Publikation
Information-Theoretic Safe Bayesian Optimization
Alessandro G. Bottero; Carlos E. Luis; Julia Vinogradska; Felix Berkenkamp; Jan Peters
In: Computing Research Repository eprint Journal (CoRR), Vol. abs/2402.15347, Pages 1-36, arXiv, 2024.
Zusammenfassung
We consider a sequential decision making task, where the goal is to optimize an unknown
function without evaluating parameters that violate an a priori unknown (safety) constraint.
A common approach is to place a Gaussian process prior on the unknown functions and
allow evaluations only in regions that are safe with high probability. Most current methods
rely on a discretization of the domain and cannot be directly extended to the continuous
case. Moreover, the way in which they exploit regularity assumptions about the constraint
introduces an additional critical hyperparameter. In this paper, we propose an information-
theoretic safe exploration criterion that directly exploits the GP posterior to identify the
most informative safe parameters to evaluate. The combination of this exploration criterion
with a well known Bayesian optimization acquisition function yields a novel safe Bayesian
optimization selection criterion. Our approach is naturally applicable to continuous domains
and does not require additional explicit hyperparameters. We theoretically analyze the
method and show that we do not violate the safety constraint with high probability and
that we learn about the value of the safe optimum up to arbitrary precision. Empirical
evaluations demonstrate improved data-efficiency and scalability