Gaussian Process surrogate
Prior over functions. Posterior after observations = Gaussian with mean + variance at each unseen point.
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Acquisition function
Expected improvement (EI): balance exploit (high mean) + explore (high variance). Or UCB, PI, entropy search.
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Algorithm
Fit GP → maximize acquisition → evaluate at new point → update GP → repeat.
Complexity
GP inference O(N³) — practical to N ≈ 1000 evaluations. Sparse GP or ensemble surrogates for larger.