CMPUT 676 - Optimization and Decision Making under Uncertainty

Overview

Many real-world problems involves making decisions, over a period of time, in the presence of different forms of uncertainty. These challenges arise in Internet advertising, energy sustainability, transportation, financial trading, healthcare, and a wide range of problems in artificial intelligence and machine learning. In different application scenarios, these specific decision problems might look different at first glance; however, the models and algorithms needed to address them are often similar.

In this research-oriented course, we will review recent developments and discuss open directions in the general field of decision-making under uncertainty via several modern optimization lenses. We will start by giving a brief introduction to convex optimization. Topics in this part include basic concepts of convex sets and convex functions, canonical convex problems, Lagrange multipliers, duality theory, KKT optimality conditions, and standard convex optimization algorithms. After that, we will discuss models and algorithms to handle different forms of uncertainty in optimization and decision-making. Major topics to be covered include: i) Online optimization and algorithms; ii) Stochastic optimization and approximation; and iii) Algorithmic game theory and mechanism design. These topics are highly interdisciplinary – they have strong ties to various disciplines such as theoretical computer science, artificial intelligence, machine learning, economics, operations research, statistics, and control. The course is theoretical in nature, but most problems considered will be motivated and illustrated by practical examples.

Objectives

• Understand the basics of optimization theory, algorithms, and applications.
• Understand how to build rigorous mathematical models and develop efficient algorithms, with provable guarantees, for optimization and decision-making under different forms of uncertainty.
• Be well prepared to conduct research in areas such as i) online optimization, learning, and decision-making; ii) stochastic optimization, learning, and approximation; and iii) algorithmic game theory, mechanism design, and auctions.

Course Work

• Homework Assignments
• Attendance and Participation
• Project (presentation + written report)