A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Gradient EM converges globally for over-parameterized Gaussian mixtures.
Extends tracking guarantees for time-varying variational inequalities.
Paper generalizes extragradient methods for solving equations and inclusions with improved convergence rates.
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 …
New algorithms tackle machine learning problems using manifold proximal point methods.
Single-timescale actor-critic finds globally optimal policy.
New convergence rates found for PnP methods using MMSE denoisers.
Random extrapolation speeds up coordinate descent for sparse and dense data.
This paper studies convergence of horospheres in CAT(0) spaces.
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…
Stochastic algorithm achieves sublinear convergence for bi-objective optimization.
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…
PPO algorithm converges to global optimality in multi-agent reinforcement learning.
New algorithm achieves sublinear regret in CMDPs without error cancellations.
The paper analyzes sampling efficiency of discrete diffusion models, providing sharp and adaptive guarantees.
Algorithm minimizes regret and converges to equilibria in Markov games.
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…
LIBO optimizes repeated bandit tasks without prior knowledge or regret.
Survey on extragradient methods for solving nonlinear equations and inclusions.
The paper shows how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.
Algorithm maximizes revenue-risk by estimating price impact kernel and optimizing control problems.
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…
Improved convergence analysis for decentralized non-convex optimization.
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…
Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending randomized CD to nonsmooth nonconvex settings, we develop a coordinate subgradi…
The paper improves convergence for linear systems using entropic mirror descent with Polyak stepsizes.
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 …
Method completes mixed matrix from complex surveys with heterogeneous missingness.
Federated learning is a new distributed machine learning framework, where a bunch of heterogeneous clients collaboratively train a model without sharing training data. In this work, we consider a practical and ubiquitous issue when deploying federated learning in mobile environments: intermittent client availability, w…
Sublinear LSVI via LSH reduces runtime to sublinear in actions.
This work creates a CS for non-negative heavy-tailed data with bounded mean.
We discuss a variant of Thompson sampling for nonparametric reinforcement learning in a countable classes of general stochastic environments. These environments can be non-Markov, non-ergodic, and partially observable. We show that Thompson sampling learns the environment class in the sense that (1) asymptotically its …
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…
Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to…
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…
GAIL with neural networks converges to global optima and has a known rate.
Temporal-difference learning (TD), coupled with neural networks, is among the most fundamental building blocks of deep reinforcement learning. However, due to the nonlinearity in value function approximation, such a coupling leads to nonconvexity and even divergence in optimization. As a result, the global convergence …
New model for Knightian uncertainty with jumps.
Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.
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…
New methods optimize functions faster with less gradient accuracy needed.
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…
Quantum algorithm speeds up Gibbs partition function estimation.
The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence rates are also limited to linear convergence. Due to the mathematical techniques, th…
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…
Gradient descent converges linearly in finite-width networks with positive NTK and compatible conditions.
Study robust recovery of low-rank matrices from corrupted measurements without rank prior.