Adjacency matrix for Branin task

[KamilDre]

Hi,

I noticed that you multiply the adjacency matrix for the Branin task by (n_v - 1) in line 22 of discretized_continuous.py. Why is this the case?

[ChangYong-Oh]

Sometimes, I multiply adj. mat. with some constant for numerical stability. The number is chosen by checking kernel values with some preliminary kernel computations before doing BO experiments. This is in a sense adjusting the prior on beta by scaling. So it is possible to adjust the priors whenever combinatorial graph size varies, but multiplying adj. mat. with constant makes BO runs consistently with the same prior independent with the combinatorial graph size.

On Tue, Mar 8, 2022 at 1:14 AM KamilDre @.***> wrote:

Hi,

I noticed that you multiply the adjacency matrix for the Branin task by (n_v

• 1) in line 22 of discretized_continuous.py. Why is this the case?

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[KamilDre]

Would you mind sharing some more information on how you "check" the kernel values and what do you compare them against to choose this scaling constant to improve stability? This would be of great help when applying COMBO to new problems.

[ChangYong-Oh]

What I did is nothing special. Because I applied to COMBO to kind of high dimensional problems in which there are 20~60 variables, kernel computation becomes the product kernel of that many kernels. So zero from numerical truncation or inf can happen. So I just checked computed kernels have reasonable values, not too many zero and no inf or nan. beta is chosen randomly from the prior I used.

On Tue, Mar 8, 2022 at 6:31 PM KamilDre @.***> wrote:

Would you mind sharing some more information on how you "check" the kernel values and what do you compare them against to choose this scaling constant to improve stability? This would be of great help when applying COMBO to new problems.

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