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. For example,when the objective functionfis known to be convex and the domainXis also convex, the problemis known asconvex optimizationand has been widely studied.
The point with the highest probability of improvement (the maximal expected utility) is selected. This is the Bayes action under this loss. Expected improvement The loss function associated with probability of improvement is somewhat odd: we get a reward for improving upon the current minimum independent of the size of the improvement! This can
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