linear program (SCLP). We will describe that nature of the exact solution of this SCLP, and explain how the nature of the exact solution of the SCLP will help in implementing the optimal control. This supports using a simplex type algorithm to solve the SCLP (following Weiss and Shindin). Ralf Werner (short talk) Consistent uncertainty sets and consistent robust estimators In statistics one is interested in the asymptotical properties of
point estimators. From this perspective we provide a fresh look at
robust estimators obtained as solutions to robust optimization problems.
PRACTICAL INFORMATION ● VenueEurandom, Mathematics and Computer Science Dept, TU Eindhoven, De Groene Loper 5, 5612 AZ EINDHOVEN, The Netherlands Eurandom is located on the campus of Eindhoven University of Technology, in the Metaforum building (4th floor)
. The university is
located at 10 minutes walking distance from Eindhoven main railway
station (take
the exit north side and walk towards the tall building on the right
with the
sign TU/e).
● RegistrationRegistration is closed.
● AccommodationFor invited spekaers, we will take care of accommodation. Other attendees will have to make their own arrangements. We have a preferred hotel, which can be booked at special rates. Please email Patty Koorn for instructions on how to make use of this special offer. For other hotels around the university, please see: Hotels (please note: prices listed are "best available"). More hotel options can be found on the webpages of the Tourist Information Eindhoven, Postbus 7, 5600 AA Eindhoven.
● TravelFor those arriving by plane, there is a convenient direct train connection between Amsterdam Schiphol airport and Eindhoven. This trip will take about one and a half hour. For more detailed information, please consult the NS travel information pages or see Eurandom web page location. Many low cost carriers also fly to Eindhoven Airport. There is a bus connection to the Eindhoven central railway station from the airport. (Bus route number 401) For details on departure times consult http://www.9292ov.nl The University can be reached easily by car from the highways leading to Eindhoven (for details, see our route descriptions or consult our map with highway connections.
● Conference facilities : Conference room, Metaforum Building MF11&12The meetingroom is equipped with a data projector, an overhead projector, a projection screen and a blackboard. Please note that speakers and participants making an oral presentation are kindly requested to bring their own laptop or their presentation on a memory stick.
● Conference SecretariatUpon arrival, participants should register with the workshop officer, and collect their name badges. The workshop officer will be present for the duration of the conference, taking care of the administrative aspects and the daytoday running of the conference: registration, issuing certificates and receipts, etc.
● CancellationShould you need to cancel your participation, please contact Patty Koorn, the Workshop Officer. ● ContactMrs. Patty Koorn, Workshop Officer, Eurandom/TU Eindhoven, koorn@eurandom.tue.nl SPONSORSThe organisers acknowledge the financial support/sponsorship of:
Last updated
121115,

