arXiv research

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

The paper addresses pricing interest rate derivatives in markets with volatility uncertainty.

Study on optimal rates for sequential probability assignment using smoothed analysis.

Paper generalizes extragradient methods for solving equations and inclusions with improved convergence rates.

Gradient EM converges globally for over-parameterized Gaussian mixtures.

GP-UCB resolves sublinear regret for kernelized bandits.

New algorithms reduce communication for sparse mean estimation in noisy distributed systems.

Stochastic algorithm achieves sublinear convergence for bi-objective optimization.

Single-timescale actor-critic finds globally optimal policy.

New algorithms tackle machine learning problems using manifold proximal point methods.

New convergence rates found for PnP methods using MMSE denoisers.

A new method solves convex optimization problems on manifolds efficiently.

The alternating gradient descent (AGD) is a simple but popular algorithm which has been applied to problems in optimization, machine learning, data ming, and signal processing, etc. The algorithm updates two blocks of variables in an alternating manner, in which a gradient step is taken on one block, while keeping the …

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties of this method, both in the exact and inexact setting, in the case when the obje…

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 algorithms reduce private bandit regret to nearly non-private levels.

Algorithm maximizes revenue-risk by estimating price impact kernel and optimizing control problems.

Federated learning algorithm improves with intermittent client availability.

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

Local LMO optimizes constrained problems using local linear minimization.

In this paper, we study and analyze the mini-batch version of StochAstic Recursive grAdient algoritHm (SARAH), a method employing the stochastic recursive gradient, for solving empirical loss minimization for the case of nonconvex losses. We provide a sublinear convergence rate (to stationary points) for general noncon…

We consider the non-stochastic version of the (cooperative) multi-player multi-armed bandit problem. The model assumes no communication at all between the players, and furthermore when two (or more) players select the same action this results in a maximal loss. We prove the first $\sqrt{T}$-type regret guarantee for th…

Two new algorithms reduce online kernel regression's computational cost while maintaining optimal regret bounds.

The paper analyzes sampling efficiency of discrete diffusion models, providing sharp and adaptive guarantees.

Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size polynomially and lead to optimal sublinear rates on (strongly) convex problems. An alternative schedule, popular in nonconvex optimization, is called \emph{geometric step decay…

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

Paper explores rate-preserving reductions between Blackwell approachability and no-regret learning.

Survey on extragradient methods for solving nonlinear equations and inclusions.

We show that Newton's method converges globally at a linear rate for objective functions whose Hessians are stable. This class of problems includes many functions which are not strongly convex, such as logistic regression. Our linear convergence result is (i) affine-invariant, and holds even if an (ii) approximate Hess…

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…

Improved convergence analysis for decentralized non-convex optimization.

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection be…

Simplifies and optimizes learning from untrusted batches with structure.

Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for minimizing a smooth convex function over a linear space spanned by a set of atoms…

Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper, we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching pursuit methods in an optimization sense, for general sets of atoms. We derive …

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 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…

Estimates population profile from small random samples.

GAIL with neural networks converges to global optima and has a known rate.

GP-PSRL achieves sublinear regret for continuous control with unbounded state space.

Study shows how much information can be learned from sparse signals with limited data.

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…

Study robust recovery of low-rank matrices from corrupted measurements without rank prior.

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…

New methods optimize functions faster with less gradient accuracy needed.

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

Random extrapolation speeds up coordinate descent for sparse and dense data.