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.