arXiv research

Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.

The paper relaxes assumptions for analyzing stochastic optimization algorithms.

New algorithms solve monotone inclusions and convex-concave minimax problems.

Optimizes solving complex min-max problems with stochastic and nonconvex elements.

Two accelerated extragradient methods converge at $O(1/k)$ rate for co-hypomonotone inclusions.

Survey on extragradient methods for solving nonlinear equations and inclusions.

VR-GHAL method solves stochastic fixed-point equations with high probability.

New model-free RL algorithm tackles robust average-reward problems with finite sample complexity analysis.

Predicts the number of polynomial additions in Buchberger's algorithm using machine learning.

The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.

This paper characterizes projective models in statistical relational learning.

Paper analyzes iterates in high-dimensional linear models and proposes estimators for their generalization error.

Paper analyzes iterative learning for concept classes and learns half-spaces.

WaveFit uses fixed-point iteration to create high-quality neural vocoders.

In this paper, we introduce the notions of an iterated planar Lefschetz fibration and an iterated planar open book decomposition and prove the Weinstein conjecture for contact manifolds supporting an open book that has iterated planar pages. For $n\geq 1$, we show that a $(2n+1)$-dimensional contact manifold $M$ suppor…

We prove that an iterated torus knot type fails the uniform thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated torus knot type supports the standard contact structure. We also show that all iterated torus knots that fail the UTP support cabling knot …

Sharp analysis of power iteration for tensor PCA, improving convergence and stopping criteria.

We deduce from the work of Chen, that the restriction morphism from closed free iterated integrals to closed iterated integrals on loops is onto. We use this to show that the module of higher order invariants of smooth functions is generated by free closed iterated integrals.

In this paper we study the smooth convex-concave saddle point problem. Specifically, we analyze the last iterate convergence properties of the Extragradient (EG) algorithm. It is well known that the ergodic (averaged) iterates of EG converge at a rate of $O(1/T)$ (Nemirovski, 2004). In this paper, we show that the last…

Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is analyzed in solving the problem. The convergence of the iterations and the optim…

An iterative SE(3)-Transformer model is developed for graph data.

Iterative method learns unknown constraints for MPC control.

Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive at the optimal solution. Value iteration is a first order method and therefore …

Iterates towards Kähler metrics with constant scalar curvature.

We give short proofs of the following two facts: Iterated principal circle bundles are precisely the nilmanifolds. Every iterated circle bundle is almost flat, and hence diffeomorphic to an infranilmanifold.

Algorithm recovers causal graphs from data with fewer tests.

Spherical T-duality for iterated sphere bundles

In this paper we investigate what kind of manifolds arise as the total spaces of iterated $S^1$-bundles. A real Bott tower studied in \cite{CMO}, \cite{KM} and \cite{KN} is an example of an iterated $S^1$-bundle. We show that the total space of an iterated $S^1$-bundle is homeomorphic to an infra-nilmanifold. A real Bo…

Improved generalization with iterate averaging and adaptive algorithms.

DSPI connects natural policy gradient to policy iteration, proving global convergence.

Strong stability of ergodic iterations proven without ergodic driving sequence.

Policy iteration is a family of algorithms that are used to find an optimal policy for a given Markov Decision Problem (MDP). Simple Policy iteration (SPI) is a type of policy iteration where the strategy is to change the policy at exactly one improvable state at every step. Melekopoglou and Condon [1990] showed an exp…

New convergence rates for shuffling gradient methods without strong convexity.

Paper refutes conjecture on tensor power iteration convergence in overcomplete models.

We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry, we show that these cluster iteration maps can be reduced to symplectic maps on a lower dimensional submanifold, provided the matrix repres…

We bound the index of a subgroup in iterated Kodaira fibrations.

The Ricci iteration is a discrete analogue of the Ricci flow. We give the first study of the Ricci iteration on a class of Riemannian manifolds that are not Kähler. The Ricci iteration in the non-Kähler setting exhibits new phenomena. Among them is the existence of so-called ancient Ricci iterations. As we show, these …

We study the Ricci iteration for homogeneous metrics on spheres and complex projective spaces. Such metrics can be described in terms of modifying the canonical metric on the fibers of a Hopf fibration. When the fibers of the Hopf fibration are circles or spheres of dimension 2 or 7, we observe that the Ricci iteration…

Last SGD iterate bounds for overparameterized linear regression.

We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on several approximate variations of the Policy Iteration algorithm: Approximate Policy Iteration, Conservative Policy Iteration (CPI), a natural adaptation of the Policy Search by Dynamic Programming a…

Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.

We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the membrane case.

LocalKMeans parallelizes Lloyd's algorithm for distributed data.

We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M can be expressed via these new integrals. The ring of exponential iterated inte…

A well-known issue of Batch Normalization is its significantly reduced effectiveness in the case of small mini-batch sizes. When a mini-batch contains few examples, the statistics upon which the normalization is defined cannot be reliably estimated from it during a training iteration. To address this problem, we presen…

Last-iterate guarantees for learning in co-coercive games under noisy feedback.

Improved matching for multiple objects using a novel reweighting method.

Iterative method 'Concent' corrects spectrum bias in covariance matrices.