Overview

This course introduces students to the mathematical foundation of learning in the presence of strategic and societal agency. This is a theory-oriented course that will draw from the statistical and computational foundations of machine learning, computer science, and economics. As a research-oriented course, a range of advanced topics will be explored to paint a comprehensive picture of classical and modern approaches to learning for the purpose of decision making. These topics include foundations of learning, foundations of algorithmic game theory, cooperative and non-cooperative games, equilibria and dynamics, learning in games, information asymmetries, mechanism design, and learning with incentives. Assigned classwork includes written proof-based homework assignments, participation in discussions and peer evaluations, scribing and contributing to creating enrichment material, and research projects.

Potential list of topics is subject to change but will likely include the following:

• Basics of offline and online learning, including VC theory, online learning, mistake bounds, etc.

• Smoothed Analysis of Learning.

• Bandits and online learning with partial information.

• Game theory and solution concepts such as Nash equilibria, Correlated Equilibria, and Stackelberg Games.

• Learning Dynamics in Games.

• Trustworthy predictions, calibration, and decision-theoretic notions of prediction quality.

• Multi-distribution and multi-objective learning.

• Fine-grained learning guarantees, multi-calibration, omni-prediction, and pan-prediction.

Prerequisites

Graduate-level mathematical maturity, including proof-based graduate-level courses in at least two, but recommended three, of the following categories:

1. Statistics and Probability, e.g., STAT205, STAT210

2. Economics, e.g., ECON207

3. Algorithms, e.g., CS270

4. Optimization, e.g., EE 227

5. Control theory, e.g., EE 221A

Please note that some of these pre-requisites play a larger role than others. For example, the course assume that you are comfortable with (1) and lack of preparation in category (1) will be hard to overcome. On the other hand, the course takes a slower approach to the introduction of category (2) concepts and lack of preparation in category (2) can be more easily overcome. It is highly recommended that you feel comfortable with at least one of category (3-5) topics, as the course is strongly algorithmic in nature.