Bayesian Optimization

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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. Convex Optimization is a commontool used across machine an exact functional form forfis not available (that is,fbehaves as a black box ), what can wedo?

The second can be increased by increasing the variance K(x;x). These two terms can be interpreted as explicitly encoding a tradeo˛ between exploitation (evaluating at points with low mean) and exploration (evaluating at points with high uncertainty). The exploitation–

  Increasing, Optimization, Bayesian, Bayesian optimization