Information-theoretic acquisition functions
This notebook illustrates the use of some information-theoretic acquisition functions in BoTorch for single and multi-objective optimization. We present a single-objective example in section 1 and a multi-objective example in section 2. Before introducing these examples, we present an overview on the different approaches and how they are estimated.
Notation
We consider the problem of maximizing a function . In the single-objective setting (), the maximum is defined as usual with respect to the total ordering over the real numbers. In the multi-objective setting (), the maximum is defined with respect to the Pareto partial ordering over vectors. By an abuse in notation, we denote the optimal set of inputs and outputs by