arXiv research

Two flat sub-Lorentzian problems on Martinet distribution differ in attainable set intersections.

The paper explores traveling along broken geodesics in Finsler submersions.

The study examines conditions for achieving a simple lower bound in estimating mean from samples.

The paper explores fairness in machine learning, focusing on Equalized Odds.

We prove dual attainment for multi-asset financial derivatives pricing.

A pricing principle is introduced for non-attainable claims in incomplete markets.

Study tests whether trade-off functions are above or below benchmarks using finite samples.

Classifies shapes of yield curves in the Svensson family.

We consider the problem of controlling a possibly unknown linear dynamical system with adversarial perturbations, adversarially chosen convex loss functions, and partially observed states, known as non-stochastic control. We introduce a controller parametrization based on the denoised observations, and prove that apply…

We study the set of volumes of constant scalar curvature one metrics on an atoroidal three-manifold.The infinum of this set is believed to be attained at a hyperbolic metric. We prove that the supremum of this set is always infinity. The technique is: minimal surfaces, Thurston norm in homology and new conformal invari…

The paper considers trading with proportional transaction costs. We give a necessary and sufficient condition for A, the cone of claims attainable from zero endowment, to be closed, and show, in general, how to represent its closure in such a way that it is the cone of claims attainable for zero endowment, for a differ…

Sharp inequalities proved for RCD spaces, showing equality conditions.

Paper develops duality theory for robust utility maximization in continuous time.

New findings on complexity limits in fixed budget bandit identification.

New algorithm achieves optimal privacy and efficiency in non-Euclidean convex optimization.

ICP improves prediction intervals for continuous outcomes at lower computational cost.

An elementary proof shows submodular functions can be represented as measure suprema.

We study distributed estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we show that adaptive estimation is possible in this setting.

Research explores Lorentzian distances on a specific geometric plane.

We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of the elliptical data. To cope with heavy-tailed elliptical distributions, a mult…

We show that the empirical risk minimization (ERM) problem for neural networks has no solution in general. Given a training set $s_1, \dots, s_n \in \mathbb{R}^p$ with corresponding responses $t_1,\dots,t_n \in \mathbb{R}^q$, fitting a $k$-layer neural network $ν_θ: \mathbb{R}^p \to \mathbb{R}^q$ involves estimation of…

Algorithm learns expert weights to minimize regret in adversarial setting.

We determine non-Hopf hypersurfaces with constant mean curvature in the complex projective plane which attain equality in a basic inequality between the maximum Ricci curvature and the squared mean curvature.

Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.

We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite sample rates, previous approaches to classification with unknown class-conditiona…

Optimal nonparametric regression estimator adapts to unknown smoothness.

In an incomplete Brownian-motion market setting, we propose a convex monotonic pricing functional for nonattainable bounded contingent claims which is compatible with prices for attainable claims. The pricing functional is defined as the convex conjugate of a generalized entropy penalty functional and an interpretation…

Decision-calibrated prediction sets improve power system operations by reducing unnecessary costs.

We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of …

A variety of cooperative multi-agent control problems require agents to achieve individual goals while contributing to collective success. This multi-goal multi-agent setting poses difficulties for recent algorithms, which primarily target settings with a single global reward, due to two new challenges: efficient explo…

New methods prove controllability of non-linear systems, extending classical results.

Investment challenge study finds luck and strategy equally important.

Generalizes optimal portfolio theory to include capital gains taxes.

We provide a full classification of all attainable term structure shapes in the two-factor Vasicek model of interest rates. In particular, we show that the shapes normal, inverse, humped, dipped and hump-dip are always attainable. In certain parameter regimes up to four additional shapes can be produced. Our results ap…

We study the power of different types of adaptive (nonoblivious) adversaries in the setting of prediction with expert advice, under both full-information and bandit feedback. We measure the player's performance using a new notion of regret, also known as policy regret, which better captures the adversary's adaptiveness…

We provide a parametric construction in terms of minimal surfaces of the Euclidean submanifolds of codimension two and arbitrary dimension that attain equality in an inequality due to De Smet, Dillen, Verstraelen and Vrancken. The latter involves the scalar curvature, the norm of the normal curvature tensor and the len…

Study real hypersurfaces in complex space forms for an inequality involving a contact invariant.

We mainly study 3-dimensional complete gradient Ricci solitons with positive sectional curvature, whose scalar curvature attains its maximum at some point. In section 2, we estimate the area growth of level sets and the volume growth of sublevel sets of a Ricci potential. In section 3, we show that the scalar curvature…

The problem of stochastic convex optimization with bandit feedback (in the learning community) or without knowledge of gradients (in the optimization community) has received much attention in recent years, in the form of algorithms and performance upper bounds. However, much less is known about the inherent complexity …

The paper estimates Betti numbers for graphs with specific curvatures, proving bounds and characterizing rigidity.

We prove that, for a Finsler space, if the weighted Ricci curvature is bounded below by a positive number and the diam attains its maximal value, then it is isometric to a standard Finsler sphere. As an application, we show that the first eigenvalue of the Finsler-Laplacian attains its lower bound if and only if the Fi…

Active learning method reduces label queries for positive examples.

We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of \emph{robust no…

New algorithm achieves small-loss bounds in online learning with improved rates.

The paper proves a new method to find the maximum Laplace eigenvalues on surfaces.

Recently Oprea gave an improved version of Chen's inequality for Lagrangian submanifolds of $\mathbb CP^n(4)$. For minimal submanifolds this inequality coincides with the original previously proved version. We consider here those non minimal 3-dimensional Lagrangian submanifolds in $\mathbb CP^3 (4)$ attaining at all p…

Scalable method bounds Lipschitz constant of generative models.

Algorithm reduces regret in safe Bayesian optimization with monotonicity constraints.