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The statistical physics of optimal control theory
Published on Oct 16, 20127502 Views
In this introductory talk, I will present my personal perspective on how stochastic control theory is related to quantum mechanics, statistical inference, statistical physics and large deviation theo
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Chapter list
The statistical physics of optimal control theory00:00
The statistical physics of control and inference (1)01:08
The statistical physics of control and inference (2)01:31
The statistical physics of control and inference (3)02:15
The statistical physics of control and inference (4)02:27
The statistical physics of control and inference (5)02:49
The statistical physics of control and inference (6)02:55
Outline (1)03:11
Outline (2)03:39
Outline (3)04:04
Control and Quantum Mechanics (1)04:29
Pontryagin minimum principle05:46
Control and Quantum Mechanics (2)07:59
Control and Quantum Mechanics (3)08:29
QM as control of distributions (1)08:39
QM as control of distributions (2)09:14
Stochastic interpretation09:48
Control and Quantum Mechanics (4)11:01
Control and Quantum Mechanics (5)12:03
Outline (3)12:32
Link between inference and statistical physics (1)12:40
Link between inference and statistical physics (2)12:43
Link between inference and statistical physics (3)12:45
Link between inference and statistical physics (4)12:46
Link between control and inference12:48
Path integral control theory (1)16:29
Path integral control theory (2)17:49
Feynman-Kac formula19:04
Posterior distribution over optimal trajectories20:36
Recap22:34
Delayed choice25:02
Estimating optimal control by sampling26:25
Importance sampling (1)27:50
Importance sampling (2)28:41
How to control a device? (1)29:15
How to control a device? (2)30:48
Acrobot30:58
Outline (3)31:46
Link between control theory and large deviations (1)32:00
Link between control theory and large deviations (2)32:54
Link between control theory and large deviations (3)34:22
Link between control theory and large deviations (4)36:18
Link between control theory and large deviations (5)39:38
KL control theory (1)40:41
KL control theory (2)41:25
KL control theory (3)42:33
KL control theory (4)43:14
Link to continuous path integral formulation43:57
Average cost KL control (Todorov 2006)44:40
Detailed balance46:14
Particle in a box47:18
KL-learning [Bierkens, Kappen 2012]47:23
Numerical experiment48:13
Summary and discussion (1)48:52
Summary and discussion (2)49:09
Summary and discussion (3)49:42
Summary and discussion (4)49:56
Summary and discussion (5)50:23
Further reading50:37
Some open questions (1)50:49
Some open questions (2)51:32
The statistical physics of control and inference (1)52:03
The statistical physics of control and inference (2)52:26
The statistical physics of control and inference (3)52:38
The statistical physics of control and inference (4)52:46
The statistical physics of control and inference (5)52:55
The statistical physics of control and inference (6)53:03