PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action...
-
date post
21-Dec-2015 -
Category
Documents
-
view
216 -
download
0
Transcript of PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action...
![Page 1: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/1.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Decision Theory: Action Problems
![Page 2: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/2.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Decision theory goes Bad?
And thus the native hue of resolutionIs sicklied o'er with the pale cast of thought,And enterprises of great pith and momentWith this regard their currents turn awry,And lose the name of action.--
Shakespeare-Hamlet
![Page 3: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/3.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Modeling a Decision task• Modeling the outcome space
– What outcomes are likely to influence the decision• Modeling the event space
– What events are relevant to the behavior• Causal• Contextual
• Modeling the beliefs– Given relevant event space, determine probabilities
• Modeling utilities– Assigning worth to outcomes on a common scale
![Page 4: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/4.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Perception vs. Action• Perceptual Utility functions
– Minimize Errors– Possible exception- Geographical slant estimation
• Action Utility functions– Minimize energy expenditure (Trajectory selection)– Minimize endpoint error (Trajectory selection– Maximize information gain (eye/head movements)– Minimize collisions (Exploratory navigation)– Questions-
• Facial movements• Speech movements• Skiing?
![Page 5: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/5.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Action Decisions
![Page 6: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/6.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Reaching for an object
Outcomes
State space
Beliefs
Values
![Page 7: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/7.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Decision tasks• Ski downhill
– Space of outcomes– State space– Beliefs– Values
![Page 8: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/8.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 9: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/9.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
The levels in the motor hierarchy are shown with the triangles between the levels indicating the reduction in the degrees of freedom between the higher and lower levels. Specifying a pattern of behavior at any level completely specifies the patterns at the level below (many-to-one: many patterns at the higher level correspond to one pattern at the lower) but is consistent with many patterns at the level above (one-to-many). Planning can be considered as the process by which particular patterns, consistent with the extrinsic task goals, are selected at each level. From (Wolpert, 1997).
Motor Control is Hierarchical
![Page 10: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/10.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Movements show typicality
![Page 11: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/11.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Optimal control theory as decision theory with dynamics (sequential decision problem)
Decisions may occur at each time step in a movement. Thus the utility function must be specified at each time.
![Page 12: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/12.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Utility of action sequencesBest movements maximize total utility– every possible movement which can achieve a goal has a utility– we select the movement with the highest utility
Traveling Salesman problem example:
Cities Entered ChicagoIowa CityBurlingtonHoustonAtlantaNew YorkPhiladelphiaTampaKansas City
![Page 13: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/13.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Minimal Energy Models for movement
QuickTime™ and aYUV420 codec decompressorare needed to see this picture.
![Page 14: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/14.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 15: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/15.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Utility Functions for reaching
Simple utility function- Minimum Jerk
Solution has the form:
Model predicts bell-shaped velocity profile.
No role for uncertainty.
![Page 16: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/16.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Task/Goal Achievement?
![Page 17: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/17.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 18: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/18.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 19: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/19.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 20: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/20.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 21: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/21.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 22: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/22.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Projectile Actions
![Page 23: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/23.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Model State space• Reach endpoint• Reach trajectory?
• Model beliefs on endpoint– Planned endpoint plus 2-D gaussian noise
![Page 24: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/24.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Model Outcomes
Land in circle 0: R0Land in circle 1: R1Reach too long: timeoutEnergy for reach: B(x,y)
Multi-Attribute Utility:EnergyTimeoutRewards
Minimize Expected Utility:
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Action = (x,y)
(x,y)
€
V (x, y) = U(Ro)P(Ro | x, y) + U(R1)P(R1 | x, y)
+ U(timeout)P(timeout | x, y) + U(B(x, y))P(B | x, y)
![Page 25: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/25.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Simulate Optimal Pointer
![Page 26: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/26.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 27: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/27.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Task - Touch the screen
![Page 28: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/28.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 29: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/29.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 30: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/30.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Well?
![Page 31: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/31.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
Eye movements• Outcome space
– End point accuracy- foveate target– Acquire relevant target information
• Event space– Eye position– Target identity
![Page 32: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/32.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 33: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/33.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
![Page 34: PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004 Decision Theory: Action Problems.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d595503460f94a39848/html5/thumbnails/34.jpg)
PSY 5018H: Math Models Hum Behavior, Prof. Paul Schrater, Spring 2004
time
Move left or right
fixation