  Research has characterized the various forms cognitive control can take,
including enhancement of goal-relevant information, suppression of
goal-irrelevant information, and overall inhibition of potential responses, and
has identified computations and neural circuits that underpin this multitude of
control types. Studies have also identified a wide range of situations that
elicit adjustments in control allocation (e.g., those eliciting signals
indicating an error or increased processing conflict), but the rules governing
when a given situation will give rise to a given control adjustment remain
poorly understood. Significant progress has recently been made on this front by
casting the allocation of control as a decision-making problem, and developing
unifying and normative models that prescribe when and how a change in
incentives and task demands will result in changes in a given form of control.
Despite their successes, these models, and the experiments that have been
developed to test them, have yet to face their greatest challenge: deciding how
to allocate control across the multiplicity of control signals that one could
engage at any given time. Here, we will lay out the complexities of the inverse
problem inherent to cognitive control allocation, and their close parallels to
inverse problems within motor control (e.g., choosing between redundant limb
movements). We discuss existing solutions to motor control`s inverse problems
drawn from optimal control theory, which have proposed that effort costs act to
regularize actions and transform motor planning into a well-posed problem.
These same principles may help shed light on how our brains optimize over
complex control configuration, while providing a new normative perspective on
the origins of mental effort.
