Related papers: Learning and Testing Convex Functions

Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we…

We consider the problem of selective inference after solving a (randomized) convex statistical learning program in the form of a penalized or constrained loss function. Our first main result is a change-of-measure formula that describes…

This paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the function value at the considered point by the averaged function value over a ball (in $l_1$-norm or…

We investigate the computational efficiency of agnostic learning for several fundamental geometric concept classes in the plane. While the sample complexity of agnostic learning is well understood, its time complexity has received much less…

There are many high dimensional function classes that have fast agnostic learning algorithms when assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be confident that…

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…

The push-forward operation enables one to redistribute a probability measure through a deterministic map. It plays a key role in statistics and optimization: many learning problems (notably from optimal transport, generative modeling, and…

Tackling semi-supervised learning problems with graph-based methods has become a trend in recent years since graphs can represent all kinds of data and provide a suitable framework for studying continuum limits, e.g., of differential…

Let $U\subseteq\mathbb{R}^d$ be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function $f:U\to\mathbb{R}$ can be approximated by real analytic convex functions, uniformly on all of $U$. We also show…

The minimization of convex objectives coming from linear supervised learning problems, such as penalized generalized linear models, can be formulated as finite sums of convex functions. For such problems, a large set of stochastic…

Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…

A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…

In this paper we investigate the problem of learning an unknown bounded function. We be emphasize special cases where it is possible to provide very simple (in terms of computation) estimates enjoying in addition the property of being…

We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…

Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper,…

We consider linear prediction with a convex Lipschitz loss, or more generally, stochastic convex optimization problems of generalized linear form, i.e.~where each instantaneous loss is a scalar convex function of a linear function. We show…

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…

Classical assumptions like strong convexity and Lipschitz smoothness often fail to capture the nature of deep learning optimization problems, which are typically non-convex and non-smooth, making traditional analyses less applicable. This…