arXiv research

Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.

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

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 approach finds solutions to games with unbounded controls.

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…

New PAC-Bayes bounds for unbounded losses using Cramér-Chernoff techniques.

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 solves nonparametric contextual bandit with unbounded contexts.

New algorithms achieve high-probability parameter-free regret in online convex optimization with heavy-tailed data.

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

New algorithm estimates Gaussian means and covariances efficiently and privately.

Develops parameter-free online mirror descent for optimal dynamic regret.

In this paper long-run risk sensitive optimisation problem is studied with dyadic impulse control applied to continuous-time Feller-Markov process. In contrast to the existing literature, focus is put on unbounded and non-uniformly ergodic case by adapting the weight norm approach. In particular, it is shown how to com…

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

Unbounded convex domains have zero mean curvature on disconnected boundaries.

Improved bounds for unbounded losses using transductive priors.

New RL policy for unbounded state space with stability guarantee.

Private learning of Gaussian Mixture Models without boundedness assumptions.

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

Neural networks cannot approximate certain functions in Sobolev spaces, leading to unbounded parameter growth.

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

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…

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.

New inequalities for unbounded functions improve denoising score matching.

Study focal surfaces of wave fronts with unbounded curvatures.

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

Study shows unbounded Pontryagin numbers on curved manifolds.

Paper tackles online control of linear systems with unbounded noise.

Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed with outdated information, and the age of the outdated information, which we cal…

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

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.

We study Online Convex Optimization in the unbounded setting where neither predictions nor gradient are constrained. The goal is to simultaneously adapt to both the sequence of gradients and the comparator. We first develop parameter-free and scale-free algorithms for a simplified setting with hints. We present two ver…

Improved sampling from Gaussian distributions with privacy constraints.

The paper extends logistic regression for unbounded majority classes and derives asymptotic properties.

New PAC-Bayes bounds for unbounded loss functions.

Geometric model of unbounded sl3 laminations with tropical coordinates.

In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice.

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).

This paper solves the normalizability crisis in sequential inference by introducing bounded information geometry.

We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.

In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature-dimension inequality $CDE'(n,K)$, which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, hea…

Study unbounded $\mathfrak{sl}_3$-laminations around punctures.

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

New algorithms improve exploration in unbounded reward settings.

We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body $C\subset \mathbb{R}^{n+1}$, without assuming any further regularity on the boundary of $C$. Motivated by an example of an unbounded convex body with null isoperimetric profile, we introduce the concept of…

Solves open problem on universally consistent online learning with unbounded losses.