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2/6/12 1 Ashutosh Saxena CS 4758/6758: Robot Learning Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals

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Page 1: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

CS 4758/6758: Robot Learning Spring 2012. Ashutosh Saxena

Ashutosh Saxena

Goals

Page 2: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Goals encoded as a Cost Function

� Which areas on the road are good?

Ashutosh Saxena

Optimizing cost function: Descent Methods

� General descent algorithm � Generalization to multiple dimensions � Problems of descent methods, possible

improvements. �  Fixes � Local Minima

Page 3: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Gradient Descent

Page 4: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 5: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 6: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 7: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 8: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 9: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 10: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 11: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 12: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 13: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 14: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Solution to step size

� Back-tracking line search.

◦  Step-size = step-size / 2 ◦ Until new function value gets smaller.

Ashutosh Saxena

Page 15: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena

Ashutosh Saxena

Page 16: Spring 2012. Ashutosh Saxena - Cornell University · Spring 2012. Ashutosh Saxena Ashutosh Saxena Goals . 2/6/12 2 Ashutosh Saxena Goals encoded as a Cost Function ! Which areas on

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Ashutosh Saxena