Introducing LogExpectedImprovement
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Summary: Pull Request resolved: pytorch#1565 This commit introduces `LogExpectedImprovement`, which computes the logarithm of the Expected Improvement acquisition function. By taking special care of numerics, it avoids numerical issues that affect `ExpectedImprovement` when evaluated at points that with high certainty do not yield improvement. In contrast, `LogExpectedImprovement` computes both values and gradients in a numerically stable fashion for points that don't yield improvement down to at least **100 orders of magnitude** lower posterior standard deviation than vanilla EI in double precision. This allows optimizers to escape the "valley of death" - regions that the surrogate is certain are bad but for which EI does not yield gradients. On the example test problem in N2901527, using `logEI` leads to better convergence compared to GPEI and similar performance as running homotopy on the target value without having to run homotopy iterations. {F822088495} Reviewed By: Balandat Differential Revision: D41890063 fbshipit-source-id: 368278afd4b2a84f66664070a70e326d0d66bedf
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Summary:
This commit introduces
LogExpectedImprovement, which computes the logarithm of the Expected Improvement acquisition function. By taking special care of numerics, it avoids numerical issues that affectExpectedImprovementwhen evaluated at points that with high certainty do not yield improvement. In contrast,LogExpectedImprovementcomputes both values and gradients in a numerically stable fashion for points that don't yield improvement down to at least 100 orders of magnitude lower posterior standard deviation than vanilla EI in double precision. This allows optimizers to escape the "valley of death" - regions that the surrogate is certain are bad but for which EI does not yield gradients.On the example test problem in N2901527, using
logEIleads to better convergence compared to GPEI and similar performance as running homotopy on the target value without having to run homotopy iterations.{F822088495}
Reviewed By: Balandat
Differential Revision: D41890063