arXiv research

Developed an efficient iterative algorithm for SVI model.

LocalKMeans parallelizes Lloyd's algorithm for distributed data.

Paper tightens privacy and generalization bounds for iterative learning.

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

We present an iterative Markov chainMonte Carlo algorithm for computingreference priors and minimax risk forgeneral parametric families. Ourapproach uses MCMC techniques based onthe Blahut-Arimoto algorithm forcomputing channel capacity ininformation theory. We give astatistical analysis of the algorithm,bounding the n…

The paper analyzes generalization of noisy iterative algorithms using communication theory.

New algorithms improve rank one signal estimation from noisy data.

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

Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and p…

Novel algorithm for Markov decision processes using rank-one approximation.

Algorithm recovers causal graphs from data with fewer tests.

Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement upon this iterative algorithms in terms of their respective performance metrics an…

In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. Recent work [Xu and Raginsky (2017)] has established a bound on the generalization error of empirical risk minimization based on the mutual information $I(S;…

Two new algorithms solve nonconvex-strongly concave problems efficiently.

Approximate dynamic programming algorithms, such as approximate value iteration, have been successfully applied to many complex reinforcement learning tasks, and a better approximate dynamic programming algorithm is expected to further extend the applicability of reinforcement learning to various tasks. In this paper w…

Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing regularizer. In this paper, motivated by the success of extrapolation techniques in accele…

This paper provides a framework to analyze stochastic gradient algorithms in a mean squared error (MSE) sense using the asymptotic normality result of the stochastic gradient descent (SGD) iterates. We perform this analysis by taking the asymptotic normality result and applying it to the finite iteration case. Specific…

Establishes geometric convergence of iterative optimization algorithms.

Faster WIND accelerates iterative BOND for LLM alignment.

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

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…

XLVINs improve data efficiency in implicit planning by leveraging latent space.

We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal gradient scheme and a new homotopy strategy for smoothness parameter. By an appropriat…

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic programming algorithms for solving Markov decision problems. These recursive stochastic a…

A new iterative K-FAC algorithm reduces training time and memory usage.

New iterative regularization method tackles non-smooth, non-strongly convex functionals.

Paper proves suboptimal convergence rate of last iterate for SGDM.

New algorithm minimizes worst-case regret in uncertain, time-varying dynamics.

While classic work in convex-concave min-max optimization relies on average-iterate convergence results, the emergence of nonconvex applications such as training Generative Adversarial Networks has led to renewed interest in last-iterate convergence guarantees. Proving last-iterate convergence is challenging because ma…

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

New algorithm improves understanding of decentralized SBO transient iteration complexity.

Machine learning (ML) training algorithms often possess an inherent self-correcting behavior due to their iterative-convergent nature. Recent systems exploit this property to achieve adaptability and efficiency in unreliable computing environments by relaxing the consistency of execution and allowing calculation errors…

Meta-learning control algorithm with finite-time guarantees for unknown systems.

TrIM improves gradient-based dimension reduction and regression.

New analysis of stochastic approximation with non-expansive mappings.

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…

This paper accelerates TV regularization algorithms by unrolling proximal gradient descent.

Iterative algorithms, like gradient descent, are common tools for solving a variety of problems, such as model fitting. For this reason, there is interest in creating differentially private versions of them. However, their conversion to differentially private algorithms is often naive. For instance, a fixed number of i…

Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simpl…

A very simple heuristic approach to the unfolding problem will be described. An iterative algorithm starts with an empty histogram and every iteration aims to add one entry to this histogram. The entry to be added is selected according to a criteria which includes a $χ^2$ test and a regularization. After a relatively s…

SNS accelerates Sinkhorn algorithm with sparse Newton iterations.

One-step policy improvement outperforms iterative RL methods on D4RL.

Algorithm recovers causal graphs in presence of latent confounders and selection bias.

IBPF algorithm tackles high-dimensional parameter learning for complex systems.

We propose a clustering-based iterative algorithm to solve certain optimization problems in machine learning, where we start the algorithm by aggregating the original data, solving the problem on aggregated data, and then in subsequent steps gradually disaggregate the aggregated data. We apply the algorithm to common m…

We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We provide proof that a random backward iteration algorithm to draw the pictures of the Julia sets, previously proven to work in the context of iteration of a rational map of degree two or more, extends to finitely gene…

Derives error bounds for stochastic iterative algorithms using Stein's method.

New algorithms solve complex minimax problems without needing derivatives.