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If I wanted to determine the parameters of a deterministic algorithm that optimise some performance measure, there are any number of well-known techniques I could try. My problem concerns an algorithm whose behaviour is stochastic. Mathematically, the aim is to maximise $\mathbb{E}f(\mathbf{x})$, where for any $\mathbf{x}$ a random value of $f(\mathbf{x})$ is calculable but $\mathbb{E}f(\mathbf{x})$ is not (except by averaging empirical values of $f(\mathbf{x})$). My efforts with gradient descent and an EA have failed, and I think it's because $f$ is too noisy. (Sampling $f$ many times at the same $\mathbf{x}$ would give a less noisy average, but is too computationally expensive.) Are there any algorithms designed for this situation?

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Bayesian Optimization can be useful to find the optimal value for black-box functions without assuming a functional form.

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