ORIE 6360

Optimization Under Uncertainty: Robust and Online Models

Course Description

Course information provided by the Courses of Study 2023-2024.

In most sequential decision problems, uncertainty evolves over time and we need to make decisions in the face of uncertainty. This is a fundamental problem arising in almost every business application where real-time decisions are based on the information revealed thus far. The uncertainty in the problem can be modeled in a number of ways (e.g., a probability distribution over some parameters or an uncertainty set for some variables) and the selection of an appropriate framework is purely a choice of the decision-maker. Such a selection depends on various considerations ranging from the availability of historical data to the tractability of the resulting optimization problem and the robustness of resulting solutions. In the first part of the class, we primarily focus on robust optimization which is a widely used paradigm to handle adversarial models of uncertainty. We also contrast robust optimization with various other paradigms such as stochastic optimization and distributionally robust optimization. In the second part of the class, we focus on discrete optimization problems under uncertainty such as two-stage facility location and sequential matching problems. We will discuss these classes of discrete problems under both the paradigm of robust optimization (worst-case scenario analysis) as well as online optimization (competitive ratio analysis). 

When Offered Spring.

Prerequisites/Corequisites Prerequisite: familiarity with basic concepts of probability and linear programming.

Satisfies Requirement Enrollment limited to: PhD students. 

• Students will be able to introduce various paradigms for Optimization under uncertainty.
• Students will be able to introduce tools to solve such problems, including ones to develop optimal or near-optimal algorithms in both static and dynamic robust settings and discuss the various tradeoffs that arise such as tractability vs. performance.
• Students will be able to discuss recent research papers and applications in the area.

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