# 2015 Informs Annual Meeting

SB14

INFORMS Philadelphia – 2015

SB14 14-Franklin 4, Marriott Sampling and Learning Methods in Stochastic Optimization Sponsor: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Peter Frazier, Assistant Professor, Cornell University, 232 Rhodes Hall, Cornell University, Ithaca, NY, 14850, United States of America, pf98@cornell.edu 1 - Variance Reduction Techniques for Sequential Sampling Methods in Stochastic Programming Jangho Park, PhD Student, The Ohio State University, 1971 Neil Avenue, Columbus, OH, 43210, United States of America, park.1814@osu.edu, Guzin Bayraksan, Rebecca Stockbridge We present variance reduction techniques, Antithetic Variates and Latin Hypercube Sampling, when used for sequential sampling procedures in stochastic programming. We discuss theoretical justification and present the resulting subtle changes in an implementation due to theoretical consideration. We empirically investigate these variance reduction techniques on a number of test problems from the literature. 2 - Multi-step Bayesian Optimization for One-dimensional Feasibility Determination Bayesian optimization methods allocate limited sampling budgets to maximize expensive-to-evaluate functions. One-step-lookahead policies are often used, but computing optimal multi-step-lookahead policies remains a challenge. We consider a specialized Bayesian optimization problem: finding the superlevel set of an expensive one-dimensional function, with a Markov process prior. We compute the Bayes-optimal sampling policy efficiently, and characterize the suboptimality of one-step lookahead. 3 - The Knowledge Gradient Policy with Regularized Trees Yan Li, Princeton, Sherrerd Hall, Charlton Street, Princeton, United States of America, yanli@princeton.edu, Han Liu, Warren Powell We propose a sequential learning policy for noisy discrete global optimization with regularized trees. Besides selecting the best alternative before the budget is exhausted, we also aim to learn the important features and the low order interactions. We derive a knowledge gradient policy for binary decision trees. Experimental work shows that the method is scalable to high dimension and efficiently learns the underlying low dimensional structures. 4 - The Knowledge Gradient with Logistic Belief Models for Binary Classification Yingfei Wang, Princeton University, Computer Science Dept., Princeton, NJ, 08540, United States of America, yingfei@princeton.edu, Warren Powell We consider sequential decision problems where the learner takes an active role in repeatedly selecting alternatives and receives the binary label of the selected alternatives. The goal is to find the best alternative with the highest response. We use logistic regression to model the response of each alternative. By formulating the problem within a dynamic programming framework, we develop a knowledge gradient policy to guide the experiment by maximizing the expected value of information. SB15 15-Franklin 5, Marriott Recent Advances on First Order Methods Sponsor: Optimization/Nonlinear Programming Sponsored Session Chair: Fatma Kilinc Karzan, Assistant Professor Of Operations Research, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, United States of America, fkilinc@andrew.cmu.edu 1 - Random Block-coordinate Gradient Projection Algorithms Massey Cashore, University of Waterloo, 77 Crossovers St, Toronto, On, M4E 3X3, Canada, jmcashor@uwaterloo.ca, Peter Frazier

2 - An Extended Frank-wolfe Method, with Applications to Low-rank Matrix Completion Paul Grigas, MIT Operations Research Center, 77 Massachusetts Ave., Cambridge, MA, 02139, pgrigas@mit.edu, Rahul Mazumder, Robert Freund We present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. We present computational guarantees for the method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates. We present computational results for large-scale matrix completion problems that demonstrate significant speed-ups in computing low- rank near-optimal solutions. 3 - First-order Methods for Robust Convex Optimization Nam Ho-nguyen, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh PA,hnh@andrew.cmu.edu, Fatma Kilinc Karzan Robust optimization is a framework to model parameter uncertainty in optimization problems. Inspired by recent developments, we present several efficient first-order methods to approximately solve robust convex optimization problems. We also introduce the notion of weighted regret online learning and the online saddle-point problem, which form key building blocks for our methods. Finally, we discuss some proximal-type algorithms for these problems. SB16 16-Franklin 6, Marriott Recent Advances in Linear and Conic Optimization Sponsor: Optimization/Linear and Conic Optimization Sponsored Session Chair: Hande Benson, Associate Professor, Drexel University, LeBow College of Business, Philadelphia, PA, 19104, United States of America, hvb22@drexel.edu 1 - A Generalization of Chubanov’s Projection Algorithm Negar Soheili, Assistant Professor Of Business Analytics, University of Illinois at Chicago, 601 S Morgan Street, University Hall 2416, Chicago, Il, 60607, United States of America, nazad@uic.edu The Chubanov’s algorithm is a projection algorithm for solving linear homogeneous feasibility problems that leverages periodic rescaling. We propose an extension of this algorithm for solving more general conic feasibility problems where our iteration bound is based on a condition measure associated with the geometry of the problem. 2 - Polynomial Time Methods for Optimal Design of Experiments for Regression using Conic Optimization David Papp, North Carolina State University, 3222 SAS Hall, Campus Box 8205, Raleigh, NC, 27695-8205, United States of America, dpapp@ncsu.edu Computing optimal experimental designs for regression addresses a fundamental problem regarding the collection of experimental data. Natural formulations of this problem are either semi-infinite convex programs or finite dimensional nonconvex programs. We shall present a novel approach that reduces the solution of the nonconvex formulation to the solution of two coupled semidefinite programs. This leads to the first polynomial time algorithm for the computation of such global optimal designs. 3 - The Parametric Simplex Method and its Application in Machine Learning Haotian Pang, Princeton University, Department of Electrical Engineering, Olden Street, Princeton, NJ, 08540, United States of America, hpang@princeton.edu, Han Liu, Robert Vanderbei, Tuo Zhao We formulate a series of machine learning problems, including Dantzig selector for sparse linear regression, CLIME for sparse precision matrix estimation and LPD rule for sparse linear discriminant analysis, into the parametric linear programming form and show that it is fast and efficient to solve it by the parametric simplex method. For the Dantzig selector model, we show that each dual iteration is guaranteed to be sparse as well as under the irrepresentable conditions. 4 - Warmstarts for Mixed-integer Second-order Cone Programming

Angelia Nedich, University of Illinois, Urbana IL, United States of America, angelia@illinois.edu, Chandramani Singh, R. Srikant

Hande Benson, Associate Professor, Drexel University, LeBow College of Business, Philadelphia, PA, 19104, United States of America, hvb22@drexel.edu

We discuss gradient projection algorithms based on random partial updates of decision variables. We analyze these algorithms with and without assuming strong convexity of the objective functions. We also present an accelerated version of the algorithm based on Nesterov’s two-step gradient method. We show that the randomized algorithms exhibit similar rates of convergence as their full gradient based deterministic counterparts.

In this talk, we will discuss warmstarting strategies after different types of cuts within an algorithm for solving mixed-integer second-order cone programming problems. The underlying SOCPs are solved using an interior-point method.

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