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This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert…
Stochastic compositional minimax problems are prevalent in machine learning, yet there are only limited established on the convergence of this class of problems. In this paper, we propose a formal definition of the stochastic compositional…
We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear…
This paper introduces a solution to the problem of selecting dynamically (online) the ``optimal'' p-norm to combat outliers in linear adaptive filtering without any knowledge on the probability density function of the outliers. The proposed…
We investigate the problem of active learning in the streaming setting in non-parametric regimes, where the labels are stochastically generated from a class of functions on which we make no assumptions whatsoever. We rely on recently…
In this paper, we consider unregularized online learning algorithms in a Reproducing Kernel Hilbert Spaces (RKHS). Firstly, we derive explicit convergence rates of the unregularized online learning algorithms for classification associated…
We propose a nonparametric method to learn the L\'evy density from probability density data governed by a nonlocal Fokker-Planck equation. We recast the problem as identifying the kernel in a nonlocal integral operator from discrete data,…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the independent and Markovian observation settings. In particular,…
We introduce Conformal Online Learning of Koopman embeddings (COLoKe), a novel framework for adaptively updating Koopman-invariant representations of nonlinear dynamical systems from streaming data. Our modeling approach combines deep…
We study the problem of nonparametric estimation under $\bL_p$-loss, $p\in [1,\infty)$, in the framework of the convolution structure density model on $\bR^d$. This observation scheme is a generalization of two classical statistical models,…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
In the last years decision-focused learning framework, also known as predict-and-optimize, have received increasing attention. In this setting, the predictions of a machine learning model are used as estimated cost coefficients in the…
Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error…
We study a generalization of the Online Convex Optimization (OCO) framework with time-varying adversarial constraints. In this setting, at each round, the learner selects an action from a convex decision set $X$, after which both a convex…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
We introduce a similarity function on formulae of signal temporal logic (STL). It comes in the form of a kernel function, well known in machine learning as a conceptually and computationally efficient tool. The corresponding kernel trick…
This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…