Bayesian optimisation under uncertain inputs

TL;DR

This paper introduces a Bayesian optimisation algorithm that accounts for uncertainty in both the evaluation outcomes and the query locations, improving optimization accuracy in physical systems with input errors.

Contribution

It proposes a novel UCB algorithm using Gaussian processes with probabilistic inputs, extending BO to uncertain input scenarios with theoretical analysis and experimental validation.

Findings

The proposed method outperforms traditional BO under input uncertainty.

Theoretical bounds are established for the new algorithm and conventional approaches.

Experimental results demonstrate improved optimization in noisy, real-world scenarios.

Abstract

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.