Bayesian Optimization Example

[caxelrud]

Can you point me to an example, using Stheno, of Bayesian Optimization with an objective that considers exploration and exploitation?

[willtebbutt]

Hiya. Unfortunately I've yet to see Stheno.jl used to do this -- if you encounter one please do report back here about it.

[caxelrud]

Hi. The following blog is very informative:
http://krasserm.github.io/2018/03/21/bayesian-optimization/
If you put together an example, I can help test it.
Not able to do it by myself since I am just migrating to Julia coding.
Thanks,

[yiyuezhuo]

I'm working on a project related to Bayesian optimization so I can write a BO example using Stheno if someone is interested.

[willtebbutt]

It would be great if someone could do some design work to specify an interface that a probabilistic model should satisfy to be compatible with Bayes Opt, and then implement Bayes Opt in terms of that interface. Then you could just hook whatever model you fancy into it.

For example, it looks like BayesianOptimization.jl goes some way towards this, but I can't tell from the package exactly what's going on. I wonder if the author @jbrea has anything to say on the matter?

[jbrea]

Hi,

thanks for pinging me.

BayesianOptimization.jl is indeed designed to work with different models.
Currently, a model of type MyModel needs to implement the following functions

m, v = mean_var(m::MyModel, x::AbstractVector)  # return scalar mean and variance of the model at x 
m, v = mean_var(m::MyModel, x::AbstractMatrix)  # return size(x,2)-dimensional vector of means and variances of the model at x
update!(m::MyModel, x, y)                       # update the model with new inputs x and observations y
y = maxy(m::MyModel)                            # return the largest observed value used to fit the model
nx, nsamples = dims(m::MyModel)                 # return the dimensionalty nx of the input and the number of samples nsamples used so far to fit the model

The code of BayesianOptimization.jl is a bit rusty. If there is interest, I can polish it a bit and document the API better.
PR's to include Shteno models (or any other kind of model) are highly welcome, of course.

Note that it is somewhat costly to fit a full GP everytime a new observation arrives,
which is why I wrote https://github.com/jbrea/ElasticPDMats.jl to update a GP with new observations.

[yiyuezhuo]

I guess @caxelrud wants an example similar to his link instead of a full function interface? Anyway this is a gist replicating the result of referenced link:

https://gist.github.com/yiyuezhuo/12e2dc828ac358f58e60ebd41b28f768

[caxelrud]

@yiyuezhuo, I am getting an error when trying you open the notebook from the gist link from your comment ( https://gist.github.com/yiyuezhuo/12e2dc828ac358f58e60ebd41b28f768 ).
I downloaded but I it fail.
Thanks

[yiyuezhuo]

@caxelrud, what error do you get? I can run this notebook without any error. Did you add the packages Stheno, Plots, Optim, Distributions?

[caxelrud]

@yiyuezhuo, I am getting an error with the Jupyter notebook. It looks corrupted for some reason. It doesn't open at the link (keep spinning and fail). I got the same problem when downloading and trying to run the Jupyter notebook in my computer.
You can also send me the Julia file. Thanks.

[yiyuezhuo]

@caxelrud, maybe you should check IJulia doc to ensure that you can run minimal Julia 1.5 example in Jupyter notebook at least.

[caxelrud]

@yiyuezhuo, I checked Jupyter Notebook and it allows me to create new notebook with Julia 1.5.0.
I will check more.
But, the message I get from Jupyter, when trying to execute the note, is the following:
Unreadable Notebook: C:\Users\inter\OneDrive_myWork\Research2020\BayesianOpt_2020\bayesian_optimization3.ipynb NotJSONError('Notebook does not appear to be JSON: '{\n "cells": [\n {\n "cell_type": "m...')

[yiyuezhuo]

@caxelrud, sorry it seems that GitHub always corrupts first updated file in gist right now for some reason, I update the gist again to fix this.

[caxelrud]

@yiyuezhuo, looks good now. I will test it. I will next apply to a much larger dimension problem. I will report my findings. Thanks!