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From linearly-solvable optimal control to trajectory optimization, and (hopefully) back
Published on Oct 16, 20124191 Views
We have identified a general class of stochastic optimal control problems which are inherently linear, in the sense that the exponentiated optimal value function satisfies a linear equation. These pro
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Chapter list
Linearly-solvable optimal control00:00
Problem formulation - 100:18
Problem formulation - 202:10
Reducing optimal control to a linear problem - 102:59
Reducing optimal control to a linear problem - 203:32
Reducing optimal control to a linear problem - 303:57
Illustration04:10
Linearly-solvable controlled diffusions05:00
Relation between the two problems - 106:44
Relation between the two problems - 207:33
Relation between the two problems - 308:29
Summary of (mostly) linear Bellman equations09:05
Comparison to generic MDP approximation10:24
Z-learning - 112:00
Z-learning - 212:21
Z-learning - 312:38
Importance sampling - 113:14
Importance sampling - 214:17
Estimation-control duality - 114:52
Estimation-control duality - 215:43
General case16:22
Linear case - 117:35
Linear case - 217:36
Maximum principle for the most likely trajectory - 117:55
Maximum principle for the most likely trajectory - 220:13
Compositionality22:07
Application to LQG24:08
Function approximation - 124:50
Function approximation - 225:24
Example: 40 adaptive Gaussian bases27:16
Remarks on function approximation - 129:27
Remarks on function approximation - 229:46
Remarks on function approximation - 330:08
Remarks on function approximation - 431:17
Trajectory optimization32:58
MuJoCo: A physics engine for control35:11
Trajectory optimization methods37:45
Model-predictive control (MPC)40:36
Contact-aware optimization42:35
Results42:39
Towards real-world applications53:15