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Numerical exploration-exploitation trade-off for large-scale function optimization
Published on Nov 07, 20132549 Views
I will show how the "optimism in the face of uncertainty" principle developed in multiarmed bandits can be extended to address large scale decision making problems. Initially motivated by the empirica
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Chapter list
Numerical exploration-exploitation tradeo for large scale function optimization00:00
Initial motivation00:05
The MoGo program [Gelly et al., 2006]05:32
No nite-time guarantee for UCT06:23
UCB applied to Trees10:14
Optimism in the face of uncertainty12:51
Optimization of a deterministic Lipschitz function13:56
Example in 1d14:44
Example in 1d (continued) - 115:53
Example in 1d (continued) - 219:37
Several issues19:53
Local smoothness is enough!22:32
Ecient implementation23:56
Near-optimality dimension30:31
Example 132:11
Example 2 - 133:02
Example 2 - 235:22
Local smoothness property38:05
Example 338:21
Example 438:29
Analysis of DOO (deterministic case)40:21
About the local smoothness assumption42:28
Experiments [1]42:42
Experiments [2]43:13
Experiments [3]43:38
Experiments [4]43:57
What if the smoothness is unknown?44:33
DIRECT algorithm [Jones et al., 1993]44:53
Illustration of DIRECT - 145:29
Illustration of DIRECT - 246:03
Limitations of DIRECT46:27
Simultaneous Optimistic Optimization (SOO)46:54
SOO algorithm47:23
Performance of SOO - 152:26
Performance of SOO - 254:51
Numerical experiments55:05
The case d = 0 is non-trivial!55:15
The case d = 056:24
Example of functions for which d = 0 - 156:35
Example of functions for which d = 0 - 256:44
d = 0?56:53
d > 057:10
SOO versus DIRECT58:10
How to handle noise?58:43
Stochastic SOO (StoSOO)58:58
Performance of StoSOO01:01:04
Range of application01:01:44
Conclusions01:03:09