Computational principal-agent problems

Collecting and processing large amounts of data is becoming increasingly crucial in our society. We model this task as evaluating a function f over a large vector x=(x1,…,xn), which is unknown, but drawn from a publicly known distribution X. In our model, learning each component of the input x is costly, but computing the output f(x) has zero cost once x is known. We consider the problem of a principal who wishes to delegate the evaluation of f to an agent whose cost of learning any number of components of x is always lower than the corresponding cost of the principal. We prove that, for every continuous function f and every ?>0, the principal can - by learning a single component xi of x-incentivize the agent to report the correct value f(x) with accuracy ?. complexity.