  Computational level explanations based on optimal feedback control with
signal-dependent noise have been able to account for a vast array of phenomena
in human sensorimotor behavior. However, commonly a cost function needs to be
assumed for a task and the optimality of human behavior is evaluated by
comparing observed and predicted trajectories. Here, we introduce inverse
optimal control with signal-dependent noise, which allows inferring the cost
function from observed behavior. To do so, we formalize the problem as a
partially observable Markov decision process and distinguish between the
agent's and the experimenter's inference problems. Specifically, we derive a
probabilistic formulation of the evolution of states and belief states and an
approximation to the propagation equation in the linear-quadratic Gaussian
problem with signal-dependent noise. We extend the model to the case of partial
observability of state variables from the point of view of the experimenter. We
show the feasibility of the approach through validation on synthetic data and
application to experimental data. Our approach enables recovering the costs and
benefits implicit in human sequential sensorimotor behavior, thereby
reconciling normative and descriptive approaches in a computational framework.
