arXiv research

New inequalities for unbounded functions improve denoising score matching.

We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and the objective function. Since the problem has unbounded domain, the objective func…

We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under th…

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

We proposed the expected energy-based restricted Boltzmann machine (EE-RBM) as a discriminative RBM method for classification. Two characteristics of the EE-RBM are that the output is unbounded and that the target value of correct classification is set to a value much greater than one. In this study, by adopting featur…

New PAC-Bayes bounds for unbounded loss functions.

We study the fundamental limits to communication-efficient distributed methods for convex learning and optimization, under different assumptions on the information available to individual machines, and the types of functions considered. We identify cases where existing algorithms are already worst-case optimal, as well…

In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional Value-at-Risk (CVaR) is a popular risk measure for modeling the aforementioned objec…

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.

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

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

Paper tackles online control of linear systems with unbounded noise.

New DRO algorithm finds robust models without strong assumptions.

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

Bayesian optimization has recently emerged as a popular and efficient tool for global optimization and hyperparameter tuning. Currently, the established Bayesian optimization practice requires a user-defined bounding box which is assumed to contain the optimizer. However, when little is known about the probed objective…

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…

New error bounds for GANs with nonlinear objective functions derived.

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

New RL policy for unbounded state space with stability guarantee.

SGD converges globally to logistic loss minima for two-layer nets.

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…

New proof confirms rolling objects can follow any path.

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.

Global convergence of SGD proven for two-layer neural nets with regularization.

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.