Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks
<|reference_start|>Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks: Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an architecture for generating predictions with uncertainty using a single operator network backbone, which presents orders of magnitude less trainable parameters than deep ensembles of comparable performance. We showcase the utility of this method for sequential decision-making by examining the problem of composite Bayesian Optimization (BO), where we aim to optimize a function $f=g\circ h$, where $h:X\to C(\mathcal{Y},\mathbb{R}^{d_s})$ is an unknown map which outputs elements of a function space, and $g: C(\mathcal{Y},\mathbb{R}^{d_s})\to \mathbb{R}$ is a known and cheap-to-compute functional. By comparing our approach to other state-of-the-art methods on toy and real world scenarios, we demonstrate that NEON achieves state-of-the-art performance while requiring orders of magnitude less trainable parameters.<|reference_end|>
@article{guilhoto2024composite,
    title={Composite Bayesian Optimization In Function Spaces Using NEON -- Neural
  Epistemic Operator Networks},
    author={Leonardo Ferreira Guilhoto, Paris Perdikaris},
    journal={arXiv preprint arXiv:2404.03099},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.03099},
    primaryClass={cs.LG cs.AI cs.CE cs.IT math.IT stat.ML}
}