In this paper, we study the properties of the Frank-Wolfe algorithm to solve the \ExactSparse reconstruction problem. We prove that when the dictionary is quasi-incoherent, at each iteration, the Frank-Wolfe algorithm picks up an atom indexed by the support. We also prove that when the dictionary is quasi-incoherent, t…
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48 results for “Frank-Wolfe iterations”
We propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full Frank-Wolfe algorithm. We also show that, when applied to the d…
We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block Frank-Wolfe algorithm reduces the per-iteration cost while maintaining linear conver…
Paper improves Frank-Wolfe algorithm's efficiency bounds.
problem Establishing efficient iteration complexity for Frank-Wolfe algorithm.
method Using metric entropy to provide lower bounds.
result Frank-Wolfe requires many iterations for certain problems.
New algorithm reduces online learning iterations by a factor of T^2/3.
problem Efficiency in online learning with smooth cost functions.
method Follow-the-Perturbed-Leader method using online primal-dual framework.
result Guaranteed T^2/3 regret for general online convex optimization.
Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating ``in-face" directions at each iteration, as well as t…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be solved in polynomial time via a natural convex relaxation, known as Compressive …
Improved Frank-Wolfe algorithm speeds up training of differentially private LASSO models.
problem Training differentially private LASSO models on sparse data.
method Adapted Frank-Wolfe algorithm for sparse inputs, reducing runtime.
result Training time reduced from to .
Improved Frank-Wolfe algorithm for generalized self-concordant functions converges quickly.
problem Efficiently solving learning problems with generalized self-concordant objectives.
method Simple Frank-Wolfe variant with open-loop step size strategy .
result Achieves convergence rate for primal and Frank-Wolfe gaps.
New algorithms improve robust covariance estimation efficiency.
problem Efficiently compute robust covariance estimation for large datasets.
method Frank-Wolfe-based algorithms for Tyler's M-estimator.
result AFW and GAFW converge linearly under mild assumptions.
The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method …
Proposes a new algorithm to improve Frank-Wolfe method efficiency.
problem Improves Frank-Wolfe method's stability and efficiency.
method Introduces 1-SFW, a one-sample stochastic Frank-Wolfe algorithm.
result Achieves optimal convergence rate and first-order stationary point.
New Frank-Wolfe algorithm speeds up SVM-type multi-category learning.
problem Improving pattern recognition performance in multi-category SVM learning.
method Developed a new optimization algorithm based on Frank-Wolfe framework for MC-SVM variants.
result Closed-form solutions for direction finding and line search in the Frank-Wolfe framework for MC-SVM.
Paper connects DP and optimization for RL, suggesting new algorithms.
problem Optimizing scalar objectives in RL.
method Drawing connections between DP and optimization algorithms.
result Links between DP schemes and optimization algorithms.
Improved Frank-Wolfe method reduces dependence on data size for empirical risk minimization.
problem Reducing dependence on number of data observations in Frank-Wolfe methods.
method Taylor-series approximated gradients applied to Frank-Wolfe method.
result Significant speed-ups over existing methods on real-world datasets.
The study provides statistical guarantees for Bayesian variational boosting.
problem Statistical and convergence issues in variational boosting.
method Proposed a novel variational family and a functional Frank-Wolfe optimization algorithm.
result Demonstrated stochastic boundedness and provided convergence rate for boosting iterates.
Complexity Issues and Randomization Strategies in Frank-Wolfe Algorithms for Machine Learningstat.ML
Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as each iteration requires to optimize a linear model, a clever implementation is cruc…
In this paper, we consider the problem of selecting representatives from a data set for arbitrary supervised/unsupervised learning tasks. We identify a subset of a data set such that 1) the size of is much smaller than and 2) efficiently describes the entire data set, in a way formalized via convex …
In this paper, we propose several improvements on the block-coordinate Frank-Wolfe (BCFW) algorithm from Lacoste-Julien et al. (2013) recently used to optimize the structured support vector machine (SSVM) objective in the context of structured prediction, though it has wider applications. The key intuition behind our i…
A dissertation on scalable projection-free optimization methods.
problem Efficient optimization algorithms for large-scale machine learning problems.
method Study of Frank-Wolfe variants and their extensions to distributed and derivative-free settings.
result Development of 1-SFW and QFW, achieving state-of-the-art complexity and efficiency.
In this work, we propose an infinite restricted Boltzmann machine~(RBM), whose maximum likelihood estimation~(MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each ite…
Unified approach to graph matching using Hilbert spaces and entropy-regularized Frank-Wolfe algorithm.
problem Graph matching problems in computer vision, pattern recognition, and bioinformatics.
method Unified view of Koopmans-Beckmann's QAP and Lawler's QAP, introducing new rules for array operations in Hilbert spaces. Entropy-regularized Frank-Wolfe (EnFW) algorithm for QAP optimization.
result Our approach significantly outperforms state-of-the-art in matching accuracy and scalability.
In this paper, the online variants of the classical Frank-Wolfe algorithm are considered. We consider minimizing the regret with a stochastic cost. The online algorithms only require simple iterative updates and a non-adaptive step size rule, in contrast to the hybrid schemes commonly considered in the literature. Seve…
Unified framework for efficient Frank-Wolfe optimization of Dominant Set Clustering.
problem Optimizing Dominant Set Clustering with various Frank-Wolfe algorithms.
method Unified framework for pairwise, standard, and away-steps Frank-Wolfe algorithms, with explicit convergence rates.
result Explicit convergence rates for Frank-Wolfe methods in Dominant Set Clustering.
