We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the difference of convex (DC) programming, and enjoys both strong computational and statist…
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48 results for “Local Strong Convexity”
Infinite Lie groups meet continuity conditions.
problem Continuity conditions for Lie groups.
method Analyzing locally -convex Lie groups.
result Infinite dimensional Lie groups have the strong Trotter property.
PF-LaCG removes the need for knowing smoothness and strong convexity parameters for locally accelerated CG.
problem Locally accelerated CG requires knowledge of smoothness and strong convexity parameters.
method Parameter-Free Locally Accelerated CG (PF-LaCG) algorithm.
result PF-LaCG achieves local acceleration without requiring knowledge of smoothness and strong convexity parameters.
Strongly convex bodies can be approximated by smooth ones.
problem Approximating strongly convex bodies with smooth ones.
method Using locally strongly convex bodies.
result Smooth approximations of strongly convex bodies exist and can be controlled in terms of Hausdorff distance.
Kernel k-Means algorithm improves clustering of non-linear data.
problem Non-convexity of kernel k-Means objective function leads to local minima.
method Generalizes MM approach to solve non-convex problem in kernel and multi-kernel settings.
result Establishes strong consistency guarantees for Kernel Power k-Means.
The paper provides recovery guarantees for CNNs with multiple kernels under polynomial sample and computational complexities.
problem Parameter recovery for non-overlapping CNNs with multiple kernels.
method Showed local strong convexity of squared loss for most popular activations, used tensor methods for initialization, and proved convergence of gradient descent.
result Gradient descent following tensor initialization converges to the global optimal with polynomial time complexity.
The study explores convex unions and completions in simplicial pseudomanifolds, revealing unexpected behavior.
problem Understanding the behavior of convex unions in simplicial pseudomanifolds.
method Generalization to simplicial pseudomanifolds, considering PL homeomorphisms and edge subdivisions.
result Unexpected behavior in convex unions and completions, including empty contraction spaces and large/small contraction spaces.
Global convergence for robust regression problems via IRLS with enhancements.
problem Global convergence for robust regression problems.
method Augmentations to IRLS to ensure global recovery and improved robustness.
result Global recovery guarantees for robust regression problems, outperforming state-of-the-art algorithms.
New FL framework handles non-i.i.d data without strong assumptions.
problem Non-identically independent distributed (non-i.i.d) data in federated learning.
method Proposes a new algorithm design strategy from primal-dual optimization.
result Achieves optimal communication efficiency and communication complexity.
New algorithms optimize decentralized convex optimization with near optimal communication and computation.
problem Decentralized convex optimization in large-scale machine learning and sensor networks.
method Novel algorithms combining Nesterov's acceleration, multi-consensus, and gradient-tracking.
result Achieves optimal computation and near optimal communication complexity, matching lower bounds.
Strong geodesic convex function and strong monotone vector field of order on Riemannian manifolds have been established. A characterization of strong geodesic convex function of order for the continuously differentiable functions has been discussed. The relation between the solution of a new variational inequal…
We identify a condition for regularity of optimal transport maps that requires only three derivatives of the cost function, for measures given by densities that are only bounded above and below. This new condition is equivalent to the weak Ma-Trudinger-Wang condition when the cost is . Moreover, we only require (n…
FastAdaBelief improves convergence rate of AdaBelief by exploiting strong convexity.
problem Improving convergence rate of AdaBelief without sacrificing generalization ability.
method Designing FastAdaBelief that adjusts step size considering strong convexity.
result Proves regret bound for FastAdaBelief.
Over-parameterization makes optimization easier for simple neural networks, even with minor extra neurons.
problem Understanding the impact of over-parameterization on optimization landscapes of shallow neural networks.
method Analyzing a simple ReLU neural network with Gaussian inputs, focusing on optimization properties and landscape changes.
result Over-parameterization makes the objective function one-point strongly convex in most directions, aiding optimization.
We establish that over a C^{2,1} manifold the exponential map of any Lipschitz connection or spray determines a local Lipeomophism and that, furthermore, reversible convex normal neighborhoods do exist. To that end we use the method of Picard-Lindelof approximation to prove the strong differentiability of the exponenti…
Learning Variational Inequalities from Data: Fast Generalization Rates under Strong Monotonicitycs.LG
This paper shows how to learn variational inequalities fast with strong monotonicity.
problem Learning variational inequalities efficiently.
method Extending convex optimization techniques to variational inequalities with strong monotonicity.
result Fast generalization rates of for learning variational inequalities.
