  We consider the problem of estimating the expected value of information (the
knowledge gradient) for Bayesian learning problems where the belief model is
nonlinear in the parameters. Our goal is to maximize some metric, while
simultaneously learning the unknown parameters of the nonlinear belief model,
by guiding a sequential experimentation process which is expensive. We overcome
the problem of computing the expected value of an experiment, which is
computationally intractable, by using a sampled approximation, which helps to
guide experiments but does not provide an accurate estimate of the unknown
parameters. We then introduce a resampling process which allows the sampled
model to adapt to new information, exploiting past experiments. We show
theoretically that the method converges asymptotically to the true parameters,
while simultaneously maximizing our metric. We show empirically that the
process exhibits rapid convergence, yielding good results with a very small
number of experiments.
