arXiv research

Logarithmic regret achieved in RL with linear function approximation.

Paper approximates Kelly betting for wealth growth.

We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are S-arithmetic Diophantine approximation results and logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on trees.

The study approximates option prices using Hermite polynomials without assuming a specific distribution.

A new interpolation method speeds up neural ODE training.

Given for instance a finite volume negatively curved Riemannian manifold $M$, we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of $M$ and their linear divergence rates under the geodesic flow. As…

New algorithm achieves logarithmic regret for adversarial online control.

We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and carefully invoking the RecursiveTensorSketch [Ahle et al. SODA 2020]. After providing concentration and approximation pro…

New MD algorithms using Tempesta logarithms for machine learning.

In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case, where the prior distribution belongs to the exponential family of distributions. The logarithm of the likelihood function is li…

Deep networks with path norm regularization can approximate analytic functions.

Local logarithmic export distributions show non-zero skewness that changes with exporter and destination characteristics.

This work improves the lottery ticket hypothesis by reducing over-parameterization requirement.

Method approximates Riemannian barycenter on manifolds.

Improved sampling for high-dimensional posteriors with underdamped Langevin.

Method identifies low-dimensional structure in high-dimensional probability measures.

The paper models financial asset prices with jumps and evaluates European option prices using numerical methods.

RQMC improves kernel-based learning by reducing deterministic error and offering computational advantages.

New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.

Improved particle approximation for mean-field neural networks.

Deep ReLU networks can efficiently approximate Sobolev and Besov functions.

We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and require only poly-logarithmically many calls to the approximation oracle per it…

New algorithms improve causal graph discovery with adaptive interventions, even under worst-case interventional costs.

Deep ReLU networks can approximate and learn smooth functions efficiently.

This paper optimizes ReLU networks for approximating Hölder continuous functions.

Study on policy gradient for stochastic bandits using diffusion approximation.

New algorithm tackles dynamic assortment optimization with knapsack constraints.

Improved likelihood-free inference by localizing and refining low-dimensional approximations.

Let $M$ be a pinched negatively curved Riemannian manifold, whose unit tangent bundle is endowed with a Gibbs measure $m_F$ associated to a potential $F$. We compute the Hausdorff dimension of the conditional measures of $m_F$. We study the $m_F$-almost sure asymptotic penetration behaviour of locally geodesic lines of…

Estimates neural network error approximating compact sets.

Algorithm approximates functions into manifolds with curvature bounds.

We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal…

New algorithm reduces switching costs in RL beyond linear MDPs.

The high computational complexity associated with training deep neural networks limits online and real-time training on edge devices. This paper proposed an end-to-end training and inference scheme that eliminates multiplications by approximate operations in the log-domain which has the potential to significantly reduc…

Paper optimizes approximating high-dimensional diffusions by independent coordinates.

Deep neural networks approximate functions in shift-invariant spaces with controlled error.

Solves approximation problems for zonoids and neural networks, closing gaps in dimensions 2 and 3.

Paper proposes a method to solve log-optimal portfolios under ambiguous return distributions.

In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…

Paper proposes an algorithm to optimize CVaR using retrospective approximation and importance sampling.

Efficient algorithms identify true hypothesis from many options with minimal actions.

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation tech…

Deep density methods improve filtering in high-dimensional systems.

We prove that almost all geodesics on a noncompact locally symmetric space of finite volume grow with a logarithmic speed -- the higher rank generalization of a theorem of D. Sullivan (1982). More generally, under certain conditions on a sequence of subsets $A_n$ of a homogeneous space $G/Γ$ ($G$ a semisimple Lie group…

Unified framework for denoising models across various spaces.

We address the problem of automatic generation of features for value function approximation. Bellman Error Basis Functions (BEBFs) have been shown to improve the error of policy evaluation with function approximation, with a convergence rate similar to that of value iteration. We propose a simple, fast and robust algor…

This paper improves deep neural network approximation for fully connected networks, achieving optimal convergence rates.

Designs efficient algorithms to maximize the expectation of Gaussian random variables.