Post on 03-Jan-2016
When Uncertainty Matters: The Selection of Rapid
Goal-Directed Movements
Julia Trommershäuser, Laurence T. Maloney, Michael S. Landy
Department of Psychology and Center for Neural Science
NYU
Motor responses have consequences
Kassi Price,2001 US Nationals
What? Where?
How?
target identification,target localization, regions to be avoided
selection of trajectory,biomechanical constraints,speed, accuracy
Why?motivation,movement goal,target selection
Movement planning
I. A Maximum Expected Gain Model of Movement under Risk
(MEGaMove)
II. Experimental test of the model
III. Conclusion
Outline
Experimental task
Start of trial:display of fixation cross (1.5 s)
Experimental task
Display of response area, 500 ms before target onset(114.2 mm x 80.6 mm)
Experimental task
Target display (700 ms)
Experimental task
Experimental task
The green target is hit: +100 points
100
100
Experimental task
Experimental task
-500
Experimental task
The red target is hit: -500 points
-500
Experimental task
-500 100
Experimental task
-500100
Scores add if both targets are hit:
Experimental task
You are too slow: -700
The screen is hit later than 700 ms after target display: -700 points.
Experimental task
Current score: 500End of trial
Experimental task
Rapidly touch a point with your fingertip.
What should you do?
100 -500
0 0
0
00 0
Responding afterthe time limit:
-700 points18 mm
Experimental task
Thought experiment
: -500 : 100 points (2.5 ¢)
x (mm)
y (m
m)
100 points
= 4.83 mm
Thought experiment
x (mm)
y (m
m)
100 points100 points
200 points
= 4.83 mm
: -500 : 100 points (2.5 ¢)
Thought experiment
x (mm)
y (m
m)
100 points100 points
300 points
100 points
= 4.83 mm
: -500 : 100 points (2.5 ¢)
Thought experiment
x (mm)
y (m
m)
100 points100 points
-100 points
100 points-400 points
= 4.83 mm
: -500 : 100 points (2.5 ¢)
Thought experiment
x (mm)
y (m
m)
100 points100 points
-32 points
100 points-400 points. . . .
= 4.83 mm
: -500 : 100 points (2.5 ¢)
Thought experiment
x (mm)
y (m
m)
-32 points
3070 points
= 4.83 mm
: -500 : 100 points (2.5 ¢)
Thought experiment
x (mm)
y (m
m)
-32 points
3070 points
2546 points
= 4.83 mm
: -500 : 100 points (2.5 ¢)
Thought experiment
x (mm)
y (m
m)
-32 points
3070 points
2257 points
= 4.83 mm
2546 points
: -500 : 100 points (2.5 ¢)
Expected gain as function of mean movement end point (x,y):
90
0
60
<-60-30
30
points per trial
x (mm)
y (m
m)
= 4.83 mm
-10 -5 0 5 10 15 20
-10
-5
-0
5
10
target: 100penalty: -500
x [mm] x [mm] x [mm]
y [m
m]
y [m
m]
y [m
m]
90
0
60
<-60-30
30
poin
ts p
er tr
ial
xy y yx x
penalty: 0 penalty: 500penalty: 100
x, y: mean movement end point [mm]
Thought experiment
= 4.83 mm
100
A Maximum Expected Gain Model of Movement Planning
Key assumption:
The mover chooses the motor strategy that maximizes the expected gain .
-500
Consequence:
The choice of motor strategy depends on
• the reward structure of the environment
• the mover's own motor variability.
Maloney, Trommershäuser, Landy, Poster, VSS 2003, SA46Trommershäuser, Maloney, Landy (2003) JOSA A, in press.
Distribution of movement end points
xhit-xmean (mm)
y hit-y
mea
n (m
m)
Subject S4, = 3.62 mm,72x15 = 1080 end points
cond 1 cond 2 cond 3 cond 4
cond 5 cond 6 cond 7 cond 8
cond 9 cond 10 cond 11 cond 120 10-10 0 10-10 0 10-10 0 10-10
010
-10
010
-10
010
-10
Movement endpoints in response to changes in penalty distance and penalty value
Test of the Model: First Results
3 penalty conditions: 0, -100, -500 points (varied between blocks)
6 stimulus configurations:(varied within block)
R 1.5R 2R
R = 9 mm
Maloney, Trommershäuser, Landy, Poster, VSS 2003, SA46Trommershäuser, Maloney, Landy (2003) JOSA A, in press.
As predicted by the model:
Subjects shifted their mean movementendpoint farther from the center ofthe green target• for higher penalty values,• for closer penalty regions.
More variable subjects won less money.
Subjects’ performance did not differ significantly from optimal.
Test of the Model: First Results
Maloney, Trommershäuser, Landy, Poster, VSS 2003, SA46Trommershäuser, Maloney, Landy (2003) JOSA A, in press.
