16-745: Optimal Control and Reinforcement Learning
Spring 2020, TT 4:30-5:50 GHC 4303
Instructor: Chris Atkeson, email@example.com
TA: Ramkumar Natarajan firstname.lastname@example.org, Office hours Thursdays 6-7 Robolounge NSH 1513
Events of Interest
Items of Interest
DeepMind researchers introduce hybrid solution to robot control problems
Ubisoft Builds New AI Algorithm that Uses Reinforcement Learning to Teach Driving to Itself,
Ancestry turned to AI to bring down cloud costs
Last year's course
Jan 14: Introduction to the course.
Goal: Introduce course.
This years emphasis is TBD
Jan 16: AlphaZero/MuZero
Goal: Introduce you to an impressive example of reinforcement learning (its biggest success). If AI had a Nobel Prize, this work would get it.
Read MuZero: The triumph of the model-based approach, and the reconciliation of engineering and machine learning approaches to optimal control and reinforcement learning.
For Jan 30: Read nice reinforcement learning paper:
Goal: Introduce you to another impressive example of reinforcement learning.
Read this article, Learning agile and dynamic motor skills for legged robots.
Just robot abuse video.
Running fast video (note asymmetry/"limp").
I have some comments in this article.
More comments from me.
Jan 21: Function Optimization Example
Goal: Introduce you to a useful tool, MATLAB
and its optimization subroutines, and show you how to use them on an example.
Robotics: redundant inverse kinematics.
Using Matlab's fminsearch and fminunc.
Using Matlab's fminsearch and fminunc, with
Using Matlab's fmincon.
Relationship of Jacobian approach to gradient descent.
Jan 23: Handling 3D Orientation
Goal: Enable you to do 3D robotics using optimization (and do the inverse kinematics assignment).
Euler angles, and
Metrics for how close two orientations are:
Metrics for 3D Rotations: Comparison and Analysis,
Rigid-Body Attitude Control: Using Rotation Matrices for Continuous, Singularity-Free Control Laws,
Closed-Loop Manipulator Control Using Quaternion Feedback
Rotation matrix for small rotations
Function optimization using
order gradient methods
Goal: Review gradient descent approaches.
A nice chapter on function optimization techniques:
Numerical Recipes in C, chapter 10
(2nd or 3rd edition, 2nd edition is electronically available for free
under Obsolete Versions):
Minimization or Maximization of Functions,
This material from any other numerical methods book is also fine.
software list 1,
conjugate gradient v2,
quasi-Newton/variable metric methods,
Reduced dimensionality second order methods.
Stanford MSandE 311;
U. Stuttgart: Toussaint
Optimization Methods for Large-Scale Machine Learning;
Identifying and attacking the saddle point problem in
high-dimensional non-convex optimization
Talk about Covariant roll-out.
Talk about robot example:
Learning agile and dynamic motor skills for legged robots.
Jan 30: Non-gradient ("derivative-free") function optimization methods:
Goal: Review non-gradient approaches.
local unimodal sampling,
Nelder Mead/Simplex/Amoeba method,
fit surfaces (for example
Response Surface Methodology (RSM),
Memory-based Stochastic Optimization, and
Derivative-free optimization: A review of algorithms and comparison of software implementations by Luis Miguel Rios and Nikolaos V. Sahinidis,
Book: Introduction to Derivative-Free Optimization
Covariance Matrix Adaptation Evolution Strategy.
Goal: Understand currently popular state of the art method.
See also Hansen web page.
Feb 4: Constraints.
Goal: Understand how to handle constraints.
Soft/hard constraints, penalty functions,
Augmented Lagrangian method,
Interior point methods vs. Simplex methods vs. soft constraint methods.
Quadratic Programming and
Sequential quadratic programming,
Goal: Understand QP components used in state of the art robot control.
Feb 4: Dynamics and Numerical Integration
Goal: Review "mental practice".
Continuous time dynamics, discrete time dynamics. Euler integration, Forward and inverse dynamics. Linearization.
Feb 6: Formulating trajectory optimization as function optimization.
Goal: Use the tools we have so far to do trajectory optimization.
Examples of formulating a trajectory optimization problem
as a function optimization problem:
Case Studies In Trajectory Optimization: Trains, Planes, And Other
Robert J. Vanderbei
Example use of AMPL
A free trial version of AMPL is available from here.
AMPL is also available for remote use through the Neos Server.
Click on SNOPT/[AMPL Input] under Nonlinearly Constrained Optimization.
Example use of Matlab: pend1-x-u,
Spacetime Optimization: Witkin paper text
Witkin paper figures
Use of splines in trajectory optimization.
Goal: Force smooth solutions.
Cubic Hermite spline.
Quintic Hermite interpolation.
Feb 11: Policy optimization I: Use function optimization.
Goal: Optimize feedback.
What is a policy?
Known in machine learning/reinforcement learning as policy search or refinement, ...
See examples in CMA-ES section for policy optimization.
Feb 11: Ways to robustify function optimization:
Goal: Tricks of the trade.
Problems: How choose method?, more of an art than a science, local minima, bad answers, discontinuities, redundant/rank deficient constraints,
bad scaling, no formulas for derivatives, you are lazy, computational cost.
Techniques: Levenberg Marquardt,
scaling and preconditioning, regularize parameters, soft constraints,
Paper on continuation methods,
Hand of God, allow constraint violations, add extra constraints, use multiple starts, use multiple methods, optimize meta-parameters (learn to learn)
Matlab recommendations for optimization,
Goal: Use of value function is what makes optimal control special.
Linear Quadratic Regulator,
Goal: An important special case.
Differential Dynamic Programming
Feb 20: Ways to reduce the curse of dimensionality
Goal: Tricks of the trade.
