CS 542 Statistical Reinforcement Learning (F21)

Theory of reinforcement learning (RL), with a focus on sample complexity analyses.

Previously taught as CS598: F20, S19, F18

Project topics and references

Canvas will be used as the main platform for announcements, discussions, and homework submissions. It is important that you join the Canvas space for this course and turn on notifications to receive announcements in a timely manner. If you enroll in the course after 08/18 or are auditing, please contact the TA (Jiawei Huang, jiaweih@illinois.edu) to add you to Canvas.


Date Lecture Comments
08/25 Overview, logistics, and MDP basics slides
08/27 MDP basics blackboard (updated: 09/01), reading homework
09/01 Bellman equations note1 (updated: 09/13)
09/03 Value Iteration blackboard (updated: 09/08)
09/08 VI  
09/10 Policy Iteration blackboard, HW2 available on Canvas
09/15 LP, concentration inequalities blackboard, see updated note1
09/17 concentration and union bound blackboard, note2, reading
09/22 Certainty equivalence blackboard (updated: 09/24), note3
09/24 CE, abstractions note4
09/29 Abstractions slides (updated: 10/01)
10/01 Abstractions hw3 available
10/06 Fitted-Q Iteration slides
10/08 FQI annotated slides (updated: 10/15)
10/13 FQI proof note5
10/15 FQI, Importance Sampling note6, hw3 due
10/20 IS blackboard (updated: 10/22)
10/22 PG, MIS Project proposal due
10/27 MIS blackboard, hw4 available
10/29 Rmax exploration blackboard (updated: 11/5), note7
11/03 Cancelled  
11/05 Linear MDP blackboard (updated: 11/10)
11/10 Linear MDP  
11/12 Bellman rank slides (updated: 11/17)
11/17 Bellman rank  
11/19 Office hour (no class)  
11/24 Fall break (no class)  
11/26 Fall break (no class)  
12/01 Partial observability slides
12/03 PSRs  
12/08 NeurIPS (no class)  
12/10 NeurIPS (no class)  
12/12   Project report due EOD

Time & Location
Wed & Fri, 12:30-01:45pm. Zoom link.

Recordings will be uploaded to MediaSpace; please subscribe if you want to be notified of new video uploadings.

Jiawei Huang (please contact the TA on Canvas)

Office Hours

Linear algebra, probability & statistics, and basic calculus. Experience with machine learning (e.g., CS 446), and preferably reinforcement learning. It is also recommended that the students are familiar with stochastic processes and numerical analysis.

Coursework & Grading
Homework may be assigned on an ad hoc basis to help students digest particular material. The main assignment will be a course project that involves literature review, reproduction of theoretical analyses in existing work, and original research (see details below). No exams. Grades decomposition: tentatively 40% homework and 60% project; subject to +-10% changes depending on the actual number of homework assignments (expected: 3).

Topics Covered in Lectures

  • Basics of MDPs and RL.
  • Sample complexity analyses of tabular RL.
  • Policy Gradient.
  • Off-policy evaluation.
  • State abstraction theory.
  • Sample complexity analyses of approximate dynamic programming.
  • PAC exploration theory (tabular).
  • PAC exploration theory (function approximation).
  • Partial observability and dynamical system modeling.

Course Project

You will work individually. You can choose one of the following three types of projects:

  • Reproduce the proofs of existing paper(s). You must fully understand the proofs and rewrite them in your own words. Sometimes a paper considers a relatively general setting and the analysis can be quite complicated. In this case you should aim at scrutinizing the results and presenting them in the cleanest possible way. Ask yourself: What’s the most essential part of the analysis? Can you introduce simplification assumptions to simplify the proofs sigificantly without trivializing the results?

  • Novel research Pick a new research topic and work on it. Be sure to discuss with me before you settle on the topic. The project must contain a significant theoretical component.

  • Something between 1 & 2 I would encourage most of you to start in this category. The idea is to reproduce the proofs of existing results and see if you can extend the analysis to a more challenging and/or interesting setting. This way, even if you do not get the new results before the end of semester, your project will just fall back to category 1.

See the link at the top of this page for potential topics. You are expected to submit a short project proposal in the middle of the semester. The proposal should consist of a short paragraph describing your project topic, the papers you plan to work on, and the original research question (if applicable).


Useful inequalities cheat sheet (by László Kozma)

Concentration of measure (by John Lafferty, Han Liu, and Larry Wasserman)

We will not follow a specific textbook, but here are some good books that you can consult:

  • Markov Decision Processes: Discrete Stochastic Dynamic Programming, by Martin Puterman.
  • Reinforcement Learning: An Introduction, by Rich Sutton and Andrew Barto. (draft available online)
  • Algorithms of Reinforcement Learning, by Csaba Szepesvari. (pdf available online)
  • Neuro-Dynamic Programming, by Dimitri Bertsekas and John Tsitsiklis.

Alekh Agarwal, Sham Kakade, Wen Sun, and I also have a draft monograph which contained some of the lecture notes from this course.

There are also many related courses whose material is available online. Here is an incomplete list (not in any particular order; list from 2019 and has not been updated since then):

  • R. Srikant. UIUC ECE 586.
  • Ron Parr. Duke CompSci 590.2.
  • Ben Van Roy. Stanford MS&E 338.
  • Ambuj Tewari and Susan Murphy. U Michigan STATS 710.
  • Susan Murphy. Harvard Stat 234.
  • Alekh Agarwal and Alex Slivkins. Columbia COMS E6998.001.
  • Daniel Russo. Columbia B9140-001.
  • Shipra Agrawal. Columbia IEOR 8100.
  • Emma Brunskill CMU 15-889e.
  • Philip Thomas. U Mass CMPSCI 687.
  • Michael Littman. Brown CSCI2951-F.