arXiv research

Modified K-means ensures local optimality with same complexity.

Local Bayesian optimization shows strong performance and converges well, contrary to folklore.

Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two procedures: (i) modeling a surrogate function; (ii) maximizing an acquisition funct…

Optimizing proper loss yields calibrated models under specific conditions.

We empirically evaluate a stochastic annealing strategy for Bayesian posterior optimization with variational inference. Variational inference is a deterministic approach to approximate posterior inference in Bayesian models in which a typically non-convex objective function is locally optimized over the parameters of t…

In support vector machine (SVM) applications with unreliable data that contains a portion of outliers, non-robustness of SVMs often causes considerable performance deterioration. Although many approaches for improving the robustness of SVMs have been studied, two major challenges remain in robust SVM learning. First, r…

Novel method for shape optimization of non-smooth PDEs.

This dissertation advances the theoretical foundation of local optimization methods in Federated Learning.

Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic inverse optimal control algorithm that scales gracefully with task dimensionality, an…

In this paper, we propose a simple, fast and easy to implement algorithm LOSSGRAD (locally optimal step-size in gradient descent), which automatically modifies the step-size in gradient descent during neural networks training. Given a function $f$, a point $x$, and the gradient $\nabla_x f$ of $f$, we aim to find the s…

Using a ramified cover of the two-sphere by the torus, we prove a local optimal inequality between the diastole and the area on the two-sphere near a singular metric. This singular metric, made of two equilateral triangles glued along their boundary, has been conjectured by E. Calabi to achieve the best ratio area over…

It is well-known that normal extremals in sub-Riemannian geometry are curves which locally minimize the energy functional. Most proofs of this fact do not make, however, an explicit use of relations between local optimality and the geometry of the problem. In this paper, we provide a new proof of that classical result,…

VCSMC improves efficiency in Bayesian phylogenetic inference.

New methods detect unfairness in multiclass classifiers using DCP.

A new dynamic learning-rate scheme for optimization.

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\ell_1$ norm. For a cl…

Inter-subject registration of cortical areas is necessary in functional imaging (fMRI) studies for making inferences about equivalent brain function across a population. However, many high-level visual brain areas are defined as peaks of functional contrasts whose cortical position is highly variable. As such, most ali…

Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point…

Standard supervised learning procedures are validated against a test set that is assumed to have come from the same distribution as the training data. However, in many problems, the test data may have come from a different distribution. We consider the case of having many labeled observations from one distribution, $P_…

New method escapes local optima in neural architecture optimization.

Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including topic modeling, recommender systems and bioinformatics. Due to the compute-intensive nature of applications that must perform repeated NMF, several parallel implementations have b…

Distributed optimization often consists of two updating phases: local optimization and inter-node communication. Conventional approaches require working nodes to communicate with the server every one or few iterations to guarantee convergence. In this paper, we establish a completely different conclusion that each node…

Lo-Hp decouples weight generation into local and global policies to improve flexibility and efficiency.

On the ground of origins of the theory of Lie groups and Lie algebras, their (co)adjoint representations, and the Pontryagin maximum principle for the time-optimal problem are given an independent foundation for methods of geodesic vector field to search for normal geodesics of left-invariant (sub-)Finsler metrics on L…

We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for…

This study shows the moment-SOS hierarchy converges in polynomial optimization over product of spheres.

Reinforcement learning for embodied agents is a challenging problem. The accumulated reward to be optimized is often a very rugged function, and gradient methods are impaired by many local optimizers. We demonstrate, in an experimental setting, that incorporating an intrinsic reward can smoothen the optimization landsc…

Improved SVI with adjustable annealing for better optimization.

We present an actor-critic framework for MDPs where the objective is the variance-adjusted expected return. Our critic uses linear function approximation, and we extend the concept of compatible features to the variance-adjusted setting. We present an episodic actor-critic algorithm and show that it converges almost su…

Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo (NSMC), a methodology that generalises the SMC framework by requiring only approxi…

Study optimizes financial strategies in markets with uncertain drift.

Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture of linear regressions, a simple instance of a discriminative latent-variable mode…

In this paper, we derive a new model of synaptic plasticity, based on recent algorithms for reinforcement learning (in which an agent attempts to learn appropriate actions to maximize its long-term average reward). We show that these direct reinforcement learning algorithms also give locally optimal performance for the…

Minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning. As most of these applications involve continuous nonconvex-nonconcave formulations, a very basic question arises---"w…

LOL-BO improves latent space Bayesian optimization over structured inputs.

In this paper we consider $l_0$ regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving $l_0$ regularized box constrained convex programming. We show that the sequence generated by these methods converges to a local minimizer.…

A new metric learning framework for signed graphs using Gershgorin disc alignment.

We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of $M$ data p…

A new geometrically-motivated algorithm for nonnegative matrix factorization is developed and applied to the discovery of latent "topics" for text and image "document" corpora. The algorithm is based on robustly finding and clustering extreme points of empirical cross-document word-frequencies that correspond to novel …

Optimizes metrics for the first curl eigenvalue on 3-manifolds.

Coagent policy gradient algorithms (CPGAs) are reinforcement learning algorithms for training a class of stochastic neural networks called coagent networks. In this work, we prove that CPGAs converge to locally optimal policies. Additionally, we extend prior theory to encompass asynchronous and recurrent coagent networ…

The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In the context of weakly-supervised CNN segmentation, we demonstrate a well-motivated…

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…

FOSC-X: An extended framework for extracting multiple optimal flat clusterings from hierarchical cluster trees

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We show that for simple overparameterized problems, adaptive methods often find drasti…

In this paper, we propose a new experimental protocol and use it to benchmark the data efficiency --- performance as a function of training set size --- of two deep learning algorithms, convolutional neural networks (CNNs) and hierarchical information-preserving graph-based slow feature analysis (HiGSFA), for tasks in …

Methods for learning to search for structured prediction typically imitate a reference policy, with existing theoretical guarantees demonstrating low regret compared to that reference. This is unsatisfactory in many applications where the reference policy is suboptimal and the goal of learning is to improve upon it. Ca…

The paper analyzes how good initial guesses affect the amount of data needed for low-rank matrix recovery.