The problem of making sequential decisions under uncertainty spans a wide range of applications that arise in science, engineering, business, transportation, energy, health and finance. In contrast with deterministic optimization that enjoys a widely used canonical framework, the academic study of decisions under uncertainty is a fragmented field. Communities working on these problems (broadly known as stochastic optimization) include operations research (stochastic programming, Markov decision processes, simulation optimization, decision analysis, bandit problems), computer science (reinforcement learning, bandit problems), optimal control (stochastic control, model predictive control, online computation), and applied mathematics (stochastic search). We refer collectively to these communities as the “jungle of stochastic optimization.”
In this workshop, I will outline a mathematical framework for modeling all of these problem classes. This framework consists of five fundamental elements (states, decisions/actions/ controls, exogenous information, transition function and objective function), and requires optimizing over policies, which is the major point of departure from deterministic optimization. We divide solution strategies for sequential problems (“dynamic programs”) between searching over a class of functions (“policy search”) and policies based on lookahead approximations (which includes Bellman’s equation, model predictive control and stochastic programming). We further divide each of these two fundamental solution approaches into two subclasses, producing four (meta)classes of policies for approaching sequential stochastic optimization problems. We claim that these classes are universal, in that a solution to any sequential decision problem will be one of these classes of policies, or a hybrid drawn from two or more classes.
I will illustrate the framework by using problems posed by the class (this will be done in advance).
Docent: Prof. Warren Powell (Princeton U.)
Venue: TUM City Campus, Room Z534
Date: April 16-17, 2020, lectures in the morning and exercises in the afternoon
Registration: Mail to email@example.com with the following information:
- Name and contact details
- Adone member/associate yes/no?
- participation in lectures and exercises, or lectures only?
AdONE PHD Seminar
Over the last several decades great strides have been made in providing optimal or near-optimal solutions to large-scale mixed integer programming (MIP) problems. The aim of this course is to investigate the most prominent of the techniques that have been developed for this purpose. These include decomposition and column generation techniques, polyhedral theory, the use of intelligent heuristics, as well as ad hoc procedures. In fact, it is rare that any one technique can be applied successfully to solve MIPs that arise in practice. What is needed is a strategy that combines insights about a particular problem with lower bounding procedures, limited enumeration, and simple methods for quickly finding good feasible solutions. Examples taken from industry will serve as a backdrop to the class discussion. Emphasis will be placed on the development of computational methods.
Docent: Prof. Jonathan F. Bard (U. of Texas at Austin)
Venue: TUM City Campus, Room 0534
Date: Aug 1st - 3rd, 2018, 9:00 – 17:30