PPT-Approximation Algorithms for Stochastic Optimization

Anupam Gupta Carnegie Mellon University SODA 2018 New Orleans stochastic optimization Question How to model and solve problems with uncertainty in inputactions data not yet . N is the process noise or disturbance at time are IID with 0 is independent of with 0 Linear Quadratic Stochastic Control 52 brPage 3br Control policies statefeedback control 0 N called the control policy at time roughly speaking we choo Some of the fastest known algorithms for certain tasks rely on chance. Stochastic/Randomized Algorithms. Two common variations. Monte Carlo. Las Vegas. We have already encountered some of both in this class. Gradient Descent Methods. Jakub . Kone. čný. . (joint work with Peter . Richt. árik. ). University of Edinburgh. Introduction. Large scale problem setting. Problems are often structured. Frequently arising in machine learning. Part I: Multistage problems. Anupam. Gupta. Carnegie Mellon University. stochastic optimization. Question: . How to model uncertainty in the inputs?. data may not yet be available. obtaining exact data is difficult/expensive/time-consuming. Anupam. Gupta. Carnegie Mellon University. stochastic optimization. Question: . How to model uncertainty in the inputs?. data may not yet be available. obtaining exact data is difficult/expensive/time-consuming. Stochastic Calculus: Introduction . Although . stochastic . and ordinary calculus share many common properties, there are fundamental differences. The probabilistic nature of stochastic processes distinguishes them from the deterministic functions associated with ordinary calculus. Since stochastic differential equations so frequently involve Brownian motion, second order terms in the Taylor series expansion of functions become important, in contrast to ordinary calculus where they can be ignored. . Michel . Gendreau. CIRRELT and MAGI. École Polytechnique de Montréal. SESO 2015 International Thematic. . Week. ENSTA and ENPC .  Paris, June 22-26, 2015. Effective solution approaches for stochastic and integer problems. Monte Carlo Tree Search. Minimax. search fails for games with deep trees, large branching factor, and no simple heuristics. Go: branching factor . 361 (19x19 board). Monte Carlo Tree Search. Instead . Processes:. An Overview. Math 182 2. nd. . sem. ay 2016-2017. Stochastic Process. Suppose. we have an index set . . We usually call this “time”. where . is a stochastic or random process . "QFT methods in stochastic nonlinear dynamics". ZIF, 18-19 March, 2015. D. Volchenkov. The analysis of stochastic problems sometimes might be easier than that of nonlinear dynamics – at least, we could sometimes guess upon the asymptotic solutions.. Stochastic . Optimization. Anupam Gupta. Carnegie Mellon University. IPCO Summer . School. Approximation . Algorithms for. Multi-Stage Stochastic Optimization. {vertex cover, . S. teiner tree, MSTs}. relaxations. via statistical query complexity. Based on:. V. F.. , Will Perkins, Santosh . Vempala. . . On the Complexity of Random Satisfiability Problems with Planted . Solutions.. STOC 2015. V. F.. Sahil . singla. . Princeton .  Georgia Tech. Joint with . danny. . Segev. . (. Tel Aviv University). June 27. th. , 2021. Given a . Finite. . Universe : . Given an . Objective. CSE 5403: Stochastic Process Cr. 3.00. Course Leaner: 2. nd. semester of MS 2015-16. Course Teacher: A H M Kamal. Stochastic Process for MS. Sample:. The sample mean is the average value of all the observations in the data set. Usually,.