arXiv research

The three operator splitting scheme was recently proposed by [Davis and Yin, 2015] as a method to optimize composite objective functions with one convex smooth term and two convex (possibly non-smooth) terms for which we have access to their proximity operator. In this short note we provide an alternative proof for the…

New data structure identifies close match from multiple distributions.

Extends model uncertainty framework to non-linear affine processes for longevity bonds and contingent claims.

The paper shows how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.

Paper extends credit portfolio valuation under model uncertainty for multiple default times.

New algorithm improves game learning with randomised optimism.

Let $Ł$ be the Laplace operator on $\R ^d$, $d\geq 3$ or the Laplace Beltrami operator on the harmonic $NA$ group (in particular on a rank one noncompact symmetric space). For the equation $Łu - \varphi(\cdot,u)=0$ we give necessary and sufficient conditions for the existence of entire bounded or large solutions under…

A new method solves convex optimization problems on manifolds efficiently.

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric space. For example, the sublinear Higson corona of n-dimensional E…

Single-timescale actor-critic finds globally optimal policy.

New framework finds periodic policies in reset-free MDPs with sublinear regret.

New model for Knightian uncertainty with jumps.

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…

New convergence rates found for PnP methods using MMSE denoisers.

This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in $L^2$ is defined as the best $L^2$-estimate, given a $σ$-subalgebra and a degree of model uncertainty. When the random vector represents the payoff…

New sublinear sketches improve ANN and KDE for massive data streams.

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …

Supplier learns to price contracts against a learning retailer.

The paper develops methods for time-varying constrained online convex optimization.

For $α\in (1,2)$, we present a generalized central limit theorem for $α$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, p…

Study $L^{2}$-harmonic forms on almost Kähler manifolds, extending vanishing theorems.

New algorithms for constrained online optimization with memory and predictions.

Memory-limited learning tackles adversarial bandits with reduced storage.

Sharp Liouville theorem for minimal graphs on manifolds with nonnegative Ricci curvature.

New method connects CAT(0) spaces to hyperbolic spaces.

We consider the problem of finding anomalies in high-dimensional data using popular PCA based anomaly scores. The naive algorithms for computing these scores explicitly compute the PCA of the covariance matrix which uses space quadratic in the dimensionality of the data. We give the first streaming algorithms that use …

We introduce a simple method for nearly simultaneous computation of all moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations commonly seen in finance. The method proposed in this papers is not restricted to any particular dynamics of the different…

Study online learning in unknown Markov games with sublinear regret.

Open problem seeks an online learning algorithm for binary classification.

Efficiently trains large GMMs with millions to billions of parameters.

Average signature of 2-bridge knots approximates sqrt(2c/π).

Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function cha…

New algorithm achieves sublinear regret in CMDPs without error cancellations.

Extends tracking guarantees for time-varying variational inequalities.

Geodesic loops escape from balls at a sublinear rate imply virtually abelian fundamental group.

Develops geometric foundations for sublinear Morse boundaries in mapping class groups and Teichmüller spaces.

LaPSRL achieves optimal regret for isoperimetric RL distributions.

New approach for distributed online optimization of non-convex losses with sublinear regret.

We study the problem of "isotropically rounding" a polytope $K\subset\mathbb{R}^n$, that is, computing a linear transformation which makes the uniform distribution on the polytope have roughly identity covariance matrix. We assume $K$ is defined by $m$ linear inequalities, with guarantee that $rB\subset K\subset RB$, w…

LIBO optimizes repeated bandit tasks without prior knowledge or regret.

GP-UCB resolves sublinear regret for kernelized bandits.

Develops sublinear Morse theory in symmetric spaces.

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting t…

We develop efficient algorithms to train $\ell_1$-regularized linear classifiers with large dimensionality $d$ of the feature space, number of classes $k$, and sample size $n$. Our focus is on a special class of losses that includes, in particular, the multiclass hinge and logistic losses. Our approach combines several…

Paper presents a faster classical algorithm for principal component regression.

Federated learning algorithm improves with intermittent client availability.