[EECS 598 - Fall 2013] Prediction and Learning: It's Only a Game |

Course Info | EECS 598-006, Fall 2013, 3 Credits |

Instructor | Jacob Abernethy, 3765 BBB, jabernet_at_umich_dot_edu |

Time, Place | MW 1:30-3pm, FXB 1008 (Updated!) |

The Details | Course Schedule, Topics and Links |

Office Hours | Tuesdays 1-2pm |

This course will focus on the problem of prediction, learning, and decision making, yet the underlying theme will involve game playing, betting and minimax analysis. We will begin by introducing the classical Weighted Majority Algorithm, and more broadly the problem of “adversarial online learning” and “regret minimization”, and this will launch us into topics such as von Neumann’s Minimax Theorem, multi-armed bandit problems, Blackwell Approachability, calibrated forecasting, and proper scoring rules. I intend to spend some time on applications to finance, like repeated gambling, universal portfolio selection, and option pricing.

**Prerequisites:** Familiarity with the analysis of algorithms, probabilistic analysis, and several similar topics. EECS 545 (Machine Learning) will be quite helpful but not strictly necessary. The material is going to be about 90% "theory" and thus potential students must have a strong mathematical background. We shall rely heavily on techniques from calculus, probability, and convex analysis, but many tools will be presented in lecture.

**Coursework:** There will be a small number of problem sets, and the final project for the course will consist of the option to do independent research or to give a literature review presentation to the class.

**Grade Breakdown**

35% for Homeworks | There will be 3-4 problem sets through the semester |

50% for Final Project | [(NEW!!) Summary of Project Ideas] Students can do a final project on reviewing some research paper, doing novel research, or implementing some algorithms in an interesting way. More details on this to come. |

15% for Participation | Students must scribe a lecture, participate in class, and can receive participation credit for answering some challenge questions. I will try to make enough opportunities for this. |

The course will not have any official textbook. But the following book (which influenced the choice of title for the course) will be quite helpful:

- "Prediction, Learning, and Games," by Nicolo Cesa-Bianchi and Gabor Lugosi

There is another text that has a few chapters I would like to cover:

- "Probability and Finance: It's Only a Game!" by Glen Shafer and Vladimir Vovk

In the last several years, several surveys have come out that explore several topics that we shall cover. I will link to them here, and will mention them in various lectures when appropriate:

- The Multiplicative Weights Update Method by Sanjeev Arora, Elad Hazan, and Satyen Kale.
- Online Learning and Online Convex Optimization survey by Shai Shalev-Shwartz.
- The convex optimization approach to regret minimization survey by Elad Hazan.
- Sasha Rakhlin's Lecture Notes.

- Lecture 1, 9/4: Course Overview and Intro to Online Learning
- Lecture 2, 9/9: Weighted Majority Algorithm
- Lecture 3, 9/11: The Exponential Weights Algorithm
- Lecture 4, 9/16: The Action Setting and Hyperexperts
- Lecture 5, 9/18: The Fixed-Share Forecaster
- Lecture 6, 9/23: Lower Bounds and Game Theory I
- Lecture 7, 9/25: Game Theory II: Nash Equilibria and von Neumann
- Lecture 8, 9/30: Game Theory III: Proof of Minimax Thm using Hedge Alg
- Lecture 9, 10/02: Applications of Minimax: LP and Boosting
- Lecture 10, 10/07: Boosting and Perceptron Algorithms
- Lecture 11, 10/09: Perceptron and Universal Portfolio Selection
- Lecture 12, 10/16: Online Convex Optimization
- Lecture 13, 10/21: Universal Portfolios Review and Online Convex Optimization
- Lecture 14, 10/23: Game-theoretic Probability in Finance
- Lecture 15, 10/28: Online Convex Optimization: Part III
- Lecture 16, 10/30: Follow the Regularized Leader
- Lecture 17, 11/04: FTRL and Applications of OCO
- Lecture 18, 11/06: The Bandit Setting
- Lecture 19, 11/11: UCB Algorithm and the Adversarial Bandit Problem
- Lecture 20, 11/13: EXP3 Algorithm
- Lecture 21, 11/18: Bandit Algorithm and Blackwell Approachability
- Lecture 22, 11/20: Blackwell's Approachability Theorem
- Lecture 23, 12/02: B.A.T. Review and Calibrated Forecasting
- Lecture 24, 12/04: Generalized Calibration and Correlated Equilibria

- Homework #1 - Due 9/25/2013
- Homework #2 - Due 10/28/2013 which requires constraints.csv defining a feasibility problem.
- Homework #3 - Due 11/27/2013

Students can see this document HERE for a full-page experience. You can also view the embedded iframe doc below BUT if you want links to open in a new page you must CTRL-click (or CMD-click on a mac). Pardon the inconvenience, I am not sure if this can be fixed.