Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on Gaussian processes, kernel machines, linear models, or linearized neural approximations, leaving a gap between theory and the nonlinear models used in practice. We develop a kernel-based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data. Our approach uses kernels over the parameter space to induce reproducing-kernel Hilbert space structures over the corresponding model class, yielding confidence bounds for models trained with broad classes of regularized convex losses. We show how these bounds can support convergence guarantees for nonlinear acquisition and surrogate models, including randomized regularized policies that select points by maximizing a trained random model. These results provide a unified route to analyzing nonlinear parametric models in Bayesian optimization and related adaptive optimization settings.

Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely on maximum information gain, non-pretrained surrogate models, or exact acquisition maximization -- assumptions that break down in modern diffusion -- BO pipelines, where pretrained diffusion models serve as powerful priors over valid structures and acquisition maximization is replaced by approximate sampling over astronomically large discrete spaces. We develop a first certificate-based expected simple-regret framework for guided-diffusion BO that avoids maximum-information-gain bounds, RKHS assumptions, and exact acquisition maximization. The central quantity in our analysis is mass lift: the increase in probability mass assigned to near-optimal designs relative to the pretrained generator. This view explains how exponential-looking finite-budget convergence and polynomial acceleration can all arise from the same mechanism. We also give practical diagnostics for estimating search exponents from finite candidate pools and a proposal-corrected resampling construction that provides a fully certified sampler instance.

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.

Published transfer-BO comparisons often estimate an average treatment effect of acquisition choice over hidden regime variables, while practitioners need the conditional effect for their specific prior quality, budget ratio, and metric. An audit of 40 transfer-BO papers from NeurIPS, ICML, ICLR, AISTATS, UAI, TMLR, JMLR, and AutoML-Conf (2022-2025) finds that 98% never vary B/|A| as a controlled axis. On the same GDSC2 benchmark, changing only the budget reverses the ranking: at B=50, Greedy outperforms UCB by 0.050 Hit@1, while at B=100, UCB outperforms Greedy by 0.035. We capture this transition with the Portable Regime Score PRS=(B/|A|)(1-rho), where rho is the prior rank correlation and can be estimated from pilot contexts before the main comparison. Across 79 conditions spanning chemistry, drug-response biology, and HPO, a hierarchical model gives beta=0.50 (p=1.1e-9), and 19% of conditions fall in an equivalence zone where |advantage|<0.01 Hit@1. In five published reversal cases, PRS predicts the winner from pre-comparison observables. A No-Free-Leaderboard proposition explains why unconditional rankings are unstable: when CATE changes sign across regimes, the reported ATE becomes a function of benchmark mixture. RegimePlanner, which estimates rho online and switches acquisition accordingly, wins all 16 HPO-B search spaces at B=100 and exceeds the matched {Greedy,UCB} per-context oracle on GDSC2 by 18%. Pre-registered predictions achieve 27/40=67.5% overall accuracy and above 90% within EMA prior families. The practical protocol is simple: report B/|A|, rho, K, and metric alongside any claimed acquisition advantage.

Decision making under uncertainty is commonly modelled as a process of competitive stochastic evidence accumulation to threshold (the drift-diffusion model). However, it is unknown how animals learn these decision thresholds. We examine threshold learning by constructing a reward function that averages over many trials to Wald's cost function that defines decision optimality. These rewards are highly stochastic and hence challenging to optimize, which we address in two ways: first, a simple two-factor reward-modulated learning rule derived from Williams' REINFORCE method for neural networks; and second, Bayesian optimization of the reward function with a Gaussian process. Bayesian optimization converges in fewer trials than REINFORCE but is slower computationally with greater variance. The REINFORCE method is also a better model of acquisition behaviour in animals and a similar learning rule has been proposed for modelling basal ganglia function.

Impactful applications such as materials discovery, hardware design, neural architecture search, or portfolio optimization require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. While Bayesian optimization has recently made significant progress in solving such problems, an in-depth analysis reveals that the current state-of-the-art methods are not reliable. Their performances degrade substantially when the unknown optima of the function do not have a certain structure. To fill the need for a reliable algorithm for combinatorial and mixed spaces, this paper proposes Bounce that relies on a novel map of various variable types into nested embeddings of increasing dimensionality. Comprehensive experiments show that Bounce reliably achieves and often even improves upon state-of-the-art performance on a variety of high-dimensional problems.

Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning. To overcome this challenge, robust satisficing (RS) seeks a robust solution to an unspecified distributional shift while achieving a utility above a desired threshold. This paper focuses on the problem of RS in contextual Bayesian optimization when there is a discrepancy between the true and reference distributions of the context. We propose a novel robust Bayesian satisficing algorithm called RoBOS for noisy black-box optimization.

Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO's local GP may remain either excessively complex or overly simple as the dimension $D$ and trust region side length $L$ vary. To address this issue, we propose a straightforward variant, AdaScale-TuRBO, which scales the GP lengthscale with both the problem dimension and trust region size, thereby preserving kernel geometry and maintaining consistent prior complexity. Empirically, we show that AdaScale-TuRBO can robustly outperform standard TuRBO and other popular high-dimensional BO methods on synthetic benchmarks and real-world trajectory planning tasks.