3 Added a link to the referenced paper.
source | link

Your understanding is correct.

BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty versus exploring further in a region with lower uncertainty, but a higher value.

By contrast, vanilla regression models assume equal variance - while you can locate the maximum of a polynomial model within some box, the search will be excessively local and not have a great exploration-exploitation tradeoff.

But this just repeats what you already know.

Typical mean functions in BO (and GPs generally) are either 0 or another constant, with all of the heavy-lifting is done by the kernel function. This is mostly a computational trick, because in this case predictions are easily made via linear algebra; otherwise, you have to resort to simulation.

The Jones 1998 paperJones 1998 paper compares GP and polynomial regression on page 464. This is not strictly the same model that you propose (choosing polynomial terms by CV), but it's consistent with your aims.

Your understanding is correct.

BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty versus exploring further in a region with lower uncertainty, but a higher value.

By contrast, vanilla regression models assume equal variance - while you can locate the maximum of a polynomial model within some box, the search will be excessively local and not have a great exploration-exploitation tradeoff.

But this just repeats what you already know.

Typical mean functions in BO (and GPs generally) are either 0 or another constant, with all of the heavy-lifting is done by the kernel function. This is mostly a computational trick, because in this case predictions are easily made via linear algebra; otherwise, you have to resort to simulation.

The Jones 1998 paper compares GP and polynomial regression on page 464. This is not strictly the same model that you propose (choosing polynomial terms by CV), but it's consistent with your aims.

Your understanding is correct.

BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty versus exploring further in a region with lower uncertainty, but a higher value.

By contrast, vanilla regression models assume equal variance - while you can locate the maximum of a polynomial model within some box, the search will be excessively local and not have a great exploration-exploitation tradeoff.

But this just repeats what you already know.

Typical mean functions in BO (and GPs generally) are either 0 or another constant, with all of the heavy-lifting is done by the kernel function. This is mostly a computational trick, because in this case predictions are easily made via linear algebra; otherwise, you have to resort to simulation.

The Jones 1998 paper compares GP and polynomial regression on page 464. This is not strictly the same model that you propose (choosing polynomial terms by CV), but it's consistent with your aims.

2 added 40 characters in body
source | link

Your understanding is correct.

BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty versus exploring further in a region with lower uncertainty, but a higher value.

By contrast, vanilla regression models assume equal variance - while you can easily locate the maximum of a regressionpolynomial model within some box, the search will be excessively local and not have a great exploration-exploitation tradeoff.

But this just repeats what you already know.

Typical mean functions in BO (and GPs generally) are either 0 or another constant, with all of the heavy-lifting is done by the kernel function. This is mostly a computational trick, because in this case predictions are easily made via linear algebra; otherwise, you have to resort to simulation.

My vague recollection is that theThe Jones 1998 paper compares GP and polynomial regression -- I'll try to find the citationon page 464. This is not strictly the same model that you propose (I read it about 18 months ago.choosing polynomial terms by CV), but it's consistent with your aims.

Your understanding is correct.

BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty versus exploring further in a region with lower uncertainty, but a higher value.

By contrast, vanilla regression models assume equal variance - while you can easily locate the maximum of a regression model, the search will be excessively local and not have a great exploration-exploitation tradeoff.

But this just repeats what you already know.

Typical mean functions in BO (and GPs generally) are either 0 or another constant, with all of the heavy-lifting is done by the kernel function. This is mostly a computational trick, because in this case predictions are easily made via linear algebra; otherwise, you have to resort to simulation.

My vague recollection is that the Jones 1998 paper compares GP and polynomial regression -- I'll try to find the citation. (I read it about 18 months ago.)

Your understanding is correct.

BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty versus exploring further in a region with lower uncertainty, but a higher value.

By contrast, vanilla regression models assume equal variance - while you can locate the maximum of a polynomial model within some box, the search will be excessively local and not have a great exploration-exploitation tradeoff.

But this just repeats what you already know.

Typical mean functions in BO (and GPs generally) are either 0 or another constant, with all of the heavy-lifting is done by the kernel function. This is mostly a computational trick, because in this case predictions are easily made via linear algebra; otherwise, you have to resort to simulation.

The Jones 1998 paper compares GP and polynomial regression on page 464. This is not strictly the same model that you propose (choosing polynomial terms by CV), but it's consistent with your aims.

1
source | link

Your understanding is correct.

BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty versus exploring further in a region with lower uncertainty, but a higher value.

By contrast, vanilla regression models assume equal variance - while you can easily locate the maximum of a regression model, the search will be excessively local and not have a great exploration-exploitation tradeoff.

But this just repeats what you already know.

Typical mean functions in BO (and GPs generally) are either 0 or another constant, with all of the heavy-lifting is done by the kernel function. This is mostly a computational trick, because in this case predictions are easily made via linear algebra; otherwise, you have to resort to simulation.

My vague recollection is that the Jones 1998 paper compares GP and polynomial regression -- I'll try to find the citation. (I read it about 18 months ago.)