Transcription of Bayesian Optimization - Washington University in St. Louis
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Bayesian Optimization - Washington University in St. Louis
Bayesian OptimizationSuppose we have a functionf:X Rthat we with to minimize on some domainX X. That is,we wish to ndx = arg minx Xf(x).In numerical analysis, this problem is typically called (global)optimizationand has been the subjectof decades of study. We draw a distinction between global Optimization , where we seek the absoluteoptimum inX, and local Optimization , where we seek to nd a local optimum in the neighborhoodof a given initial common approach to Optimization problems is to make some assumptions aboutf.
Perhaps the ˙rst acquisition function designed for Bayesian optimization was probability of im-provement. Suppose f0= minf is the minimal value of fobserved so far. Probability of improvement evaluates fat the point most likely to improve upon this value. This corresponds to the following utility function2 associated with evaluating fat a ...
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