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Path integral control from probabilistic viewpoint
Published on Oct 16, 20124247 Views
We show that stochastic control problems with a particular cost structure involving a relative entropy term admit a purely probabilistic solution, without the necessity of applying the dynamic program
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Chapter list
Path integral control from probabilistic viewpoint00:00
Motivation Path integral control (1)00:34
Motivation Path integral control (2)01:39
Kullback-Leibler divergence / relative entropy02:55
Kullback-Leibler divergence weighted optimization03:44
Girsanov’s theorem I04:51
Girsanov’s theorem II (1)05:59
Girsanov’s theorem II (2)06:30
KL weighted optimization of diffusions I (1)06:59
KL weighted optimization of diffusions I (2)07:14
KL weighted optimization of diffusions I (3)07:27
KL divergence for controlled diffusion (1)07:49
KL divergence for controlled diffusion (2)08:29
KL weighted optimization of diffusions II - classical solution (1)08:43
KL weighted optimization of diffusions II - classical solution (2)09:00
KL weighted optimization of diffusions II - classical solution (3)09:09
KL weighted optimization of diffusions III - probabilistic approach (1)09:20
KL weighted optimization of diffusions III - probabilistic approach (2)09:52
KL weighted optimization of diffusions III - probabilistic approach (3)10:05
KL weighted optimization of diffusions III - probabilistic approach (4)10:08
Example (1)10:50
Example (2)14:37
Example (3)14:58
Example (4)15:05
Example (5)15:21
Example (6)15:32
Example (7)15:41
Solution using Malliavin calculus (1)16:16
Solution using Malliavin calculus (2)17:03
Running maximum M(t)17:20
Example: C (1)17:52
Example: C (2)18:06
Example: C (3)18:35
Example: C (4)19:18
Summary of KL-weighted optimization of diffusion20:02
References21:07