What autocorrelation tells us about motor variability: Insights from dart throwing

In sports such as golf and darts it is important that one can produce ballistic movements of an object towards a goal location with as little variability as possible. A factor that influences this variability is the extent to which motor planning is updated from movement to movement based on observed errors. Previous work has shown that for reaching movements, our motor system uses the learning rate (the proportion of an error that is corrected for in the planning of the next movement) that is optimal for minimizing the endpoint variability. Here we examined whether the learning rate is hard-wired and therefore automatically optimal, or whether it is optimized through experience. We compared the performance of experienced dart players and beginners in a dart task. A hallmark of the optimal learning rate is that the lag-1 autocorrelation of movement endpoints is zero. We found that the lag-1 autocorrelation of experienced dart players was near zero, implying a near-optimal learning rate, whereas it was negative for beginners, suggesting a larger than optimal learning rate. We conclude that learning rates for trial-by-trial motor learning are optimized through experience. This study also highlights the usefulness of the lag-1 autocorrelation as an index of performance in studying motor-skill learning

What autocorrelation tells us about motor variability: insights from dart throwing.

In sports such as golf and darts it is important that one can produce ballistic movements of an object towards a goal location with as little variability as possible. A factor that influences this variability is the extent to which motor planning is updated from movement to movement based on observed errors. Previous work has shown that for reaching movements, our motor system uses the learning rate (the proportion of an error that is corrected for in the planning of the next movement) that is optimal for minimizing the endpoint variability. Here we examined whether the learning rate is hard-wired and therefore automatically optimal, or whether it is optimized through experience. We compared the performance of experienced dart players and beginners in a dart task. A hallmark of the optimal learning rate is that the lag-1 autocorrelation of movement endpoints is zero. We found that the lag-1 autocorrelation of experienced dart players was near zero, implying a near-optimal learning rate, whereas it was negative for beginners, suggesting a larger than optimal learning rate. We conclude that learning rates for trial-by-trial motor learning are optimized through experience. This study also highlights the usefulness of the lag-1 autocorrelation as an index of performance in studying motor-skill learning

Effect of learning rate on variance and serial correlation.

<p><b>A</b> Simulated set of 45 movement endpoints if learning rate <i>B</i> = 0 (i.e., no corrections). Consecutive endpoints are connected by lines. Endpoints were generated using the model of van Beers (2009) with <i>w</i> = 0.2, where <i>w</i> is the proportion of the total effect of motor noise that arises during motor planning. <b>B</b> The vertical component of the endpoints shown in <b>A</b> plotted as a function of the trial number. <b>C</b> The same as in <b>A</b>, but now for <i>B</i> = 0.39, which is the optimal learning rate for this value of <i>w</i>. <b>D</b> The vertical component of the endpoints shown in <b>C</b> plotted as a function of the trial number. <b>E</b> The same as in <b>A</b>, but now for <i>B</i> = 1 (i.e., correct for the full error). The same set of random numbers was used in <b>A</b>, <b>C</b> and <b>E</b>, only the value of <i>B</i> varied. <b>F</b> The vertical component of the endpoints shown in <b>E</b> plotted as a function of the trial number.</p

All endpoints of all participants in the Dart task.

<p>The circles denote the edges of the concentric rings on the dartboard, dots indicate the positions where the dart landed and red ellipses represent 95% confidence ellipses of the endpoints. All participants hit the dartboard in every trial.</p

Observed relation between the performance in the two tasks.

<p><b>A</b> Variance in the Reach task as a function of variance in the Dart task. Each data point represents a participant. <b>B</b> ACF(1) in the Reach task as a function of ACF(1) in the Dart task.</p

Mean variance and autocorrelation in the two tasks.

<p><b>A</b> Variance in the Dart task. <b>B</b> Variance in the Reach task. <b>C</b> ACF(1) in the Dart task. <b>D</b> ACF(1) in the Reach task. In all panels, bars indicate the mean of all participants per group, and error bars denote the between-participant standard error. *: <i>p</i><0.05, **: <i>p</i><0.01, ***: <i>p</i><0.001, NS: <i>p</i>>0.05.</p

Representative examples of errors as a function of trial number in the Dart task.

<p>The vertical component of each endpoint is shown. A value of 0 denotes the bullseye. <b>A</b> Data from an Expert. <b>B</b> Data from a Beginner.</p

Effect of <i>w</i> on the optimal learning rate and the ACF(1).

<p><b>A</b> Variance as a function of learning rate <i>B</i> for different values of <i>w</i> (the proportion of the total motor variance that arises during motor planning) according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0064332#pone.0064332.e001" target="_blank">equation 1</a>. The variance is expressed in units of Σ<i>_mot</i>. The location of the minimum (indicated by small circles) depends on the value of <i>w</i>. <b>B</b> ACF(1) as a function of learning rate <i>B</i> for different values of <i>w</i> according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0064332#pone.0064332.e002" target="_blank">equation 2</a>. The learning rate for which the ACF(1) vanishes is equal to the learning rate for which the variance (in <b>A</b>) is minimal. <b>C</b> Variance plotted as a function of ACF(1) according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0064332#pone.0064332.e004" target="_blank">Equation 4</a>. This figure shows directly that for each value of <i>w</i> the variance is minimal if ACF(1) = 0.</p

Observed relation between variance and autocorrelation.

<p><b>A</b> ACF(1) as a function of variance for the Dart task. Each data point represents a participant. Dots surrounded by a circle indicate the two youngest Experts, who were in the age range of the Beginners. <b>B</b> ACF(1) as a function of variance for the Reach task.</p