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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 an objective function represented by a nonlinear parametric belief model, while simultaneously learning the unknown parameters, 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 generates sequences that converge asymptotically to the true parameters, while simultaneously maximizing the objective function. We show empirically that the process exhibits rapid convergence, yielding ...

Optimal Learning for Stochastic Optimization with Nonlinear Parametric Belief Models