Related papers: An application of proof mining to the proximal poi…
We study efficient PAC learning of homogeneous halfspaces in $\mathbb{R}^d$ in the presence of malicious noise of Valiant (1985). This is a challenging noise model and only until recently has near-optimal noise tolerance bound been…
In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces. To do this, we first develop a unified framework allowing computations with probability measures. We show…
The inference of evolutionary histories is a central problem in evolutionary biology. The analysis of a sample of phylogenetic trees can be conducted in Billera-Holmes-Vogtmann tree space, which is a CAT(0) metric space of phylogenetic…
The Koml\'os$\unicode{x2013}$Major$\unicode{x2013}$Tusn\'ady (KMT) inequality for partial sums is one of the most celebrated results in probability theory. Yet its practical application has been hindered by a lack of practical constants.…
Uncertainty quantification is a key component of machine learning models targeted at safety-critical systems such as in healthcare or autonomous vehicles. We study this problem in the context of meta learning, where the goal is to quickly…
The distance from calibration, introduced by B{\l}asiok, Gopalan, Hu, and Nakkiran (STOC 2023), has recently emerged as a central measure of miscalibration for probabilistic predictors. We study the fundamental problems of computing and…
The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. We…
Proximal point algorithm has found many applications, and it has been playing fundamental roles in the understanding, design, and analysis of many first-order methods. In this paper, we derive the tight convergence rate in subgradient norm…
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…
A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…
We introduce three metrics on the set of quantum probability measures over a compact Hausdorff space and characterize them in terms of the completely bounded norm of the corresponding unital completely positive maps. We extend the existing…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to…
The Krasnosel'ski\u{\i}--Mann and Halpern iterations are classical schemes for approximating fixed points of nonexpansive mappings in Banach spaces, and have been widely studied in more general frameworks such as $CAT(\kappa)$ and, more…
We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…
We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit…
We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…
A reliable representation of uncertainty is essential for the application of modern machine learning methods in safety-critical settings. In this regard, the use of credal sets (i.e., convex sets of probability distributions) has recently…
The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent…
We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fej\'er monotone sequences in a broad metric context. Concretely, our result explicitly constructs a rate of convergence for such process, both in mean…