When Uncertainty Matters: The Selection of Rapid, Goal-Directed Movements J. Trommershäuser, L. T. Maloney , M. S. Landy, Psychology and Neural Science, New York University Supported by NIH EY08266 and HFSP RG0109/1999-B, J.T. funded by the DFG (Emmy-Noether *: M aximum E xpected Ga in Model of Move ment planning VSS 2003 TALK Sarasota, FL Movement under Risk Kassi Price, 2001 US Nationals The green target is hit: +100 points 100 100 The red target is hit: -500 points -500 x (mm) y (mm) 100 points 100 points -32 points 100 points -400 points . . . . = 4.83 mm : -500 : 100 points (2.5 ¢) x (mm) y (mm) -32 points 3070 points = 4.83 mm : -500 : 100 points (2.5 ¢) Expected Gain Surface 90 0 60 <-60 -30 30 points per trial x (mm) y (mm) = 4.83 mm -10-5 0 5 10 15 20 -10 -5 -0 5 10 target: 100 penalty: -500 x [mm] x [mm] x [mm] y [mm] y [mm] y [mm] 90 0 60 <-60 -30 30 points per trial x y y y x x penalty: 0 penalty: 500 penalty: 100 x, y: mean movement end point [mm] = 4.83 mm Key assumption: The mover chooses the motor strategy that maximizes the expected gain , taking into account motor uncertainty. 100 -500 Consequence: The choice of motor strategy depends on • the reward structure of the environment • the mover's own motor variability. Trommershäuser, Maloney, Landy (2003) JOSA A, in press. Trommershäuser, Maloney, Landy (2003) Spatial Vision, 16, 255-275. Maloney, Trommershäuser, Landy (2003) VSS Mean movement end points with stimulus configurations at different orientations. 5 “practiced movers” 1 session: 12 warm- up trials, 6x2x16 trials per session, 24 data points per condition 2 penalty conditions: 0 and -500 points Experiment 1 1 2 3 4 R = 9 mm x (mm) y (mm) S1 exp., penalty = 500 model, penalty = 500 x exp., penalty = 0 Results: Mean movement end points with more complex configurations. 5 “practiced movers” 1 session: 12 warm- up trials, 6x2x16 trials per session, 24 data points per condition 2 penalty conditions: 0 and -500 points Experiment 2 x (mm) exp., penalty = 500 model, penalty = 500 x exp., penalty = 0 x (mm) x (mm) y (mm) y (mm) S1 S2 S3 S4 S5 x (mm) Results: x (mm) x (mm) y (mm) y (mm) MEGaMove* Model for Movement under Risk MEGaMove Model: Effect of Motor Uncertainty MEGaMove Model: The Expected Gain Surface The Experimental Task Speeded movement: Hit targets, with Fingertip, avoid penalties. 700 ms time limit. S2 S3 S5 S4 The MEGaMove* Model predicts that subjects will take account of their own motor uncertainty in planning movements. Here we report the outcomes of two experimental tests of the model in simple environments where there are explicit gains and losses associated with the outcomes of movements. Our results indicate that humans take both costs and their own movement uncertainty into account in planning movement. In this simple task, a motor strategy is characterized by the distribution of end points around a mean end point. Each mean end point corresponds to an expected gain. This expected gain depends only on the subject’s motor uncertainty and the rewards and penalties present in the environment. We can compute, for any subject, an expected gain surface.