Graphically discrete groups have strong rigidity properties.
problem Understanding the rigidity of group actions on graphs.
method Introducing graphical discreteness and proving rigidity properties.
result Free products of graphically discrete groups are action rigid.
Let be open and convex. We show that every (not necessarily Lipschitz or strongly) convex function can be approximated by real analytic convex functions, uniformly on all of . In doing so we provide a technique which transfers results on uniform approximation on bounded …
STL-SGD accelerates Local SGD by gradually increasing communication periods.
problem Reducing communication complexity in distributed SGD.
method Gradually increasing communication periods while decreasing learning rate.
result Significant reduction in communication complexity with improved convergence rates.
New method for blind over-the-air computation without CSI.
problem Over-the-air computation without channel information.
method Wirtinger flow solution with random initialization.
result Statistical optimality and global convergence of the method.
Estimate Collapsibility of Causal Effects in Completed Partial DAGs via Strong d-Convex Hullsstat.ML
Estimate collapsibility of causal effects in CPDAGs via strong d-convex hulls.
problem Estimate causal effects in CPDAGs.
method Use strong d-convex hulls to characterize minimal collapsible sets.
result Efficient algorithm for obtaining collapsible sets in DAGs and CPDAGs.
Proves local strong solutions for General Landau-Lifshitz-Bloch equation.
problem Proving existence of solutions for complex equations.
method Analytical proof of local strong solutions.
result Local strong solutions exist for General Landau-Lifshitz-Bloch equation.
This paper is concerned with the problem of determining whether a projective-equivalence class of sprays is the geodesic class of a Finsler function. We address both the local and the global aspects of this problem. We present our results entirely in terms of a multiplier, that is, a type (0,2) tensor field along the t…
Entropy convexity characterizes strong energy condition in spacetimes.
problem Characterizing strong energy condition in nonsmooth spacetimes.
method Lifting fractional powers of Lorentz distance to probability measures and showing geodesic convexity of Boltzmann-Shannon entropy.
result Strong energy condition is equivalent to geodesic convexity of Boltzmann-Shannon entropy.
The paper tackles control policy learning for unknown systems using convex optimization.
problem Learning control policies for unknown linear dynamical systems to maximize a quadratic reward function.
method Sequential convex programming to optimize expected reward over posterior system parameter distribution.
result The method achieves reliable local convergence and robust stability, demonstrated with strong performance and robustness in simulations and real-world applications.
In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation function…
The paper proves stability of curvature bounds in geometric analysis.
problem Stability of local Riemannian Ricci curvature bounds under convergence.
method Gromov-Hausdorff convergence, Lagrangian approach, heat flow, weak gradients, Evolution Variational Inequality.
result Almost everywhere existence of Euclidean weak tangents.
Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysiscs.LG
New algorithms improve distributed optimization under specific conditions.
problem Distributed optimization problems with high communication costs.
method SVRS and AccSVRS algorithms combining gradient sliding and variance reduction.
result Achieved better communication complexity in distributed optimization.
SAGA is a fast incremental gradient method on the finite sum problem and its effectiveness has been tested on a vast of applications. In this paper, we analyze SAGA on a class of non-strongly convex and non-convex statistical problem such as Lasso, group Lasso, Logistic regression with regularization, linear r…
SAdam improves Adam's performance for strongly convex functions.
problem Improving Adam's performance for strongly convex functions.
method Developed SAdam, a variant of Adam, which exploits strong convexity.
result Achieves a data-dependent regret bound for strongly convex functions.
New framework explains why nonconvex methods work well in low-rank matrix estimation.
problem Nonconvex low-rank matrix estimation problems in machine learning.
method Developed a theoretical framework revealing a benign regularizer.
result Nonconvex procedures can behave well due to a disguised convexity.
