Julia Trommershäuser

Decision Making, Movement Planning, and Statistical Decision Theory

We discuss behavioral studies directed at understanding how probability information is represented in motor and economic tasks. By formulating the behavioral tasks in the language of statistical decision theory, we can compare performance in equivalent tasks in different domains. Subjects in traditional economic decision-making tasks often misrepresent the probability of rare events and typically fail to maximize expected gain. By contrast, subjects in mathematically equivalent movement tasks often choose movement strategies that come close to maximizing expected gain. We discuss the implications of these different outcomes, noting the evident differences between the source of uncertainty and how information about uncertainty is acquired in motor and economic tasks.

Optimal Compensation for Changes in Task-Relevant Movement Variability

Effective movement planning should take into account the consequences of possible errors in executing a planned movement. These errors can result from either sensory uncertainty or variability in movement planning and production. We examined the ability of humans to compensate for variability in sensory estimation and movement production under conditions in which variability is increased artificially by the experimenter. Subjects rapidly pointed at a target region that had an adjacent penalty region. Target and penalty hits yielded monetary rewards and losses. We manipulated the task-relevant variability by perturbing visual feedback of finger position during the movement. The feedback was shifted in a random direction with a random amplitude in each trial, causing an increase in the task-relevant variability. Subjects were unable to counteract this form of perturbation. Rewards and penalties were based on the perturbed, visually specified finger position. Subjects rapidly acquired an estimate of their new variability in <120 trials and adjusted their aim points accordingly. We compared subjects performance to the performance of an optimal movement planner maximizing expected gain. Their performance was consistent with that expected from an optimal movement planner that perfectly compensated for externally imposed changes in task-relevant variability. When exposed to novel stimulus configurations, aim points shifted in the first trial without showing any detectable trend across trials. These results indicate that subjects are capable of changing their pointing strategy in the presence of externally imposed noise. Furthermore, they manage to update their estimate of task-relevant variability and to transfer this estimate to novel stimulus configurations.

Humans Rapidly Estimate Expected Gain in Movement Planning

We studied human movement planning in tasks in which subjects selected one of two goals that differed in expected gain. Each goal configuration consisted of a target circle and a partially overlapping penalty circle. Rapid hits into the target region led to a monetary bonus; accidental hits into the penalty region incurred a penalty. The outcomes assigned to target and penalty regions and the spatial arrangement of those regions were varied. Subjects preferred configurations with higher expected gain whether selection involved a rapid pointing movement or a choice by key press. Movements executed to select one of two goal configurations exhibited the same movement dynamics as pointing movements directed at a single configuration, and were executed with the same high efficiency. Our results suggest that humans choose near-optimal strategies when planning their movement, and can base their selection of strategy on a rapid judgment about the expected gain associated with possible movement goals.

Dynamic integration of information about salience and value for saccadic eye movements

Humans shift their gaze to a new location several times per second. It is still unclear what determines where they look next. Fixation behavior is influenced by the low-level salience of the visual stimulus, such as luminance, contrast, and color, but also by high-level task demands and prior knowledge. Under natural conditions, different sources of information might conflict with each other and have to be combined. In our paradigm, we trade off visual salience against expected value. We show that both salience and value information influence the saccadic end point within an object, but with different time courses. The relative weights of salience and value are not constant but vary from eye movement to eye movement, depending critically on the availability of the value information at the time when the saccade is programmed. Short-latency saccades are determined mainly by salience, but value information is taken into account for long-latency saccades. We present a model that describes these data by dynamically weighting and integrating detailed topographic maps of visual salience and value. These results support the notion of independent neural pathways for the processing of visual information and value.

Optimality of human movement under natural variations of visual-motor uncertainty

Biological movements are prone to error. Different movements lead to different errors, and the distributions of errors depend on movement amplitude and direction. Movement planning would benefit from taking this variability into account, by applying appropriate corrections for movements associated with the different shapes and sizes of error distributions. Here we asked whether the human nervous system can do so. In a game-like task, participants performed rapid sequences of goal-directed pointing movements in different directions, toward stimulus configurations presented at different eccentricities on a slanted touch screen. The task was to accumulate rewards by hitting target regions and to minimize losses by avoiding penalty regions. The distributions of endpoint errors varied in size and degree of anisotropy across stimulus locations. Our participants adjusted their movements toward the different locations accordingly. We compared human behavior with the optimal behavior predicted by ideal movement planner maximizing expected gain. In most cases, human behavior was indistinguishable from optimal. This is evidence that human movement planning approaches statistical optimality by representing the task-relevant movement variability.

