when uncertainty matters: the selection of rapid goal-directed movements

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)


300 points

100 points

= 4.83 mm

: -500 : 100 points (2.5 ¢)

Thought experiment

x (mm)

y (m

m)


-100 points

100 points-400 points

= 4.83 mm

: -500 : 100 points (2.5 ¢)

Thought experiment

x (mm)

y (m

m)


-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


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


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)


Model prediction: configuration 1

y (m

m)

model, penalty = 500x

model, penalty = 0


x (mm)



y (m

m)


model, penalty = 0


x (mm)


y (m

m)

exp., penalty = 500model, penalty = 500x

exp., penalty = 0

Comparison with experiment


x (mm)

x (mm)

y (m

m)

y (m

m)

S1 S2 S3

S4 S5


exp., penalty = 0

x (mm)


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)



y (m

m)


model, penalty = 0


x (mm)


y (m

m)


exp., penalty = 0

Comparison with experiment


x (mm)

x (mm)

y (m

m)

y (m

m)

S1 S2 S3

S4 S5


exp., penalty = 0

x (mm)


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

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


Distribution ofmovement end points

20

10

0

-10

-20

Distribution of movement end points

xhit-xmean (mm)

y hit-y

mea

n (m

m)


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

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

when uncertainty matters: the selection of rapid goal-directed movements

Documents

data points

points3070 points2257

points3070 points2546

penalty distance

penalty value test

target display

closer penalty regions

block2 penalty conditions