New algorithm reduces adaptive regret without projections.
problem Computational expense of projections in online convex optimization.
method Lazy gradient-based algorithm with set-membership computations.
result Near-optimal adaptive regret bounds for general convex functions.
Boosted Frank-Wolfe accelerates optimization for nonconvex problems.
problem Optimizing nonconvex and quasar-convex objectives efficiently.
method Developed a novel step size strategy for stochastic Frank-Wolfe, extending it to various gradient estimators.
result Boosted Frank-Wolfe achieves faster convergence rates than non-boosted Frank-Wolfe.
Frank-Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of Machine Learning. The ability to work with cheap projection-free iterations and the incremental nature of the method make FW a very effective choice for many l…
A fast metric learning framework using Gershgorin disc alignment.
problem Learning effective metrics for graph-based data.
method Fast projection-free metric learning via Gershgorin disc alignment.
result Efficiently computed graph metric matrices outperform competing methods.
Stochastic approximation algorithms show exponential progress bounds.
problem Analyzing the convergence of stochastic approximation algorithms.
method Developed geometric ergodicity proofs to establish exponential concentration bounds.
result Proved faster convergence rates for specific algorithms.
Unified view of Lion and Muon as Stochastic Frank-Wolfe methods.
problem Optimization of constrained problems in deep learning.
method Interpreting Lion and Muon as Stochastic Frank-Wolfe methods and extending the approach to heavy-tailed noise.
result Convergence guarantees and KKT point convergence for Lion and Muon.
This work proposes a new algorithm for training a re-weighted L2 Support Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Candès et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In particular, the margin required for each training vector is set independently, defining a n…
We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their projection-free property and their ability to exploit structured constraints. However,…
Accelerated optimization methods improve robustness and privacy in estimation.
problem Improving robustness and privacy in estimation methods.
method Accelerated gradient methods based on Frank-Wolfe and projected gradient descent, with tailored learning rates and Nesterov's momentum.
result Reduction in iteration complexity, leading to stronger statistical guarantees.
We study --both in theory and practice-- the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with non-convex constraints, under standard assumptions. In diverse scenaria, we observe that …
We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank structure of its updates to ac…
Momentum accelerates Frank Wolfe algorithms on certain problems.
problem Improving convergence rate of Frank Wolfe algorithms.
method Introducing momentum into Frank Wolfe algorithms and proving faster convergence rate.
result Accelerated Frank Wolfe (AFW) converges with a faster rate of .
The Frank-Wolfe method and its extensions are well-suited for delivering solutions with desirable structural properties, such as sparsity or low-rank structure. We introduce a new variant of the Frank-Wolfe method that combines Frank-Wolfe steps and steepest descent steps, as well as a novel modification of the "Frank-…
We introduce a few variants on Frank-Wolfe style algorithms suitable for large scale optimization. We show how to modify the standard Frank-Wolfe algorithm using stochastic gradients, approximate subproblem solutions, and sketched decision variables in order to scale to enormous problems while preserving (up to constan…
Three online algorithms for submodular maximization with varying feedback types.
problem Maximizing submodular functions under different feedback models.
method Mono-Frank-Wolfe, Bandit-Frank-Wolfe, Responsive-Frank-Wolfe.
result Achieved -regret bounds for each algorithm.
Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling high dimensional constrained problems, as the projection step becomes computationa…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we provide a unified viewpoint for several first-order optimization techniques such as …
We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only requires to solve a linear minimization problem over a small \emph{subset} of the or…
New method solves constrained self-concordant minimization problems efficiently.
problem Constrained self-concordant minimization problems.
method Newton Frank-Wolfe method using linear minimization oracles.
result The method uses nearly the same number of linear minimization calls as the Frank-Wolfe method.
We propose a rank- variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation (-SVD) in Frank-Wolfe with a top- singular-vector computation (-SVD), which can be done by repeatedly applying -SVD times. …
New algorithm improves CRF inference and learning.
problem Efficient inference and learning for dense CRFs.
method Regularized Frank-Wolfe algorithm for nonconvex CRF optimization.
result Regularized Frank-Wolfe outperforms mean field and CNN baselines.
Improved Frank-Wolfe algorithm for polytopes converges linearly with dimension dependence on optimal face.
problem Efficiently solving convex minimization problems over polytopes with linear rate.
method Revisiting Frank-Wolfe algorithm with strict complementarity assumption and away-steps.
result Linear convergence rate independent of polytope dimension for optimal face.
Optimized projection-free algorithms for online learning: construction and worst-case analysismath.OC
Optimized algorithms for online learning with linear constraints improve performance and provide worst-case analysis.
problem Improving online learning algorithms for constrained optimization problems.
method Developed an optimized variant of an online Frank-Wolfe algorithm and used semidefinite programming for numerical analysis.
result No pure online Frank-Wolfe algorithm can have a better regret guarantee than O(T^3/4) without additional assumptions.
Improved Frank-Wolfe algorithm for constrained convex optimization with nearest extreme point oracle.
problem Constrained smooth convex minimization with limited linear optimization oracle access.
method Frank-Wolfe algorithm with nearest extreme point oracle.
result Improved complexity bounds for specific feasible sets, including linear convergence for polytopes.