Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models. © 2010 Nagengast et al.

Principles of sensorimotor learning.

The exploits of Martina Navratilova and Roger Federer represent the pinnacle of motor learning. However, when considering the range and complexity of the processes that are involved in motor learning, even the mere mortals among us exhibit abilities that are impressive. We exercise these abilities when taking up new activities - whether it is snowboarding or ballroom dancing - but also engage in substantial motor learning on a daily basis as we adapt to changes in our environment, manipulate new objects and refine existing skills. Here we review recent research in human motor learning with an emphasis on the computational mechanisms that are involved.

Computational mechanisms of sensorimotor control.

In order to generate skilled and efficient actions, the motor system must find solutions to several problems inherent in sensorimotor control, including nonlinearity, nonstationarity, delays, redundancy, uncertainty, and noise. We review these problems and five computational mechanisms that the brain may use to limit their deleterious effects: optimal feedback control, impedance control, predictive control, Bayesian decision theory, and sensorimotor learning. Together, these computational mechanisms allow skilled and fluent sensorimotor behavior.

Principles of sensorimotor learning

The exploits of Martina Navratilova and Roger Federer represent the pinnacle of motor learning. However, when considering the range and complexity of the processes that are involved in motor learning, even the mere mortals among us exhibit abilities that are impressive. We exercise these abilities when taking up new activities-whether it is snowboarding or ballroom dancing-but also engage in substantial motor learning on a daily basis as we adapt to changes in our environment, manipulate new objects and refine existing skills. Here we review recent research in human motor learning with an emphasis on the computational mechanisms that are involved. © 2011 Macmillan Publishers Limited. All rights reserved.

Gone in 0.6 seconds: the encoding of motor memories depends on recent sensorimotor states.

Real-world tasks often require movements that depend on a previous action or on changes in the state of the world. Here we investigate whether motor memories encode the current action in a manner that depends on previous sensorimotor states. Human subjects performed trials in which they made movements in a randomly selected clockwise or counterclockwise velocity-dependent curl force field. Movements during this adaptation phase were preceded by a contextual phase that determined which of the two fields would be experienced on any given trial. As expected from previous research, when static visual cues were presented in the contextual phase, strong interference (resulting in an inability to learn either field) was observed. In contrast, when the contextual phase involved subjects making a movement that was continuous with the adaptation-phase movement, a substantial reduction in interference was seen. As the time between the contextual and adaptation movement increased, so did the interference, reaching a level similar to that seen for static visual cues for delays >600 ms. This contextual effect generalized to purely visual motion, active movement without vision, passive movement, and isometric force generation. Our results show that sensorimotor states that differ in their recent temporal history can engage distinct representations in motor memory, but this effect decays progressively over time and is abolished by ∼600 ms. This suggests that motor memories are encoded not simply as a mapping from current state to motor command but are encoded in terms of the recent history of sensorimotor states.

Insula and striatum mediate the default bias.

Humans are creatures of routine and habit. When faced with situations in which a default option is available, people show a consistent tendency to stick with the default. Why this occurs is unclear. To elucidate its neural basis, we used a novel gambling task in conjunction with functional magnetic resonance imaging. Behavioral results revealed that participants were more likely to choose the default card and felt enhanced emotional responses to outcomes after making the decision to switch. We show that increased tendency to switch away from the default during the decision phase was associated with decreased activity in the anterior insula; activation in this same area in reaction to "switching away from the default and losing" was positively related with experienced frustration. In contrast, decisions to choose the default engaged the ventral striatum, the same reward area as seen in winning. Our findings highlight aversive processes in the insula as underlying the default bias and suggest that choosing the default may be rewarding in itself.

Choosing to make an effort: the role of striatum in signaling physical effort of a chosen action.

The possibility that we will have to invest effort influences our future choice behavior. Indeed deciding whether an action is actually worth taking is a key element in the expression of human apathy or inertia. There is a well developed literature on brain activity related to the anticipation of effort, but how effort affects actual choice is less well understood. Furthermore, prior work is largely restricted to mental as opposed to physical effort or has confounded temporal with effortful costs. Here we investigated choice behavior and brain activity, using functional magnetic resonance imaging, in a study where healthy participants are required to make decisions between effortful gripping, where the factors of force (high and low) and reward (high and low) were varied, and a choice of merely holding a grip device for minimal monetary reward. Behaviorally, we show that force level influences the likelihood of choosing an effortful grip. We observed greater activity in the putamen when participants opt to grip an option with low effort compared with when they opt to grip an option with high effort. The results suggest that, over and above a nonspecific role in movement anticipation and salience, the putamen plays a crucial role in computations for choice that involves effort costs.

Differential encoding of losses and gains in the human striatum.

