Informs Annual Meeting Phoenix 2018

T E C H N I C A L S E S S I O N S

Sunday, 8:00AM - 9:30AM

How to Navigate the Technical Sessions

n SA01 North Bldg 121A Adjustable and Distributionally Robust Optimization Sponsored: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Dimitri Papadimitriou, Nokia Bell Labs, Brussels, 1190, Belgium 1 - Distributionally Robust Risk-constrained Dynamic Asset Allocation Model Tito Homem-de-Mello, Universidad Adolfo Ibáñez, Santiago, Chile, Davi Valladao, Thuener Silva Dynamic stochastic programming for asset allocation suffer from low out-of- sample performance due to discrepancies between the underlying stochastic processes and the actual prices. To enhance performance, we propose a distributionally robust dynamic portfolio optimization with one-period risk constraints considering transaction costs and a Markovian temporal dependence with ambiguous transition matrix. Assuming a ambiguity set based on a nominal transition matrix and the total variation distance measure, we develop a computationally tractable reformulation and present out-of-sample results. 2 - Efficient Stochastic Gradient Descent for Distributionally Robust Optimization We propose a new stochastic gradient descent algorithm to efficiently solve min- max formulations that arise naturally in distributionally robust learning. Current approaches do not scale well because the formulations include as decision variables a probability mass function over the whole collection of data samples. Our proposal is to approximate the optimization over the uncertainty set by sub- sampling the support, progressively increasing this support to cover the entire dataset as the iterates proceed. We develop asymptotic guarantees on how fast the support set should grow to optimally, in a strong statistical sense, balance the computational effort with the required level of accuracy. 3 - Distributionally Robust Optimization with Decision Dependent Ambiguity Sets Sanjay Mehrotra, Northwestern University, Dept of I. E. / M. S. C246 Tech Inst, 2145 Sheridan Road, Evanston, IL, 60208-3119, United States, Fengqiao Luo We study distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. Two-stage decision dependent stochastic programs are a special case. We give dual formulations for ambiguity sets based on moment constraints, Wasserstein metric, phi-divergence and multi- variate Kolmogorov-Smirnov sets. In the finite scenario case, the dual formulations have a finite number of constraints. In certain more general cases, the dual problems are non-convex semi-infinite programs. 4 - Benders Decomposition for Adjustable Robust Optimization Problems Dimitri Papadimitriou, Nokia Bell Labs, Rue du Charme 24, Brussels, 1190, Belgium Consider two-stage adjustable robust programs with continuous second-stage variables and covering constraints with both left and right-hand side uncertainty. Such programs model situations where, for instance, without requiring optimal production conditions, both allocation and production variables adjust (per- customer and per-location, respectively) to satisfy uncertain demands, and allocation decisions are constrained by local production. We analyze the properties of the resulting Affinely Adjustable Robust Counterpart (AARC) formulation when the decision-making policies are limited to (piecewise) affine rules, i.e., the continuous adjustable variables are approximated by affine function of the uncertain data. Then, we propose a robust formulation of the uncertain mixed-integer linear program that exploits its decomposable structure into first and second stage decision problems. Next, we detail an exact algorithm for the solving of such problems that relies on the Benders decomposition method while accounting for the properties of the extreme points characterizing polyhedral uncertainty sets. This method relies on dynamic cutting-plane generation. More precisely, under the relatively complete recourse assumption, it performs by iteratively generating optimality cuts/cutting planes (obtained from the dual subproblem), adding them to the master problem and solving the resulting master problem such that its lower and upper bounds converge and thus, an optimal solution of the original uncertain problem can be obtained. This paper also investigates possible strategies to reduce the convergence time of the Benders decomposition algorithm to the optimal solution by maintaining balance between the number of iterations and the number as well as the type of cuts produced at each iteration. Soumyadip Ghosh, IBM TJ Watson Research Center, 1101 Kitchawan Road, Route 134, Yorktown Heights, NY, 10598, United States, Mark S. Squillante, Ebisa Wollega

There are four primary resources to help you understand and navigate the Technical Sessions: • This Technical Session listing, which provides the most detailed information. The listing is presented chronologically by day/time, showing each session and the papers/abstracts/authors within each session.

The Session Codes

Room number. Room locations are also indicated in the listing for each session.

SA01

Time Block. Matches the time blocks shown in the Program Schedule.

The day of the week

Time Blocks

Sunday - Monday 8:00am - 9:30am 10:00am - 10:50am 11:00am – 12:30pm 1:30pm – 3:00pm 3:10pm - 4:00pm 4:30pm – 6:00pm Tuesday 7:30am - 9:00am 9:30am - 10:20am 10:30am - 12:00pm 12:05pm - 1:35pm 2:00pm - 3:30pm 3:40pm - 4:30pm 4:35pm – 6:05pm Wednesday 8:00am - 9:30am 10:00am - 10:50am 11:00am - 12:30pm 3:20pm - 4:50pm

Rooms and Locations /Tracks All tracks / technical sessions will be held in the Phoenix Convention Center & Hyatt Regency Phoenix.

1