arXiv research

New inequalities for unbounded functions improve denoising score matching.

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

New PAC-Bayes bounds for unbounded loss functions.

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

Kolmogorov neural networks can represent various types of functions.

New aggregation strategy handles unbounded losses with regret bounds.

For a domain $Ω\subset\mathbb R^n$, we introduce the concept of a uniformly $C^m$ defining function. We characterize uniformly $C^m$ defining functions in terms of the signed distance function for the boundary and provide a large class of examples of unbounded domains with uniformly $C^m$ defining functions. Some of ou…

We study ancient solutions of polynomial growth to both continuous-time and discrete-time heat equations on graphs with unbounded Laplacians. We generalize Colding and Minicozzi's theorem [CM19] on manifolds, and the result [Hua19] on graphs with normalized Laplacians to the setting of graphs with unbounded Laplacians:…

Paper tackles online control of linear systems with unbounded noise.

Metric WPD for pseudo-Anosov maps shows many unbounded quasi-morphisms.

This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an opt…

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

After establishing some new global facts (like a measure theoretic structure theorem and approximation results) about complex-valued functions with bounded variation on arbitrary noncompact Riemannian manifolds, we extend results of Miranda/the second author/Paronetto/Preunkert and of Carbonaro/Mauceri on the heat semi…

Study bandit problems with BMO functions, achieving poly-log $δ$-regret.

New RL policy for unbounded state space with stability guarantee.

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies -- t…

New approach to concentration inequalities for unbounded state space dynamical systems.

LLA shows strong performance in Bayesian optimization but has unbounded search space issues.

We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertain…

New neural network rates for unbounded domains with weighted Sobolev spaces.

We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endo…

Theory for deep neural network approximation of score function and its derivatives.

We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit w…

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

New analysis shows a gap between Gaussian RKHS and neural networks on unbounded domains.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

Paper tackles unbounded density ratio estimation for covariate shift adaptation.

Paper solves a complex equation for unbounded convex sets.

We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a smooth classical solution to the corresponding HJB equation. Moreover, some verif…

New margin-based learning guarantees improve generalization bounds.

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

Golden L surface has unbounded bunching of saddle connections

New method stabilizes saddle-point optimization with unbounded gradients.

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…

Paper develops estimators for unbounded density ratios with applications in error control.

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…

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.

Study focal surfaces of wave fronts with unbounded curvatures.

Study uses spectral risk for learning with heavy-tailed data.

In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain. This problem comes from the study of mean curvature flow and its generalization, the flow by powers of mean curvature. Our approach is…

Karl Menger's 1934 paper on the St. Petersburg paradox contains mathematical errors that invalidate his conclusion that unbounded utility functions, specifically Bernoulli's logarithmic utility, fail to resolve modified versions of the St. Petersburg paradox.

Paper tackles robust deep learning from weakly dependent data with unbounded loss and input.

Note improves confidence bounds for random variables.

In this paper, we adapt stochastic Perron's method to analyze a stochastic target problem with unbounded controls in a jump diffusion set-up. With this method, we construct a viscosity sub-solution and super-solution to the associated Hamiltonian-Jacobi-Bellman (HJB) equations. Under comparison principles, uniqueness o…

We consider complete non-compact manifolds with either a sub-quadratic growth of the norm of the Riemann curvature, or a sub-quadratic growth of both the norm of the Ricci curvature and the squared inverse of the injectivity radius. We show the existence on such a manifold of a distance-like function with bounded gradi…

Study shows unbounded Pontryagin numbers on curved manifolds.

Deep neural networks classify unbounded Gaussian mixture data without dimensionality issues.

New PAC-Bayes training method improves model generalization for unbounded loss.