This work proposes ACTC for adaptive distributed learning under communication constraints.
problem Adaptive distributed learning in networks with communication constraints.
method ACTC (Adapt-Compress-Then-Combine) strategy with diffusion exchange of compressed updates.
result ACTC iterates converge to the optimizer with significant bit savings.
Harmonic functions on compact symmetric spaces exhibit strong convexity properties.
problem Understanding the convexity of harmonic functions on compact symmetric spaces.
method Analyzing the nonnegativity of the Laplacian powers of harmonic functions.
result Harmonic functions on compact symmetric spaces have nonnegative Laplacian powers, demonstrating strong convexity.
We propose a projected semi-stochastic gradient descent method with mini-batch for improving both the theoretical complexity and practical performance of the general stochastic gradient descent method (SGD). We are able to prove linear convergence under weak strong convexity assumption. This requires no strong convexit…
Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image s…
Asynchronous L-BFGS speeds up non-convex optimization.
problem Non-convex optimization challenges in machine learning.
method Asynchronous stochastic L-BFGS algorithm for non-convex optimization.
result Achieves an ergodic convergence rate of and linear speedup.
Totally geodesic submanifolds in convex cores are properly immersed and have finite volume.
problem Characterizing totally geodesic submanifolds in geometrically finite manifolds.
method Analysis of totally geodesic submanifolds in the convex core of geometrically finite rank-one locally symmetric manifolds.
result Every maximal totally geodesic submanifold of dimension at least two in the convex core is properly immersed and has finite volume, and only finitely many such submanifolds can occur.
In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optim…
Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.
problem Optimizing smooth unconstrained problems with geometrically adapted directions.
method Yau's Affine Normal Descent (YAND) uses the equi-affine normal of level-set hypersurfaces as search directions.
result YAND converges globally under standard smoothness assumptions and locally quadratically near nondegenerate minimizers.
A new algorithm solves signed Fréchet regression on manifolds with bounded curvature.
problem Signed Fréchet regression on Riemannian manifolds with bounded curvature.
method Proximal DC algorithm (FRIDA) for computing signed Fréchet regression fits.
result Existence and interiority of minimizers, strong convexity of proximal subproblems, and convergence to stationary points.
We show that for a very general class of curvature functions defined in the positive cone, the problem of finding a complete strictly locally convex hypersurface in satisfying with a prescribed asymptotic boundary at infinity has at least one smooth solution with uniformly bounded hyperbol…
Quantized Decentralized Gradient Descent (QDGD) solves distributed optimization with quantized communications.
problem Minimizing the sum of smooth and strongly convex functions over a network of distributed agents with quantized communications.
method Proposes QDGD algorithm combining quantized and local information for decentralized gradient descent.
result Achieves vanishing mean solution error under strong convexity and smoothness assumptions.
OBD algorithm optimizes online convex optimization with strong convexity and switching costs.
problem Online convex optimization with strong convexity and switching costs.
method Online Balanced Descent (OBD) algorithm for -strongly convex costs with near-optimal dynamic regret and per-round accuracy for -smooth sequences.
result OBD achieves a competitive ratio of for -strongly convex costs.
New method improves optimization and DP in FL.
problem Combining strong DP and optimization in FL.
method Combining clipping, momentum, and error feedback.
result Optimal convergence rate and near optimal DP guarantees.
A Richer Theory of Convex Constrained Optimization with Reduced Projections and Improved Ratesmath.OC
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a linear optimization under the inequality constraint are time-consuming, which render …
This paper improves stochastic approximation for smooth and strongly convex functions.
problem Improving convergence rate of stochastic approximation for smooth and strongly convex functions.
method Utilizes both smoothness and strong convexity conditions to achieve faster convergence rates.
result Demonstrates an risk bound, potentially faster than .
Optimal control in changing systems without strong convexity assumptions.
problem Adversarial changes in convex costs for unknown linear systems.
method Non-convex lower confidence bounds and computationally-efficient regret minimization.
result Achieves -regret rate, optimal compared to best stabilizing controller.
Epoch-GDA achieves optimal convergence rate for SCSC min-max problems.
problem Solving stochastic min-max problems with strong convexity and strong concavity.
method Epoch-wise stochastic gradient descent ascent method (Epoch-GDA) without additional assumptions.
result Achieves the optimal rate of for the duality gap of general SCSC min-max problems.