Authors: Gaston Plat, Paul Saves, Nathalie Bartoli, Thierry Lefebvre, Joseph Morlier
Organizations: DTIS, ONERA, Université de Toulouse, Toulouse, 31000, France. · Université de Toulouse, ISAE-SUPAERO Toulouse, 31000, France · Fédération ENAC ISAE-SUPAERO ONERA, Université de Toulouse, Toulouse, 31000, France. · IRIT, UMR 5505 CNRS, Université Toulouse Capitole, Toulouse, 31000, France
Modern design optimization frameworks aim first and foremost for models with the most accurate predictions without balancing computational overhead. It remains a reason why scaled architecture and multidisciplinary design optimization problems are difficult to address, even with sample-efficient Bayesian optimizers. In this paper, a metric quantifying the computational energy footprint is introduced within a Bayesian optimization framework to guide the parameter setting of a model towards configurations that balance both performance and frugality. The computer experiments highlighted existing tradeoffs between optimum convergence and the underlying energy footprint, and sometimes resulted in both a better-found optimum and lower energy consumption.
Figures & tables
Figure 1: Taxonomy example of hierarchical inclusion-exclusion relationships. A basic example is given for the neural architecture of a multilayer perceptron (MLP).
Figure 2: MLP for 28x28 pixel digit image (MNIST LeCun et al. (2010) ) classification. 6000 (10%) images are used for training, whereas 54000 are used for testing (90%).
Table 3
Figure 3: Pareto front between computational energy footprint and error on test data across 1 repetition, with 3 samples of the Pareto set.
Figure 4: 10-bar truss structure subjected to two external loads P. Axial stresses are constrained within the material yield stress.
Bayesian Optimization (BO) is widely adopted for data-efficient optimization in scientific and engineering applications, yet its computational cost is rarely evaluated alongside optimization performance. Here we present a systematic, compute-aware study of BO that evaluates surrogate models along two axes: optimization quality and computational frugality. Across eight benchmark functions and nine real-world datasets spanning materials science, mechanics, robotics, chemistry, and machine learning, we benchmark four surrogate models: Gaussian Processes, Random Forests, NGBoost, and Bayesian Adaptive Spline Surfaces. We show that Gaussian Process-based BO consistently incurs the highest time and memory overhead without delivering superior optimization or sample efficiency. In contrast, scalable alternatives achieve equal or better performance at a fraction of the computational cost. Motivated by these findings, we introduce a surrogate-recommendation framework that predicts the most suitable BO surrogate from inexpensive dataset characteristics. Together, these results establish FruBO as a reproducible, compute-aware baseline for Bayesian Optimization and provide practical guidance for surrogate selection under limited computational and experimental budgets.
Institute of Informatics and Telecommunications, National Centre for Scientific Research "Demokritos", Agia Paraskevi, Greece. · Department of Mechanical Engineering and Aeronautics, University of Patras, Patras Greece. · Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece. +4
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and adaptively employing a mixture of global exploration and local exploitation, this method has been used for optimization in many fields including machine learning, automotive engineering and reinforcement learning. However, the standard method suffers from two problems: 1) with cubic computational complexity in the training-set size it eventually becomes computationally infeasible to train the model, and 2) globally modeling the objective function is not necessarily optimal given the local nature of minimization. Using flexible and recursive binary partitioning of the search space, we adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme, thereby ameliorating both standard shortcomings. We compare our method against a commonly used Bayesian optimization library on seven challenging test functions, ranging in dimensionality from 6 to 124, and show that our method achieves superior optimization performance in all tests. In addition our method has linear computational complexity.
Jesse Schneider, William J. Welch
Department of Statistics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
Bayesian optimization (BO) is a popular technique for sample-efficient optimization of black-box functions. In many applications, the parameters being tuned come with a carefully engineered default configuration, and practitioners only want to deviate from this default when necessary. Standard BO, however, does not aim to minimize deviation from the default and, in practice, often pushes weakly relevant parameters to the boundary of the search space. This makes it difficult to distinguish between important and spurious changes and increases the burden of vetting recommendations when the optimization objective omits relevant operational considerations. We introduce BONSAI, a default-aware BO policy that prunes low-impact deviations from a default configuration while explicitly controlling the loss in acquisition value. BONSAI is compatible with a variety of acquisition functions, including expected improvement and upper confidence bound (GP-UCB). We theoretically bound the regret incurred by BONSAI, showing that, under appropriate conditions, it retains the no-regret property of vanilla GP-UCB and removes irrelevant changes. Across many real-world applications, we empirically find that BONSAI substantially reduces the number of non-default parameters in recommended configurations while maintaining competitive optimization performance with little effect on wall time. Its candidate-generation cost averages only 1.5× that of standard BO, compared with 7-34× for prior sparse-BO methods.
Samuel Daulton, David Eriksson, Maximilian Balandat +1