Movement endpoints in response to novel stimulus configurations.
5 “practiced movers”1 session: 12 warm-up
trials, 6x2x16 trials per session,24 data points per condition
4 stimulus configurations:(varied within block)
2 penalty conditions:0 and -500 points (varied between blocks)
Test of the model: Experiment 1
1 2 3 4
R = 9 mm
Results: Experiment 1
x (mm)
Subject S5, = 2.99 mm
Model prediction:
y (m
m)
model, penalty = 0
x (mm)
Subject S5, = 2.99 mm
Model prediction: configuration 1
y (m
m)
model, penalty = 500x
model, penalty = 0
Results: Experiment 1
x (mm)
Subject S5, = 2.99 mm
Model prediction: configuration 2
y (m
m)
model, penalty = 500x
model, penalty = 0
Results: Experiment 1
x (mm)
Subject S5, = 2.99 mm
Model prediction: configuration 3
y (m
m)
model, penalty = 500x
model, penalty = 0
Results: Experiment 1
x (mm)
Subject S5, = 2.99 mm
Model prediction: configuration 4
y (m
m)
model, penalty = 500x
model, penalty = 0
Results: Experiment 1
x (mm)
Subject S5, = 2.99 mm
y (m
m)
exp., penalty = 500model, penalty = 500x
exp., penalty = 0
Comparison with experiment
Results: Experiment 1
x (mm)
x (mm)
y (m
m)
y (m
m)
S1 S2 S3
S4 S5
exp., penalty = 500model, penalty = 500x
exp., penalty = 0
x (mm)
Results: Experiment 1
Movement endpoints in response to morecomplex stimulus configurations.
5 “practiced movers”1 session: 12 warm-up
trials, 6x2x16 trials per session,24 data points per condition
4 “more complex” configurations:(varied within block)
2 penalty conditions:0 and -500 points (varied between blocks)
Test of the model: Experiment 2
1 2 3 4
R = 9 mm
x (mm)
Subject S5, = 2.99 mm
Model prediction: configuration 1
y (m
m)
model, penalty = 500x
model, penalty = 0
Results: Experiment 2
x (mm)
Subject S5, = 2.99 mm
Model prediction: configuration 2
y (m
m)
model, penalty = 500x
model, penalty = 0
Results: Experiment 2
x (mm)
Subject S5, = 2.99 mm
Model prediction: configuration 3
y (m
m)
model, penalty = 500x
model, penalty = 0
Results: Experiment 2
x (mm)
Subject S5, = 2.99 mm
Model prediction: configuration 4
y (m
m)
model, penalty = 500x
model, penalty = 0
Results: Experiment 2
x (mm)
Subject S5, = 2.99 mm
y (m
m)
exp., penalty = 500model, penalty = 500x
exp., penalty = 0
Comparison with experiment
Results: Experiment 2
x (mm)
x (mm)
y (m
m)
y (m
m)
S1 S2 S3
S4 S5
exp., penalty = 500model, penalty = 500x
exp., penalty = 0
x (mm)
Results: Experiment 2
Conclusion
Subjects shift their mean movement endpoints in response to changes in penalties and location of the penalty region as predicted by our model.
In our model, subjects are ideal movement planners who choose movement strategies to maximize expected gain.
Movement planning takes extrinsic costs and the subject’s own motor uncertainty into account.
Thank you!
Configuration 1 Configuration 7Configuration: Configuration:
Results: Experiment 1 and 2
Configuration 1 Configuration 7Configuration: Configuration:
Results: Experiment 1 and 2
Q-Q Plot
Observed Value
Exp
ecte
d N
orm
al V
alue
xhit-xmean (mm)
y hit-y
mea
n (m
m)
xhit-xmean (mm)
yhit-ymean (mm)
-20 -10 0 10 20
-20
-10
0
10
20
-20
-10
0
10
20
Subject S4, = 3.62 mm,72x15 = 1080 end points
Distribution ofmovement end points
20
10
0
-10
-20
Distribution of movement end points
xhit-xmean (mm)
y hit-y
mea
n (m
m)
Subject S4, = 3.62 mm,72x15 = 1080 end points
0, pos 1 200, pos 1 400, pos 1 800, pos 1
0, pos 2 200, pos 2 400, pos 2 800, pos 2
0, pos 3 200, pos 3 400, pos 3 800, pos 30 10-10 0 10-10 0 10-10 0 10-10
010
-10
010
-10
010
-10
Experiment 1: Results
Experiment 1: Results
Subject score performance
S3 3.33 mm
$15.80 97.57%
S5 3.38 mm
$15.40 99.92%
S1 3.46 mm
$15.73 98.60%
S4 4.43 mm
$14.58 107.67%
S2 4.86 mm
$13.08 104.92%
Experiment 1: Results