Related papers: Tighter Confidence Bounds for Sequential Kernel Re…
We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…
We study the stochastic contextual bandit problem, where the reward is generated from an unknown function with additive noise. No assumption is made about the reward function other than boundedness. We propose a new algorithm, NeuralUCB,…
General predictive models do not provide a measure of confidence in predictions without Bayesian assumptions. A way to circumvent potential restrictions is to use conformal methods for constructing non-parametric confidence regions, that…
This paper presents the framework \textbf{GUARD} (\textbf{G}uided robot control via \textbf{U}ncertainty attribution and prob\textbf{A}bilistic kernel optimization for \textbf{R}isk-aware \textbf{D}ecision making) that combines traditional…
Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…
Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples…
Constrained Markov Decision Processes are a class of stochastic decision problems in which the decision maker must select a policy that satisfies auxiliary cost constraints. This paper extends upper confidence reinforcement learning for…
Large Language Models (LLMs) exhibit impressive capabilities yet suffer from sensitivity to slight input context variations, hampering reliability. Conventional metrics like accuracy and perplexity fail to assess local prediction…
The multi-armed bandit (MAB) problem is a foundational framework in sequential decision-making under uncertainty, extensively studied for its applications in areas such as clinical trials, online advertising, and resource allocation.…
We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the…
Adversarial examples pose a security threat to many critical systems built on neural networks (such as face recognition systems, and self-driving cars). While many methods have been proposed to build robust models, how to build certifiably…
While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems.…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
Many real-world optimization problems involve an expensive ground-truth oracle (e.g., human evaluation, physical experiments) and a cheap, low-fidelity prediction oracle (e.g., machine learning models, simulations). Meanwhile, abundant…
Upper Confidence Bound (UCB) algorithms are a widely-used class of sequential algorithms for the $K$-armed bandit problem. Despite extensive research over the past decades aimed at understanding their asymptotic and (near) minimax…
Stochastic multi-armed bandits (MABs) provide a fundamental reinforcement learning model to study sequential decision making in uncertain environments. The upper confidence bounds (UCB) algorithm gave birth to the renaissance of bandit…
Kernelized bandits, also known as Bayesian optimization (BO), has been a prevalent method for optimizing complicated black-box reward functions. Various BO algorithms have been theoretically shown to enjoy upper bounds on their cumulative…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…