arXiv research

Paper tackles online control of linear systems with unbounded noise.

Improved SGD with AdaGrad stepsizes adapts to unknown parameters and unbounded gradients.

We consider the problem of unconstrained online convex optimization (OCO) with sub-exponential noise, a strictly more general problem than the standard OCO. In this setting, the learner receives a subgradient of the loss functions corrupted by sub-exponential noise and strives to achieve optimal regret guarantee, witho…

Paper studies Adam's convergence under relaxed assumptions, proving a rate of O(poly(log T)/sqrt(T)).

There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain concentration. Existing methods address this problem by constructing an approximat…

Nonlinear SGD achieves high-probability rates in non-convex optimization with heavy-tailed noise.

Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.

Maximal concentration bounds for stochastic approximation with heavy-tailed noise.

AdaGrad-Norm achieves optimal convergence rates for non-convex objectives without tuning.

New method stabilizes saddle-point optimization with unbounded gradients.

New method for faster convergence in non-convex optimization with unbounded smoothness.

Linear regression models contaminated by Gaussian noise (inlier) and possibly unbounded sparse outliers are common in many signal processing applications. Sparse recovery inspired robust regression (SRIRR) techniques are shown to deliver high quality estimation performance in such regression models. Unfortunately, most…

Study on online regression with noise, achieving near-optimal regret bounds.

Study improves robust nonparametric regression in heavy-tailed noise.

Adding noise controls capacity of function compositions.

New method for spot volatility estimation with reduced microstructure noise.

PMT uses public data moments to make DP feasible for unbounded data.

Efficiently learns halfspaces with malicious noise, near-optimal label complexity.

Last-iterate guarantees for learning in co-coercive games under noisy feedback.

In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support vector machines (SVMs) essentially only require that the data-generating process sa…

A new macroscopic market making model connects market making and optimal execution.

We develop a Markovian approximation for SVV models to compute hedging strategies.

Privacy-preserving SGD with heavy-tailed noise achieves differential privacy guarantees.

Two new algorithms improve performance in adversarial bandits with unbounded losses.

This paper analyzes M-estimators under infinite-variance noise in high dimensions.

Noise addition prevents overfitting in adaptive data analysis.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

Study shows exponential gap in sample complexity between noisy and non-noisy recurrent neural networks.

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or …

The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.

Golden L surface has unbounded bunching of saddle connections

We construct an unbounded representative for the shriek class associated to the embeddings of spheres into Euclidean space. We equip this unbounded Kasparov cycle with a connection and compute the unbounded Kasparov product with the Dirac operator on $\mathbb R^{n+1}$. We find that the resulting spectral triple for the…

This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded framework, we extend our analysis to the more challenging unbounded case. Our methodolo…

Adam converges with high probability under unconstrained non-convex smooth stochastic optimizations.

It is shown that the compactly supported identity component of the diffeomorphism group of the 2-dimensional punctured torus $\mathbb T^2_p$ is an unbounded group. It follows that the fragmentation norm of $\mathbb T^2_p$ is unbounded.

We consider the problem of minimizing a convex objective function $F$ when one can only evaluate its noisy approximation $\hat{F}$. Unless one assumes some structure on the noise, $\hat{F}$ may be an arbitrary nonconvex function, making the task of minimizing $F$ intractable. To overcome this, prior work has often focu…

New inequalities for unbounded functions improve denoising score matching.

Study focal surfaces of wave fronts with unbounded curvatures.

Study shows unbounded Pontryagin numbers on curved manifolds.

New algorithms recover signals robustly against outliers and heavy-tailed noise.

We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.

New approach finds solutions to games with unbounded controls.

The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

New aggregation strategy handles unbounded losses with regret bounds.

Improved sampling from Gaussian distributions with privacy constraints.

The paper analyzes stability of random matrix products with Markovian noise.

New PAC-Bayes bounds for unbounded loss functions.

Geometric model of unbounded sl3 laminations with tropical coordinates.