Effects of salience and reward information during saccadic decisions under risk

Previous work has demonstrated that humans select visuomotor strategies maximizing expected gain during speeded hand movements under risk; see, e.g., [Trends Cogn. Sci. 12, 291 (2008)]; [Glimcher, eds., Neuroeconomics: Decision Making and the Brain (Elsevier, 2008), p. 95]. Here we report a similar study in which we recorded saccadic eye movements in a saccadic decision task in which monetary rewards and losses were associated with the final position of the eye movement. Saccades into a color-coded target region won points; saccades into a partially overlapping or abutting penalty region could yield a loss. The points won during the experiment were converted into a small monetary bonus at the end of the experiment. We compared participants winnings to the score of an optimal observer maximizing expected gain that was calculated based on each participants saccadic endpoint variability, similar to a recent model of optimal movement planning under risk [J. Opt. Soc. Am. A 20, 1419 (2003)]; [Spatial Vis. 16, 255 (2003)]. We used three different experimental paradigms with different interstimulus intervals (Gap, No Gap, and Overlap) to manipulate saccadic latencies and a fourth experiment (Memory) with a prolonged 500 ms delay period. Our results show that our subjects took the reward information, as specified by the different penalties, into account when making saccades and fixated onto or very close to the target region and less into the penalty region. However, the selected strategies differed significantly from optimal strategies maximizing expected gain in conditions when the magnitude of reward or penalty was changed. Furthermore, scores were notably affected by stimulus saliency. They were higher when the target region was filled and the penalty region outlined by a thin line, as compared to conditions in which the target was indicated by a less salient stimulus. Scores were particularly poor in trials with the shortest latencies (120-140 ms) mostly obtained in the Gap paradigm. At longer latencies scores improved considerably for latencies longer than 160 ms. This was in line with an improvement in accuracy for single targets up to 160 ms. Our results indicate that processing both of reward information and of stimulus saliency affect the programming of saccades, with a dominating contribution of stimulus saliency for eye movements with faster latencies.

Visual estimation under risk

We investigate whether observers take into account their visual uncertainty in an optimal manner in a perceptual estimation task with explicit rewards and penalties for performance. Observers judged the mean orientation of a briefly presented texture consisting of a collection of line segments. The mean and, in some experiments, the variance of the distribution of line orientations changed from trial to trial. Subjects tried to maximize the number of points won in a bet on the mean texture orientation. They placed their bet by rotating a visual display that indicated two ranges of orientations: a reward region and a neighboring penalty region. Subjects won 100 points if the mean texture orientation fell within the reward region, and subjects lost points (0, 100, or 500, in separate blocks) if the mean orientation fell in the penalty region. We compared each subjects performance to a decision strategy that maximizes expected gain (MEG). For the nonzero-penalty conditions, this ideal strategy predicts subjects will adjust the payoff display to shift the center of the reward region away from the perceived mean texture orientation, putting the perceived mean orientation on the opposite side of the reward region from the penalty region. This shift is predicted to be larger for (1) larger penalties, (2) penalty regions located closer to the payoff region, and (3) larger stimulus variability. While some subjects performance was nearly optimal, other subjects displayed a variety of suboptimal strategies when stimulus variability was high and changed unpredictably from trial to trial.

Limits to Human Movement Planning in Tasks with Asymmetric Gain Landscapes

We studied human movement planning in a task with predefined costs and benefits to movement outcome. Participants pointed rapidly at stimulus configurations consisting of a target region and up to two penalty regions. Hits on the target and penalty regions resulted in monetary gains and losses. In previous studies involving single penalty regions or other symmetric target-penalty configurations, performance was optimal in the sense of maximizing expected gain. In this study, more complex, asymmetric configurations were used in which the two penalty regions carried different penalties. With these configurations, the landscape of expected gain as a function of mean end point (MEP) was spatially asymmetric. Further, the optimal movement plan with these configurations was sometimes counterintuitive (e.g., one should aim slightly inside the lesser penalty region). In one asymmetric condition, four out of six naïve participants performed suboptimally, indicating that there are limits to human movement planning. Further, the suboptimal performance was inconsistent with a model in which participants misestimate motor variability but otherwise optimally plan their movement.

Learning Stochastic Reward Distributions in a Speeded Pointing Task

Recent studies have shown that humans effectively take into account task variance caused by intrinsic motor noise when planning fast hand movements. However, previous evidence suggests that humans have greater difficulty accounting for arbitrary forms of stochasticity in their environment, both in economic decision making and sensorimotor tasks. We hypothesized that humans can learn to optimize movement strategies when environmental randomness can be experienced and thus implicitly learned over several trials, especially if it mimics the kinds of randomness for which subjects might have generative models. We tested the hypothesis using a task in which subjects had to rapidly point at a target region partly covered by three stochastic penalty regions introduced as “defenders.” At movement completion, each defender jumped to a new position drawn randomly from fixed probability distributions. Subjects earned points when they hit the target, unblocked by a defender, and lost points otherwise. Results indicate that after ∼600 trials, subjects approached optimal behavior. We further tested whether subjects simply learned a set of stimulus-contingent motor plans or the statistics of defenders movements by training subjects with one penalty distribution and then testing them on a new penalty distribution. Subjects immediately changed their strategy to achieve the same average reward as subjects who had trained with the second penalty distribution. These results indicate that subjects learned the parameters of the defenders jump distributions and used this knowledge to optimally plan their hand movements under conditions involving stochastic rewards and penalties.

The Expected Utility of Movement

Publisher Summary Movement planning shares the same structure as economic decision-making. Subjects in movement tasks are generally found to be very good at choosing motor strategies that come close to maximizing expected gain. In contrast, subjects in economic decision- making typically fail to maximize expected gain. Moreover, the sources of uncertainty in motor tasks are endogenous; they reflect the organisms own uncertainty in planning movement while, in contrast, uncertainty in economic tasks is typically imposed by the experimenter. Thus, probabilistic information from cognition, perception, and movement has different origins. Movement planning is well described by simple models that maximize expected gain while there is no single model of economic decision-making that captures all of the complexity of human behavior. Careful study of the neural circuitry underlying decision-making in the form of movement could lead to a better understanding of how the brain gathers information to make decisions and transforms them into movement.