Documentation, especially on the botorch.org landing page, should reflect current best practices

[esantorella]

This is the current "Get Started" example on botorch.org:

# Fit a model
import torch
from botorch.models import SingleTaskGP
from botorch.fit import fit_gpytorch_mll
from botorch.utils import standardize
from gpytorch.mlls import ExactMarginalLogLikelihood

train_X = torch.rand(10, 2)
Y = 1 - torch.linalg.norm(train_X - 0.5, dim=-1, keepdim=True)
Y = Y + 0.1 * torch.randn_like(Y)  # add some noise
train_Y = standardize(Y)

gp = SingleTaskGP(train_X, train_Y)
mll = ExactMarginalLogLikelihood(gp.likelihood, gp)
fit_gpytorch_mll(mll)

# Construct an acquisition function
from botorch.acquisition import UpperConfidenceBound

UCB = UpperConfidenceBound(gp, beta=0.1)

# Optimize the acquisition function
bounds = torch.stack([torch.zeros(2), torch.ones(2)])
candidate, acq_value = optimize_acqf(
    UCB, bounds=bounds, q=1, num_restarts=5, raw_samples=20,
)
candidate  # tensor([0.4887, 0.5063])

This code doesn't follow best practices in a few ways:

• It uses standardize rather than a transform, so predictions will be in the transformed space, which can be hard to interpret. The Standardize outcome transform would be better.
• It doesn't illustrate use of the Normalize input transform. I appreciate the concision of this example, but I think it's oversimplified; a user who runs this code on different data will get a warning telling them to normalize and not know how to do it.
• The data and bounds are in single precision, which will also generate a warning.
• We're more likely to recommend an acquisition function in the LogEI family than UCB.

Ideally, all references to standardize would be removed and there would be an audit of tutorials and other documentation for adherence to current best practices, but fixing the landing page would be a great improvement.