- Lecturer: www.snn.ru.nl/~bertk
Bert Kappen

- chapter 1 from the book Dynamic programming and optimal control by Dimitri Bertsekas. Copies 1a Copies 1b Here are his slides for Bertsekas' course.
- my ICML 2008 tutorial text will be published in a book Inference and Learning in Dynamical Models (Cambridge University Press 2010), edited by David Barber, Taylan Cemgil and Sylvia Chiappa. The ICML 2008 tutorial website containts other tutorial material and pointers to useful further material.
- Extensions of that material based using both published and unpublished results of the last years.
- These are the slides for the course.

Date | Topic | Material | Recommended exercises | ||

1 | Feb 8 11-13 hours |
Discrete time control dynamic programming Bellman equation Continuous time control Hamilton-Jacobi-Bellman Equation Pontryagin Minimum Principle |
Bertsekas 2-5, 13-14, 18, 21-32 (2nd ed.) Bertsekas 2-5, 10-12, 16-27, 30-32 (1nd ed.) Kappen ICML tutorial 1.2, 1.3 slides |
Bertsekas 1.1 a and b, 1.2
extra exercise 1, 2a,b | |

2 | Feb 9 11-13 hours |
Recap of PMP and examples Inverse control Stochastic differential equations Stochastic optimal control LQ examples, Portfolio management |
Kappen ICML tutorial 1.4 slides |
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3 | Feb 21 10-13 hours |
Dual control: the problem of joint inference and control Path integral control theory |
Kappen ICML tutorial 1.5, 1.6, 1.7 | extra exercise 2c, 3 | |

4 | Feb 22 10-13 hours |
Path integral control theory MC Sampling solution Laplace approximation Numerical examples (particle in a box, Darts, N joint arm, Coordination of agents, Robot learning) Risk sensitive control KL control theory and link to path integrals |
Kappen ICML tutorial 1.7 Theodorou et al., AISTATS 2010 Mensink et al., ECAI 2010 van den Broek et al., JAIR 2008 van den Broek et al., UAI 2010 Kappen et al, arxiv:0901.0633 2009 |
extra exercise 4,5
Matlab code for n joint problem Here is a directory of matlab files, which allows you to run and inspect the variational approximation for the n joint stochastic control problem as discussed in the tutorial text section 1.6.7. Type tar xvf njoints.tar to unpack the directory and simply run file1.m. In file1.m you can select demo1 (3 joint arm) or demo2 (10 joint arm). You can also try larger n but be sure to adjust eta for the smoothing of the variational fixed point equations. You can compare the results with exact cmputation (only recommendable for 2 joints) by setting METHOD='exact'. There is also an implementation of importance sampling (does not work very well) and Metropolis Hastings sampling (works nice, but not as stable as the variational approximation). |