Bayesian optimisation under uncertain inputs
This addresses a common issue in optimization problems with physical components, offering a solution for scenarios where input uncertainty is significant, though it appears incremental as it builds on existing BO methods.
The paper tackles the problem of Bayesian optimization when both the function evaluation and the query location are uncertain, proposing a UCB algorithm that uses Gaussian processes with probability distributions as inputs. It provides theoretical results and experimental evaluation, showing performance improvements in simulated scenarios with synthetic and real data.
Bayesian optimisation (BO) has been a successful approach to optimise functions which are expensive to evaluate and whose observations are noisy. Classical BO algorithms, however, do not account for errors about the location where observations are taken, which is a common issue in problems with physical components. In these cases, the estimation of the actual query location is also subject to uncertainty. In this context, we propose an upper confidence bound (UCB) algorithm for BO problems where both the outcome of a query and the true query location are uncertain. The algorithm employs a Gaussian process model that takes probability distributions as inputs. Theoretical results are provided for both the proposed algorithm and a conventional UCB approach within the uncertain-inputs setting. Finally, we evaluate each method's performance experimentally, comparing them to other input noise aware BO approaches on simulated scenarios involving synthetic and real data.