The paper introduces a curvature‑aware Expected Free Energy (EFE) acquisition function for Bayesian optimization, designed to jointly learn and optimize an underlying function. It demonstrates that, under certain assumptions, EFE reduces to familiar criteria such as Upper Confidence Bound, Lower Confidence Bound, and Expected Information Gain, and provides unbiased convergence guarantees for concave functions. Empirical results on a Van der Pol oscillator system identification task and a two‑dimensional oscillatory benchmark show that the adaptive EFE achieves competitive performance in both regret and mean squared error, outperforming typical acquisition functions that excel in only one metric.
arXiv:2609.26021v1 Announce Type: new Abstract: Dynamic black-box optimization presents significant challenges for Bayesian Optimization (BO), as the objective function evolves over time, causing opt...
arXiv:2408. 11629v2 Announce Type: replace Abstract: We propose a statistical-learning framework for optimization algorithms.
arXiv:2606. 02351v1 Announce Type: new Abstract: Bayesian optimization (BO) is a popular and effective approach for tuning expensive, noisy experiments, but requires the formulation of an explicit objective function.
arXiv:2606. 07134v1 Announce Type: new Abstract: Information-theoretic acquisition functions such as Entropy Search (ES) offer a principled exploration-exploitation framework for Bayesian optimization (BO).
arXiv:2601. 07094v2 Announce Type: replace-cross Abstract: Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function.
The review explores how control theory, optimal transport, probabilistic inference, non‑equilibrium thermodynamics, and machine learning are interconnected through the optimization of free‑energy‑like functionals under dynamical or statistical constraints. It presents a conceptual thread linking these five fields and illustrates the ideas with applications in reinforcement learning, variational inference, and generative modeling. The article is written for readers without prior familiarity, beginning with physics principles.
arXiv:2606. 08438v1 Announce Type: cross Abstract: Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\mathbf{x}^{\star}$.
arXiv:2610.00446v1 Announce Type: cross Abstract: As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its v...
arXiv:2601. 10222v2 Announce Type: replace-cross Abstract: Optimization is central to both modern machine learning (ML) and scientific machine learning (SciML), yet the structure of the underlying optimization problems differs substantially across these domains.
arXiv:2607. 20152v1 Announce Type: cross Abstract: Active Inference (AIF) frames adaptive behavior as the minimization of expected free energy (EFE), combining epistemic and pragmatic objectives within a single variational principle.
arXiv:2607. 29225v1 Announce Type: new Abstract: 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.
The paper presents a method that uses Constrained Bayesian Optimization (CBO) to minimize the energy consumption of machine learning models while ensuring their generalization performance stays above a specified threshold. By treating energy usage as the primary objective and performance as a constraint, the authors demonstrate that CBO can reduce training energy costs on both regression and classification tasks without sacrificing predictive accuracy.