Policy Optimization II: Optimization using model-based gradients
Goal: The Chain Rule Is Powerful.
Goal: How To Handle Bad Models.
Robustness to random disturbances, varying initial conditions, parametric
model error, structural modeling error such as
high frequency unmodelled dynamics,
and model jumps (touchdown and liftoff during walking, for example).
Monte Carlo trajectory/policy optimization.
Monte carlo financial planning.
Robustness using Linear Matrix Inequalities
Goal: Handling Parametric Uncertainty.
Robustness to parametric uncertainty in the linear(ized) model.
Tutorial on LMIs,
Slides: Continuous time stability slide 47, Discrete time stability slide 51
Receding Horizon Control
(a.k.a. Model Predictive Control (MPC))
Goal: Online Optimization.
Robustness: Policy Optimization with Multiple Models.
Goal: A powerful tool to handle all kinds of uncertainty.
Monte-Carlo, DP, and DDP approaches to Multiple Models.
Goal: Explicitly model uncertainty.
Gaussian Propagation (like Kalman Filter),
Unscented (like Unscented Filter), Second Order Kalman Filter (See Kendrick below).
Review of Gaussians slides
State estimation slides
Matlab Kalman filter example
minimum jerk trajectory subroutine.
Example mobile robot Kalman filter slides
Robustness and state estimation:
Goal: How to combine state estimation and control.
Linear-quadratic-Gaussian control (LQG),
Separation principle, Certainty equivalence,
Example of bad interactions, Loop Transfer Recovery (LTR),
A paper on the topic,
Policy optimization approaches.
Information state DP.
Local Approaches to Dual Control/Stochastic DDP
Information state trajectory optimization.
Stochastic Control for Economic Models,
David Kendrick, Second Edition 2002.
A*-like algorithms: R*
Avoiding obstacles using sampling-based methods: RRT,
Random Sampling DP
Avoiding obstacles using gradient methods: CHOMP
Learning From Demonstration
Reinforcement Learning: Model free policy gradient. Use trajectories to
Kober, J.; Peters, J. (2011). Policy Search for Motor Primitives in Robotics, Machine Learning, 84, 1-2, pp.171-203
NIPS Tutorial 2016: Deep Reinforcement Learning Through Policy Optimization
10-703 lecture notes I
Proximal Policy Optimization
Reinforcement Learning: Model free actor-critic: Model Q function to determine outcomes.
10-703 lecture notes II
Continuous control with deep reinforcement learning
What's new (2018 version)?
Comparison of various RL methods
Freek Stulp and Olivier Sigaud. Path Integral Policy Improvement with Covariance Matrix Adaptation. In Proceedings of the 29th International Conference on Machine Learning (ICML), 2012.
Linear policies work: Towards Generalization and Simplicity in Continuous Control
Simple random search provides a competitive approach to reinforcement learning
Simple Nearest Neighbor Policy Method for Continuous Control Tasks, reddit commentary
Neural Network Dynamics
for Model-Based Deep Reinforcement Learning
with Model-Free Fine-Tuning
Deep Reinforcement Learning for Dexterous Manipulation with Concept Networks
Evolution Strategies as a Scalable Alternative to Reinforcement Learning
Inverse Reinforcement Learning.
What's new (2017 version)?
Combine trajectory optimization (model-based) and policy learning (model-free).
I did some work on this 20+ years ago. Now it is coming back.
Robot Learning From Demonstration, ICML '97, (postscript),
Learning tasks from a single demonstration, ICRA '97,
Nonparametric Model-Based Reinforcement Learning, NIPS '97,
Using Local Trajectory Optimizers To Speed Up Global Optimization in Dynamic Programming, NIPS 93
Random Sampling of States in Dynamic Programming, Trans SMC, 2008
Combining Model-Based and Model-Free Updates for Trajectory-Centric Reinforcement Learning
Create primitives and learn to combine them. (Libin Liu).
Google semantic event chains
another Cheng paper
What did the Berkeley folks say?
half of Sergey Levine's lecture
lecture on Transfer, Learning to Learn
See last slide of Abbeel's lecture
Review of Traditional Approaches
Trajectory optimization based on integrating the dynamics:
calculus of variations,
Discrete time Pontryagin's minimum principle,
Pontryagin's minimum principle,
multiple shooting methods,
Learning during optimization
Goal: Learn how taking derivatives is much easier than you thought.
Gaussian Process Optimization.
Goal: The role of knowledge in optimization.
When solving the same kind of problem many times:
Learn about the function: remember previous answers, bases of attraction,
features like saddle points (zero gradients), optimization paths, ...
Learn about which optimization method works best: Meta-optimization.
Assume or learn a structure for the function (kernel in GP is an example).
Finding Better Ways To Do Task
Goal: Think about an important current research problem.
April 28 & 30: Project presentations
May 17 (May 12 for graduating students): Final project writeup (web page) due.
Assignment 0 (Due Jan. 20): Send CGA and TA email:
Who are you?
Why are you here?
What research do you do?
Describe any optimization you have done (point me to papers or
web pages if they exist).
Any project ideas?
What topics would you especially like the course to cover?
Be sure your name is obvious in the email, and you mention the course
name or number. I teach more than one course, and a random email from
email@example.com is hard for me to process.
Assignment 1 (Due Jan 27): Using Optimization
to do Inverse Kinematics
The project will involve performing a substantial dynamic optimization,
and writing a paper about it. The writeup is as important as the programming
(if not more so) and will be in the format of a conference paper
(more on that later). Those of you who already have a dynamic optimization
problem you are working on for your research should work on that (subject
to the Professor's approval). Another option is to work on the problem
described below (subject
to the Professor's approval).