Studies on human monetary prediction and decision making emphasize the role of the striatum in encoding prediction errors for financial reward. However, less is known about how the brain encodes financial loss. Using Pavlovian conditioning of visual cues to outcomes that simultaneously incorporate the chance of financial reward and loss, we show that striatal activation reflects positively signed prediction errors for both. Furthermore, we show functional segregation within the striatum, with more anterior regions showing relative selectivity for rewards and more posterior regions for losses. These findings mirror the anteroposterior valence-specific gradient reported in rodents and endorse the role of the striatum in aversive motivational learning about financial losses, illustrating functional and anatomical consistencies with primary aversive outcomes such as pain.

Predictive neural coding of reward preference involves dissociable responses in human ventral midbrain and ventral striatum.

Food preferences are acquired through experience and can exert strong influence on choice behavior. In order to choose which food to consume, it is necessary to maintain a predictive representation of the subjective value of the associated food stimulus. Here, we explore the neural mechanisms by which such predictive representations are learned through classical conditioning. Human subjects were scanned using fMRI while learning associations between arbitrary visual stimuli and subsequent delivery of one of five different food flavors. Using a temporal difference algorithm to model learning, we found predictive responses in the ventral midbrain and a part of ventral striatum (ventral putamen) that were related directly to subjects' actual behavioral preferences. These brain structures demonstrated divergent response profiles, with the ventral midbrain showing a linear response profile with preference, and the ventral striatum a bivalent response. These results provide insight into the neural mechanisms underlying human preference behavior.

Motor effort alters changes of mind in sensorimotor decision making.

After committing to an action, a decision-maker can change their mind to revise the action. Such changes of mind can even occur when the stream of information that led to the action is curtailed at movement onset. This is explained by the time delays in sensory processing and motor planning which lead to a component at the end of the sensory stream that can only be processed after initiation. Such post-initiation processing can explain the pattern of changes of mind by asserting an accumulation of additional evidence to a criterion level, termed change-of-mind bound. Here we test the hypothesis that physical effort associated with the movement required to change one's mind affects the level of the change-of-mind bound and the time for post-initiation deliberation. We varied the effort required to change from one choice target to another in a reaching movement by varying the geometry of the choice targets or by applying a force field between the targets. We show that there is a reduction in the frequency of change of mind when the separation of the choice targets would require a larger excursion of the hand from the initial to the opposite choice. The reduction is best explained by an increase in the evidence required for changes of mind and a reduced time period of integration after the initial decision. Thus the criteria to revise an initial choice is sensitive to energetic costs.

Twitching in sensorimotor development from sleeping rats to robots.

It is still not known how the 'rudimentary' movements of fetuses and infants are transformed into the coordinated, flexible and adaptive movements of adults. In addressing this important issue, we consider a behavior that has been perennially viewed as a functionless by-product of a dreaming brain: the jerky limb movements called myoclonic twitches. Recent work has identified the neural mechanisms that produce twitching as well as those that convey sensory feedback from twitching limbs to the spinal cord and brain. In turn, these mechanistic insights have helped inspire new ideas about the functional roles that twitching might play in the self-organization of spinal and supraspinal sensorimotor circuits. Striking support for these ideas is coming from the field of developmental robotics: when twitches are mimicked in robot models of the musculoskeletal system, the basic neural circuitry undergoes self-organization. Mutually inspired biological and synthetic approaches promise not only to produce better robots, but also to solve fundamental problems concerning the developmental origins of sensorimotor maps in the spinal cord and brain.

Flexible representations of dynamics are used in object manipulation.

To manipulate an object skillfully, the brain must learn its dynamics, specifying the mapping between applied force and motion. A fundamental issue in sensorimotor control is whether such dynamics are represented in an extrinsic frame of reference tied to the object or an intrinsic frame of reference linked to the arm. Although previous studies have suggested that objects are represented in arm-centered coordinates [1-6], all of these studies have used objects with unusual and complex dynamics. Thus, it is not known how objects with natural dynamics are represented. Here we show that objects with simple (or familiar) dynamics and those with complex (or unfamiliar) dynamics are represented in object- and arm-centered coordinates, respectively. We also show that objects with simple dynamics are represented with an intermediate coordinate frame when vision of the object is removed. These results indicate that object dynamics can be flexibly represented in different coordinate frames by the brain. We suggest that with experience, the representation of the dynamics of a manipulated object may shift from a coordinate frame tied to the arm toward one that is linked to the object. The additional complexity required to represent dynamics in object-centered coordinates would be economical for familiar objects because such a representation allows object use regardless of the orientation of the object in hand.

A key role for similarity in vicarious reward.

Humans appear to have an inherent prosocial tendency toward one another in that we often take pleasure in seeing others succeed. This fact is almost certainly exploited by game shows, yet why watching others win elicits a pleasurable vicarious rewarding feeling in the absence of personal economic gain is unclear. One explanation is that game shows use contestants who have similarities to the viewing population, thereby kindling kin-motivated responses (for example, prosocial behavior). Using a game show-inspired paradigm, we show that the interactions between the ventral striatum and anterior cingulate cortex subserve the modulation of vicarious reward by similarity, respectively. Our results support studies showing that similarity acts as a proximate neurobiological mechanism where prosocial behavior extends to unrelated strangers.

Nash equilibria in multi-agent motor interactions.

Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.