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



The green target is hit: +100 points 100  Experimental task



-500  Experimental task The red target is hit: -500 points -500

 Experimental task

 Experimental task 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: 500 End of trial Experimental task

Rapidly touch a point with your fingertip. What should you do? Responding after the time limit: -700 points 18 mm Experimental task

Thought experiment : -500 : 100 points (2.5 ¢) x (mm) y (mm) 100 points  = 4.83 mm

Thought experiment x (mm) y (mm) 100 points 200 points  = 4.83 mm : -500 : 100 points (2.5 ¢)

Thought experiment x (mm) y (mm) 100 points 300 points 100 points  = 4.83 mm : -500 : 100 points (2.5 ¢)

Thought experiment x (mm) y (mm) 100 points -100 points 100 points -400 points  = 4.83 mm : -500 : 100 points (2.5 ¢)

Thought experiment x (mm) y (mm) 100 points -32 points 100 points -400 points..  = 4.83 mm : -500 : 100 points (2.5 ¢)

Thought experiment x (mm) y (mm) -32 points 3070 points  = 4.83 mm : -500 : 100 points (2.5 ¢)

Thought experiment x (mm) y (mm) -32 points 3070 points 2546 points  = 4.83 mm : -500 : 100 points (2.5 ¢)

Thought experiment x (mm) y (mm) -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): < points per trial x (mm) y (mm)  = 4.83 mm target: 100 penalty: -500

x [mm] y [mm] < points per trial xyyyxx penalty: 0penalty: 500penalty: 100 x, y: mean movement end point [mm] Thought experiment  = 4.83 mm

 100 A M aximum E xpected Ga in Model of Move ment Planning Key assumption: 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.

Distribution of movement end points x hit -x mean (mm) y hit -y mean (mm) Subject S4,  = 3.62 mm, 72x15 = 1080 end points cond 1cond 2cond 3cond 4 cond 5cond 6cond 7cond 8 cond 9cond 10cond 11cond

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) R1.5R2R R = 9 mm Maloney, Trommershäuser, Landy, Poster, VSS 2003, SA46 Trommershäuser, Maloney, Landy (2003) JOSA A, in press.

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. Test of the Model: First Results Maloney, Trommershäuser, Landy, Poster, VSS 2003, SA46 Trommershäuser, 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 R = 9 mm

Results: Experiment 1 x (mm) Subject S5,  = 2.99 mm Model prediction: y (mm) model, penalty = 0

x (mm) Subject S5,  = 2.99 mm Model prediction: configuration 1 y (mm) model, penalty = 500 x model, penalty = 0 Results: Experiment 1

x (mm) Subject S5,  = 2.99 mm Model prediction: configuration 2 y (mm) model, penalty = 500 x model, penalty = 0 Results: Experiment 1

x (mm) Subject S5,  = 2.99 mm Model prediction: configuration 3 y (mm) model, penalty = 500 x model, penalty = 0 Results: Experiment 1

x (mm) Subject S5,  = 2.99 mm Model prediction: configuration 4 y (mm) model, penalty = 500 x model, penalty = 0 Results: Experiment 1

x (mm) Subject S5,  = 2.99 mm y (mm) exp., penalty = 500 model, penalty = 500 x exp., penalty = 0 Comparison with experiment Results: Experiment 1

x (mm) y (mm) S1S2S3 S4S5 exp., penalty = 500 model, penalty = 500 x exp., penalty = 0 x (mm) Results: Experiment 1

Movement endpoints in response to more complex 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 R = 9 mm

x (mm) Subject S5,  = 2.99 mm Model prediction: configuration 1 y (mm) model, penalty = 500 x model, penalty = 0 Results: Experiment 2

x (mm) Subject S5,  = 2.99 mm Model prediction: configuration 2 y (mm) model, penalty = 500 x model, penalty = 0 Results: Experiment 2

x (mm) Subject S5,  = 2.99 mm Model prediction: configuration 3 y (mm) model, penalty = 500 x model, penalty = 0 Results: Experiment 2

x (mm) Subject S5,  = 2.99 mm Model prediction: configuration 4 y (mm) model, penalty = 500 x model, penalty = 0 Results: Experiment 2

x (mm) Subject S5,  = 2.99 mm y (mm) exp., penalty = 500 model, penalty = 500 x exp., penalty = 0 Comparison with experiment Results: Experiment 2

x (mm) y (mm) S1S2S3 S4S5 exp., penalty = 500 model, penalty = 500 x 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 1Configuration 7 Configuration: Results: Experiment 1 and 2

Configuration 1Configuration 7 Configuration: Results: Experiment 1 and 2

Q-Q Plot Observed Value Expected Normal Value x hit -x mean (mm) y hit -y mean (mm) x hit -x mean (mm) y hit -y mean (mm) Subject S4,  = 3.62 mm, 72x15 = 1080 end points Distribution of movement end points

Distribution of movement end points x hit -x mean (mm) y hit -y mean (mm) Subject S4,  = 3.62 mm, 72x15 = 1080 end points 0, pos 1200, pos 1400, pos 1800, pos 1 0, pos 2200, pos 2400, pos 2800, pos 2 0, pos 3200, pos 3400, pos 3800, pos

Experiment 1: Results

Subject  score performance S33.33 mm$ % S53.38 mm$ % S13.46 mm$ % S44.43 mm$ % S24.86 mm$ % Experiment 1: Results