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This paper studies some asymptotic properties of adaptive algorithms widely used in optimization and machine learning, and among them Adagrad and Rmsprop, which are involved in most of the blackbox deep learning algorithms. Our setup is the…

Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a curvature-aware local BO method that targets a (modified) Newton step by jointly learning gradient…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

We propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to…

Many important problems in science and engineering, such as drug design, involve optimizing an expensive black-box objective function over a complex, high-dimensional, and structured input space. Although machine learning techniques have…

Bayesian optimization (BO) is a sample-efficient global optimization algorithm for black-box functions which are expensive to evaluate. Existing literature on model based optimization in conditional parameter spaces are usually built on…

We consider the problem of constrained multi-objective blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number…

Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian…

We are interested in derivative-free optimization of high-dimensional functions. The sample complexity of existing methods is high and depends on problem dimensionality, unlike the dimensionality-independent rates of first-order methods.…

We propose an improved evolution strategy (ES) using a novel nonlocal gradient operator for high-dimensional black-box optimization. Standard ES methods with $d$-dimensional Gaussian smoothing suffer from the curse of dimensionality due to…

In this study, we consider simulation-based worst-case optimization problems with continuous design variables and a finite scenario set. To reduce the number of simulations required and increase the number of restarts for better local…

Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important…

We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity…

Contextual policy search allows adapting robotic movement primitives to different situations. For instance, a locomotion primitive might be adapted to different terrain inclinations or desired walking speeds. Such an adaptation is often…

Generating adversarial examples in a black-box setting retains a significant challenge with vast practical application prospects. In particular, existing black-box attacks suffer from the need for excessive queries, as it is non-trivial to…

We present a novel black box optimization algorithm called Hessian Estimation Evolution Strategy. The algorithm updates the covariance matrix of its sampling distribution by directly estimating the curvature of the objective function. This…

Alignment of Large Language Models (LLMs) typically relies on Reinforcement Learning from Human Feedback (RLHF) with gradient-based optimizers such as Proximal Policy Optimization (PPO) or Group Relative Policy Optimization (GRPO). While…

We study spectral algorithms in the setting where kernels are learned from data. We introduce the effective span dimension (ESD), an alignment-sensitive complexity measure that depends jointly on the signal, spectrum, and noise level…

A black-box optimization algorithm such as Bayesian optimization finds extremum of an unknown function by alternating inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such…

Bayesian optimization (BO) is a sample efficient approach to automatically tune the hyperparameters of machine learning models. In practice, one frequently has to solve similar hyperparameter tuning problems sequentially. For example, one…