Optimal compensation for changes in
effective movement variability
in planning movement under risk
Julia Trommershäuser 1, Sergei Gepshtein 2,
Larry Maloney 1, Mike Landy 1, Marty Banks 2
1:
Dept. of Psychology and Center for Neural Science
NYU, New York, USA
2: School of Optometry, UC Berkeley, Berkeley, USA
Sarasota, May 3, 2004
Motor responses have consequences.
Trommershäuser, Maloney, Landy (2003). JOSA A, 20,1419.
Trommershäuser, Maloney, Landy (2003). Spat. Vis., 16, 255.
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
Outline
I.
Optimal Performance:
A Maximum Expected Gain Model
of Movement under Risk (MEGaMove)
II.
Human vs. Optimal Performance:
Compensation for Changes in
Effective Movement Variability
III. Conclusion
Optimal visuo-motor strategy
The optimal mover chooses the motor
strategy that maximizes the
expected gain.
-500 100
Trommershäuser, Maloney, Landy (2003). JOSA A, 20,1419.
Trommershäuser, Maloney, Landy (2003). Spat. Vis., 16, 255.
Distribution of movement endpoints:
Bivariate Gaussian, width :
yhit-ymean (mm)
20
10
0
-10
-20  = 3.62 mm,
72x15 = 1080 end points
-20 -10
0
10
20
xhit-xmean (mm)
Optimal visuo-motor strategy
optimal mean end point
σ = 3.48 mm
Optimal visuo-motor strategy
optimal mean end point
σ = 3.48 mm
What if we change your
movement variability?
Optimal visuo-motor strategy
optimal mean end point
optimal mean end point, increased noise
σ = 3.48 mm
σ = 6.19 mm
Optimal visuo-motor strategy
Parameters of the model:
• reward structure of experiment: -500 100
experimenter-imposed
• subject’s movement variability :
measured
 = 4.17 mm
 = 3.23 mm
Optimal visuo-motor strategy
Parameters of the model:
• reward structure of experiment: -500 100
experimenter-imposed
• subject’s movement variability :
measured
All parameters estimated.
Parameter-free predictions !
Outline
I.
Optimal Performance:
A Maximum Expected Gain Model
of Movement under Risk (MEGaMove)
II.
Human vs. Optimal Performance:
Compensation for Changes in
Effective Movement Variability
III. Conclusion
Experiment
Manipulation of effective
movement variability:
perturbation of visual feedback
Experiment
Perturbation of visual feedback:
 increase in effective variability
Experiment
Visually-imposed changes in effective
movement variability.
Idea:
• finger visually represented by red point
• on each trial: unpredictable perturbation
of the visual feedback of the finger tip
• Points are scored based on the perturbed
finger position
Experiment
Visually-imposed changes in effective
movement variability.
Perturbation of the
visual feedback of
the finger tip by
Δx 
 Δy 
 
2
 σpert
: Gaussian  0, 
  0
 
0 

2
σpert  

Medium increase in noise:  pert = 4.5 mm
 pert = 6 mm
High increase in noise:
Experiment
Visually-imposed changes in effective
movement variability.
Experimental set-up:
3
3
Added
noise
4
Penalties Configurations
Design
near
middle
varied
within
blocks
Reward: 100
Penalties: 0 -200 -500
σpert :
0 mm
4.5 mm 6 mm
varied
between
blocks
varied
between
sessions
(retraining)
Design
• Six subjects
• 1 practice session: 300 trials,
decreasing time limit
• per noise condition:
1 learning session: 300 trials
2 sessions of data collection: 360 trials each
(40 repetitions per condition)
• Payment: 1000 points = 25¢
Results
Additivity of Variances
Optimal visuo-motor strategy
optimal mean end point, no added noise
optimal mean end point, σ pert = 6 mm
σ eff = 3.48 mm
σ eff = 6.19 mm
Results
Scores: average subject data
near
middle
Results
Scores: actual vs. optimal performance
near
middle
near, -200
middle, -200
near, -500
middle, -500
Results
Shift in end points: average subject data
near
middle
Results
Shift in end points: actual vs. optimal shifts
near
near, -200
middle, -200
near, -500
middle, -500
middle
Conclusions
Movement planning takes
extrinsic costs and the
subject’s own motor
uncertainty into account.
Subjects combine visual
and motor variability to
compensate for changes
in effective movement variability.
Subjects do not differ significantly from
ideal movement planners that maximize gain.
Thank you!
Results
Learning of “new” effective variability
learning session
actual finger position
σpert = 4.5 mm
σpert = 6 mm
Results: trial-by-trail analysis
Results: trial-by-trail analysis
Experiment 2
Movement endpoints in response to changes
in relative movement variability
Stimulus configurations:
small:
large:
6.3 mm
9 mm
Movement variability  remains constant.
Relative to stimulus size  is larger for
the small configuration.

Experiment 2
Movement endpoints in response to changes
in relative movement variability
Stimulus configurations:
small:
large:
6.3 mm

/R
9 mm

1
larger relative variability 
/R
1
smaller relative variability 
Experiment 2
Movement endpoints in response to changes
in relative movement variability
4 stimulus configurations in 2 sizes:
small: R = 6.3 mm
large: R = 9 mm
(varied within blocks)
R
2 penalty conditions: 0 and -500 points
(varied between blocks)
1 practice session: 300 trials, decreasing time limit
1 session: 16 warm-up trials, 6x2x32 trials
2R
Experiment 2: Results
Subject 1:  = 3.16 mm
x/R = 1.1
x/R = 0.7
large, penalty = 0
small, penalty = 0
large, penalty = 500
small, penalty = 500
x model
Experiment 2: Results
(Data corrected for constant pointing bias)
Experiment 2: Results
(Data corrected for constant pointing bias)
Experiment 2: Results
(Data corrected for constant pointing bias)
Experiment 2: Results
(Data corrected for constant pointing bias)
Experiment 2: Results
(Data corrected for constant pointing bias)
Experiment 2: Results
(Data corrected for constant pointing bias)
Experiment 2: Results
Subjects shift their relative mean
movement endpoints farther when their
relative movement variability increases.
Subjects win less money in conditions with
higher relative motor variability.
In most conditions subjects are around
95% of optimal performance.
Distribution of movement end points
right, middle
penalty
0
10
-10
10
right, near
0
left, near
10
-10
0
-200
-400
-10
0
yhit-ymean (mm)
left, middle
-10
0
10 -10
 = 3.62 mm,
72 data points per condition
0
10 -10
0
10
xhit-xmean (mm)
-10
0
10
Experimental task
Acknowledgements
Berkeley:
NYU:
Marty Banks
Sergei Gepshtein
Mike Landy
Larry Maloney
Thank you!
Support
Deutsche Forschungsgemeinschaft (Emmy-Noether-Programme);
Grant EY08266 from the National Institute of Health;
Grant RG0109/1999-B from the Human Frontiers Science Program.
A Maximum Expected Gain Model of Movement Planning
Key assumption:
The mover chooses the visuo-motor
strategy that maximizes the
expected gain Γ.
-500 100
Expected gain Γ of
mean movement end point (x,y):
Γ(x, y) = Vgreen P(green | x, y) + Vred P(red | x, y)
P(green |x, y) =

dx dy  phit  x, y  |x, y 
green
Trommershäuser, Maloney, Landy (2003). JOSA A, 20,1419.
Trommershäuser, Maloney, Landy (2003). Spat. Vis., 16, 255.