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
Movement planning
Why?
motivation,
movement goal,
target selection
What?
Where?
target identification,
target localization,
regions to be avoided
How?
selection of trajectory,
biomechanical constraints,
speed, accuracy
Outline
I.
A Maximum Expected Gain Model
of Movement under Risk
(MEGaMove)
II.
Experimental test of the model
III. Conclusion
Experimental task
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
The red target is hit:
-500 points
-500
-500
Experimental task
Experimental task
Scores add if both
targets are hit:
-500 100
-500 100
Experimental task
Experimental task
You are too slow: -700
The screen is hit
later than 700 ms
after target display:
-700 points.
Experimental task
Current score: 500
End of trial
Experimental task
Rapidly touch a point with your fingertip.
0
0
Responding after
the time limit:
-700 points
0
-500
0
0
100
0
What should you do?
18 mm
Thought experiment
: -500
: 100 points (2.5 ¢)
y (mm)
100 points
x (mm)
 = 4.83 mm
Thought experiment
: -500
: 100 points (2.5 ¢)
100 points
100 points
y (mm)
200 points
x (mm)
 = 4.83 mm
Thought experiment
: -500
: 100 points (2.5 ¢)
y (mm)
100 points
100 points
100 points
300 points
x (mm)
 = 4.83 mm
Thought experiment
: -500
: 100 points (2.5 ¢)
y (mm)
100 points
100 points
100 points
-400 points
-100 points
x (mm)
 = 4.83 mm
Thought experiment
: -500
: 100 points (2.5 ¢)
....
y (mm)
100 points
100 points
100 points
-400 points
-32 points
x (mm)
 = 4.83 mm
Thought experiment
: -500
: 100 points (2.5 ¢)
-32 points
y (mm)
3070 points
x (mm)
 = 4.83 mm
Thought experiment
: -500
: 100 points (2.5 ¢)
-32 points
y (mm)
3070 points
2546 points
x (mm)
 = 4.83 mm
Thought experiment
: -500
: 100 points (2.5 ¢)
-32 points
y (mm)
3070 points
2546 points
2257 points
x (mm)
 = 4.83 mm
Expected gain as function of
mean movement end point (x,y):
points
per trial
y (mm)
10
5
90
60
30
0
-30
<-60
-0
-5
-10
-10 -5 0 5
x (mm)
 = 4.83 mm
10 15 20
target: 100
penalty: -500
Thought experiment
points per trial
penalty: 0
y
penalty: 100
x
y
penalty: 500
x
y
x
90
60
30
0
-30
<-60
x [mm]
 = 4.83 mm
y [mm]
y [mm]
y [mm]
x, y: mean movement end point [mm]
x [mm]
x [mm]
A Maximum Expected Gain Model of Movement Planning
Key assumption:
-500 100
The mover chooses the motor strategy
that maximizes the expected gain .
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, SA46
Trommershäuser, Maloney, Landy (2003) JOSA A, in press.
-10
cond 2
cond 3
cond 4
cond 5
cond 6
cond 7
cond 8
cond 9
cond 10
cond 11
cond 12
10
-10
0
10
cond 1
-10
0
yhit-ymean (mm)
0
10
Distribution of movement end points
-10
0
10 -10
Subject S4,  = 3.62 mm,
72x15 = 1080 end points
0
10 -10
0
10
xhit-xmean (mm)
-10
0
10
Test of the Model: First Results
Movement endpoints in response to changes
in penalty distance and penalty value
R = 9 mm
6 stimulus configurations:
(varied within block)
R
1.5R
2R
3 penalty conditions: 0, -100, -500 points
(varied between blocks)
Maloney, Trommershäuser, Landy, Poster, VSS 2003, SA46
Trommershäuser, Maloney, Landy (2003) JOSA A, in press.
Test of the Model: First Results
As predicted by the model:
Subjects shifted their mean movement
endpoint farther from the center of
the green target
• for higher penalty values,
• for closer penalty regions.
More variable subjects won less money.
Subjects’ performance did not differ
significantly from optimal.
Maloney, Trommershäuser, Landy, Poster, VSS 2003, SA46
Trommershäuser, Maloney, Landy (2003) JOSA A, in press.
Test of the model: Experiment 1
Movement endpoints in response to novel
stimulus configurations.
4 stimulus
configurations:
(varied within block)
1
2
2 penalty conditions:
0 and -500 points (varied between blocks)
5 “practiced movers”
1 session: 12 warm-up trials,
6x2x16 trials per session,
24 data points per condition
3
4
R = 9 mm
Results: Experiment 1
Model prediction:
y (mm)
model, penalty = 0
x (mm)
Subject S5,  = 2.99 mm
Results: Experiment 1
Model prediction: configuration 1
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
model, penalty = 0
model, penalty = 500
Results: Experiment 1
Model prediction: configuration 2
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
model, penalty = 0
model, penalty = 500
Results: Experiment 1
Model prediction: configuration 3
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
model, penalty = 0
model, penalty = 500
Results: Experiment 1
Model prediction: configuration 4
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
model, penalty = 0
model, penalty = 500
Results: Experiment 1
Comparison with experiment
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
exp., penalty = 0
exp., penalty = 500
model, penalty = 500
y (mm)
Results: Experiment 1
S1
S2
S3
y (mm)
x (mm)
x
S4
S5
x (mm)
x (mm)
exp., penalty = 0
exp., penalty = 500
model, penalty = 500
Test of the model: Experiment 2
Movement endpoints in response to more
complex stimulus configurations.
4 “more complex”
configurations:
(varied within block)
1
2
2 penalty conditions:
0 and -500 points (varied between blocks)
5 “practiced movers”
1 session: 12 warm-up trials,
6x2x16 trials per session,
24 data points per condition
3
4
R = 9 mm
Results: Experiment 2
Model prediction: configuration 1
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
model, penalty = 0
model, penalty = 500
Results: Experiment 2
Model prediction: configuration 2
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
model, penalty = 0
model, penalty = 500
Results: Experiment 2
Model prediction: configuration 3
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
model, penalty = 0
model, penalty = 500
Results: Experiment 2
Model prediction: configuration 4
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
model, penalty = 0
model, penalty = 500
Results: Experiment 2
Comparison with experiment
y (mm)
x
x (mm)
Subject S5,  = 2.99 mm
exp., penalty = 0
exp., penalty = 500
model, penalty = 500
y (mm)
Results: Experiment 2
S1
S2
S3
y (mm)
x (mm)
x
S4
S5
x (mm)
x (mm)
exp., penalty = 0
exp., penalty = 500
model, penalty = 500
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!
Results: Experiment 1 and 2
Configuration:
Configuration 1
Configuration:
Configuration 7
Results: Experiment 1 and 2
Configuration:
Configuration 1
Configuration:
Configuration 7
Q-Q Plot
Distribution of
movement end points
20
xhit-xmean (mm)
Expected Normal Value
10
yhit-ymean (mm)
20
10
0
-10
-20
-20
-10
0
10
xhit-xmean (mm)
Subject S4,  = 3.62 mm,
72x15 = 1080 end points
20
0
-10
-20
yhit-ymean (mm)
20
10
0
-10
-20
Observed Value
-10
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 3
10
-10
0
10
0, pos 1
-10
0
yhit-ymean (mm)
0
10
Distribution of movement end points
-10
0
10 -10
Subject S4,  = 3.62 mm,
72x15 = 1080 end points
0
10 -10
0
10
xhit-xmean (mm)
-10
0
10
Experiment 1: Results
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%