**PENN CIS 625, SPRING 2012: COMPUTATIONAL LEARNING THEORY
**

Prof. Michael Kearns

mkearns@cis.upenn.edu

Dr. Jake Abernethy

jaber@seas.upenn.edu

Mondays
12-3 PM

307 Levine Hall
(NOTE ROOM CHANGE)

**IMPORTANT NOTE:**
Since the first Monday of the term (Jan 16) is MLK Day, the first class meeting will be on
**Monday, Jan 23.**

URL for this page:
www.cis.upenn.edu/~mkearns/teaching/COLT

A previous incarnation of this course:
www.cis.upenn.edu/~mkearns/teaching/COLT/colt08.html

**COURSE DESCRIPTION**

This course is an introduction to Computational Learning Theory, a field which attempts to provide algorithmic, complexity-theoretic and probabilistic foundations to modern machine learning and related topics.

The first part of the course will closely follow portions of An Introduction to Computational Learning Theory, by M. Kearns and U. Vazirani (MIT Press). We will cover perhaps 6 or 7 of the chapters in K&V over (approximately) the first half of the course, often supplementing with additional readings and materials. Copies of K&V will be available at the Penn bookstore. The second portion of the course will focus on a number of models and topics in learning theory not covered in K&V.

The course will give a broad overview of the kinds of problems and techniques typically studied in Computational Learning Theory, and provide a basic arsenal of powerful mathematical tools for analyzing machine learning problems.

Topics likely to be covered include:

**COURSE FORMAT, REQUIREMENTS, AND PREREQUISITES **

Much of the course will be in fairly traditional "chalk talk" lecture format, but with ample opportunity for discussion, participation, and critique. The course will meet once a week on Mondays from 12 to 3. Lunch will be served.

While there are no specific formal prerequisites, background or courses in algorithms, complexity theory, discrete math, combinatorics, probability theory and statistics will prove helpful, as will "mathematical maturity" in general. We will be examining detailed proofs throughout the course. If you have questions about the desired background, please ask me. Auditors and occasional participants are welcome.

The course requirements for registered students are active in-class participation, a couple of problem sets, possibly co-leading a class discussion, and a final project. The final projects can range from actual research work, to a literature survey, to solving some additional problems.

Mon Feb 20

[MK] Boosting continued: Adaboost and analysis; introduction to learning with classification noise;
a statistics-only algorithm for learning conjunctions; introduction to the statistical query learning model.

READING: K&V Chapter 5; supplementary reading:

Mon Feb 27

[MK] Classification noise and statistical query learning continued:
noise-tolerance of all SQ algorithms; almost all PAC algorithms are in SQ;
separating PAC and SQ; the SQ dimension and relationship to VC dimension.

Mon Mar 5

Spring break; no class meeting.

Mon Mar 12

[MK] Learning and cryptography; representation-independence hardness results;
learning DFAs from examples and membership queries.

READING: K&V Chapters 6,7,8.

PROBLEM SET #2, DUE AS HARDCOPY IN CLASS MAR 26: Solve the following problems from K&V: 5.1, 5.3, 5.4, 7.3, 8.3. You are free to collaborate on the homework assignments, but please turn in separate write-ups and acknowledge your collaborations. Please do not attempt to look up solutions in the literature.

INFORMATION ON COURSE PROJECTS.

For those of you registered for credit in the course,
your final assignment will be a course project, for which you have three choices:

You are welcome to send email to Prof Kearns proposing what your final project will be in order to get feedback and advice.

The deadline for final projects will be May 8, via email to Prof Kearns.

Mon Mar 19

[JA] Adversarial online learning; halving, weighted majority, and perceptron algorithms;
game, minimax via weighted majority, and boosting.

READING: While the notation and details may differ in class, the following online notes are relevant.

Mon Mar 26

[MK] PAC analysis of reinforcement learning; efficient exploration and exploitation.

READING:

Mon Apr 2

[JA] Continued: No-regret learning, online convex optimziation, and related topics.

READING:

UPDATE ON COURSE PROJECTS.

at least part of class on
April 16,
be devoted to discussion of your course projects --- Jake and I will have brief
individual meetings with each person/team about your proposed project. In preparation
for this, you should all send both Jake and I an email sketching your proposed project
by
FRIDAY APRIL 13.
The purpose of the email is not that you
have your project entirely figured out, but to get you thinking about what you want to
do. The more specific, the better, but it's also fine to say you want to think about papers
or problems in some particular area that interests you. That way in the meetings Jake
and I can suggest directions, or papers to look at, etc.
Please make the subject line of your email "CIS 625 Project" so we can easily sort.

It is permitted for you to work in small teams on a joint project, but we'll expect a proportionally more ambitious project in such cases.

Mon Apr 9

[JA] More fun with no-reget, online learning, convex optimization, etc.

READING: Papers from last week's discussion:

For this lecture, students should try to read through page 9 of Elad Hazan's review article on online convex optimization:

For students that want to know more, and for possible project ideas, here are some links:

Mon Apr 16

[JA] Jake finishes up his lectures on online convex optimization.

READING: TBD.

Mon Apr 23

[MK] Some drawbacks of no-regret learning; some topics in ML and finance.

READING: