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            <title xml:lang="en">Bayesian optimization with derivatives acceleration</title>
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                <forename type="first">Guillaume</forename>
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                <forename type="first">Rodolphe</forename>
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                <forename>Florent</forename>
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            <funder>This action beneﬁted from the support of the Chair Stress Test, Risk Management and Financial Steering, led by the French Ecole polytechnique and its foundation and sponsored by BNP Paribas. This research also beneﬁted from the consortium in Applied Mathematics CIROQUO (https://doi.org/10.5281/zenodo.6581217), gathering partners in technological and academia in the development of advanced methods for Computer Experiments.</funder>
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            <idno type="halRefHtml">&lt;i&gt;Journée Parcimonie, Optimisation et Problèmes Inverses Lyon Saint-Etienne Savoie (POPILSS 2025)&lt;/i&gt;, Jun 2025, Annecy, France</idno>
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            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="FAYOL-ENSMSE" corresp="EMSE">FAYOL - Institut Henri Fayol</idno>
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            <note type="commentary">Guillaume Perrin, first author. Rodolphe Le Riche, second author, invited speaker of the workshop.</note>
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            <note type="invited" n="1">Yes</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="0">No</note>
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                    <forename type="first">Guillaume</forename>
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              <p>Bayesian optimization algorithms form an important class of methods to minimize functions that are costly to evaluate, which is a very common situation. These algorithms iteratively infer Gaussian processes from past observations of the function and decide where new observations should be made through the maximization of an acquisition criterion. Often, in particular in engineering practice, the objective function is defined on a compact set such as in a hyper-rectangle of a d-dimensional real space, and the bounds are chosen wide enough so that the optimum is inside the search domain. In this situation, this work provides a way to integrate in the acquisition criterion the a priori information that these functions, once modeled as GP trajectories, should be evaluated at their minima, and not at any point as usual acquisition criteria do. We propose an adaptation of the widely used Expected Improvement acquisition criterion that accounts only for GP trajectories where the first order partial derivatives are zero and the Hessian matrix is positive definite. The new acquisition criterion keeps an analytical, computationally efficient, expression. This new acquisition criterion is found to improve Bayesian optimization on a test bed of functions made of Gaussian process trajectories in dimensions 2, 3 and 5. The addition of first and second order derivative information is particularly useful for multimodal functions.</p>
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