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We study an algorithm-independent, worst-case lower bound for the Gaussian process (GP) bandit problem in the frequentist setting, where the reward function is fixed and has a bounded norm in the known reproducing kernel Hilbert space…

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…

This paper is in the field of stochastic Multi-Armed Bandits (MABs), i.e. those sequential selection techniques able to learn online using only the feedback given by the chosen option (a.k.a. $arm$). We study a particular case of the rested…

Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…

By leveraging the representation power of deep neural networks, neural upper confidence bound (UCB) algorithms have shown success in contextual bandits. To further balance the exploration and exploitation, we propose…

Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints. One of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural…

Bayesian Optimization (BO) is a sample-efficient optimization algorithm widely employed across various applications. In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such…

Bayesian optimization (BO) with preference-based feedback has recently garnered significant attention due to its emerging applications. We refer to this problem as Bayesian Optimization from Human Feedback (BOHF), which differs from…

Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions. The characteristics of the unknown function depend heavily on the assumed GP prior. Most work in the literature assume…

The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is…

In this paper, we consider algorithm-independent lower bounds for the problem of black-box optimization of functions having a bounded norm is some Reproducing Kernel Hilbert Space (RKHS), which can be viewed as a non-Bayesian Gaussian…

We propose a simple model selection approach for algorithms in stochastic bandit and reinforcement learning problems. As opposed to prior work that (implicitly) assumes knowledge of the optimal regret, we only require that each base…

The multi-armed bandit (MAB) problem is a classical problem that models sequential decision-making under uncertainty in reinforcement learning. In this study, we propose a new generalized upper confidence bound (UCB) algorithm (GWA-UCB1) by…

Gaussian process (GP) surrogates are the default tool for emulating expensive computer experiments, but cubic cost, stationarity assumptions, and Gaussian predictive distributions limit their reach. We propose Generative Bayesian…

Bayesian optimization (BO) is a powerful paradigm for derivative-free global optimization of a black-box objective function (BOF) that is expensive to evaluate. However, the overhead of BO can still be prohibitive for problems with highly…

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…

We study how to learn optimal interventions sequentially given causal information represented as a causal graph along with associated conditional distributions. Causal modeling is useful in real world problems like online advertisement…

Under data distributions which may be heavy-tailed, many stochastic gradient-based learning algorithms are driven by feedback queried at points with almost no performance guarantees on their own. Here we explore a modified "anytime…

Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we…

Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds…