Posteriors
A BoTorch Posterior object is a layer of
abstraction that separates the specific model used from the evaluation (and
subsequent optimization) of acquisition functions.
In the simplest case, a posterior is a lightweight wrapper around an explicit
distribution object from torch.distributions (or gpytorch.distributions).
However, a BoTorch Posterior can be any distribution (even an implicit one),
so long as one can sample from that distribution. For example, a posterior could
be represented implicitly by some base distribution mapped through a neural network.
While the analytic acquisition functions assume that the posterior is a
multivariate Gaussian, the Monte-Carlo (MC) based acquisition functions do not make any
assumptions about the underlying distribution. Rather, the MC-based acquisition
functions only require that the posterior can generate samples through an rsample
method. As long as the posterior implements the Posterior
interface, it can be used with an MC-based acquisition function. In addition, note that
gradient-based acquisition function optimization requires the ability to back-propagate
gradients through the MC samples.
For GP models based on GPyTorch for which the posterior distribution is a
multivariate Gaussian,
GPyTorchPosterior should be used.