When Uncertainty Matters: The Selection of Rapid Goal-Directed Movements

1. 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

2. Motor responses have consequences Kassi Price, 2001 US Nationals

3. motivation, movement goal, target selection Why? Movement planning target identification, target localization, regions to be avoided What? Where? selection of trajectory, biomechanical constraints, speed, accuracy How?

4. Outline • A Maximum Expected Gain Model • ofMovement under Risk • (MEGaMove) • Experimental test of the model • Conclusion

5. Experimental task

6. Experimental task Start of trial: display of fixation cross (1.5 s) L

7. Experimental task Display of response area, 500 ms before target onset (114.2 mm x 80.6 mm) L

8. Experimental task Target display (700 ms) L

9. Experimental task L

10. The green target is hit: +100 points 100 Experimental task L 100

11. Experimental task L

12. The red target is hit: -500 points -500 Experimental task L -500

13. Experimental task L

14. Scores add if both targets are hit: -500 100 Experimental task L -500 100

15. Experimental task L

16. Experimental task The screen is hit later than 700 ms after target display: -700 points. You are too slow: -700

17. Experimental task End of trial Current score: 500

18. Experimental task Rapidly touch a point with your fingertip. 0 0 0 Responding after the time limit: -700points -500 100 18 mm 0 0 0 What should you do?

19. : -500 : 100 points (2.5 ¢) Thought experiment 100 points y (mm) x (mm)  = 4.83 mm

20. : -500 : 100 points (2.5 ¢) Thought experiment 100 points 100 points 200 points y (mm) x (mm)  = 4.83 mm

21. : -500 : 100 points (2.5 ¢) Thought experiment 100 points 100 points 100 points 300 points y (mm) x (mm)  = 4.83 mm

22. : -500 : 100 points (2.5 ¢) Thought experiment 100 points 100 points 100 points -400 points y (mm) -100 points x (mm)  = 4.83 mm

23. : -500 : 100 points (2.5 ¢) Thought experiment 100 points 100 points 100 points -400 points y (mm) . . . . -32 points x (mm)  = 4.83 mm

24. : -500 : 100 points (2.5 ¢) Thought experiment -32 points 3070 points y (mm) x (mm)  = 4.83 mm

25. : -500 : 100 points (2.5 ¢) Thought experiment -32 points 3070 points y (mm) 2546 points x (mm)  = 4.83 mm

26. : -500 : 100 points (2.5 ¢) Thought experiment -32 points 3070 points y (mm) 2546 points 2257 points x (mm)  = 4.83 mm

27. 90 60 30 points per trial 0 10 -30 <-60 5 -0 -5 -10 -10 -5 0 5 10 15 20 Expected gain as function of mean movement end point (x,y): y (mm) target: 100 penalty: -500 x (mm)  = 4.83 mm

28. 90 penalty: 0 penalty: 100 penalty: 500 60 30 0 -30 points per trial <-60 y x y x y x y [mm] y [mm] y [mm] x [mm] x [mm] x [mm] Thought experiment x, y: mean movement end point [mm]  = 4.83 mm

29. Consequence: • The choice of motor strategy • dependson • the reward structure of the • environment • the mover's own motor variability. L Maloney, Trommershäuser, Landy, Poster, VSS 2003, SA46 Trommershäuser, Maloney, Landy (2003) JOSA A, in press. A Maximum Expected Gain Model of Movement Planning Key assumption: The mover chooses the motor strategy that maximizes the expected gain . -500 100

30. cond 5 cond 1 cond 9 cond 10 cond 2 cond 6 cond 11 cond 3 cond 7 cond 12 cond 4 cond 8 -10 -10 -10 -10 -10 -10 -10 0 0 0 0 0 0 0 10 10 10 10 10 10 10 Distribution of movement end points yhit-ymean (mm) xhit-xmean (mm) Subject S4,  = 3.62 mm, 72x15 = 1080 end points

31. R 1.5R 2R 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) 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.

32. 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.

33. 1 2 3 4 Test of the model: Experiment 1 Movement endpoints in response to novel stimulus configurations. 4 stimulus configurations: (varied within block) 2 penalty conditions: 0 and -500 points (varied between blocks) R = 9 mm 5 “practiced movers” 1 session: 12 warm-up trials, 6x2x16 trials per session, 24 data points per condition

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

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

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

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

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

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

40. exp., penalty = 0 exp., penalty = 500 model, penalty = 500 x Results: Experiment 1 y (mm) S1 S2 S3 x (mm) y (mm) S4 S5 x (mm) x (mm)

41. Test of the model: Experiment 2 Movement endpoints in response to more complex stimulus configurations. 1 2 3 4 4 “more complex” configurations: (varied within block) 2 penalty conditions: 0 and -500 points (varied between blocks) R = 9 mm 5 “practiced movers” 1 session: 12 warm-up trials, 6x2x16 trials per session, 24 data points per condition

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

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

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

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

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

47. exp., penalty = 0 exp., penalty = 500 model, penalty = 500 x Results: Experiment 2 y (mm) S1 S2 S3 x (mm) y (mm) S4 S5 x (mm) x (mm)

48. 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!

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

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