In this paper, we study Clifford-Wolf translations of Finsler spaces. We first give a characterization of Clifford-Wolf translations of Finsler spaces in terms of Killing vector fields. In particular, we show that there is a natural correspondence between Clifford-Wolf translations and the Killing vector fields of cons…
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48 results for “Wolfe conditions”
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.
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.
New neural network approach for projection-free optimization.
problem Feasibility constraints in optimization problems.
method Designing projection-free convex optimization algorithms as Frank-Wolfe Networks.
result LSTM-learned optimizers outperform hand-designed and unconstrained optimizers.
The Frank-Wolfe (FW) optimization algorithm has lately re-gained popularity thanks in particular to its ability to nicely handle the structured constraints appearing in machine learning applications. However, its convergence rate is known to be slow (sublinear) when the solution lies at the boundary. A simple less-know…
This work extends Ledoit-Wolf shrinkage to unknown mean covariance estimation.
problem Large dimensional covariance matrix estimation with unknown mean under Kolmogorov asymptotics.
method Extending Ledoit-Wolf linear shrinkage to translation-invariant estimators, proving their convergence properties.
result A new estimator outperforms other standard estimators empirically.
In this paper, we introduce a new type of Finsler metrics, called -metrics. We define the notion of the good datum of a homogeneous -metric and use that to study the geometric properties. In particular, we give a formula of the S-curvature and deduce a condition for the S-curvature to be vanishing…
New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.
problem Rank-constrained optimization problems with linear matrix inequalities.
method Investigates Dantzig-Wolfe relaxation and develops conditions for exactness.
result Conditions for extreme point, convex hull, and objective exactness.
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.
We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center who will obtain an estimate of a parameter related to observations of all terminals. It is well known that if the transmission rates are in the Sle…
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.
New method solves stochastic optimization problems with affine constraints.
problem Stochastic optimization problems with affine constraints.
method Stochastic Frank-Wolfe method.
result Guarantees convergence rates for objective residual and feasibility gap.
A Clifford-Wolf translation of a connected Finsler space is an isometry which moves each point the same distance. A Finsler space is called Clifford-Wolf homogeneous if for any two points there is a Clifford-Wolf translation such that . In this paper, we give a complete classifi…
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.
Improved Frank-Wolfe algorithms for large-scale optimization.
problem Efficiently solving large-scale optimization problems.
method Modifications to Frank-Wolfe algorithm using stochastic gradients, approximate solutions, and sketched variables.
result Achieves optimal convergence rate of for large problems.
A Clifford-Wolf translation of a connected Finsler space is an isometry which moves each point the sam distance. A Finsler space is called Clifford-Wolf homogeneous if for any two point there is a Clifford-Wolf translation such that . In this paper, we study Clifford-Wolf transl…
Paper studies Frank-Wolfe algorithm for solving sparse reconstruction problems.
problem Sparse reconstruction problem
method Frank-Wolfe algorithm applied to quasi-incoherent dictionaries
result Algorithm converges exponentially fast for quasi-incoherent dictionaries
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.
Study formal properties of SU(2) and SO(3) bundles over Wolf spaces.
problem Formality of total spaces of SU(2) and SO(3) bundles over Wolf spaces.
method Formality analysis using symmetric positive quaternionic Kähler manifolds.
result All 3-Sasakian homogeneous spaces are formal, but some Wolf spaces are not.
Paper proposes a Frank-Wolfe solver for symmetric NMF under simplicial constraint.
problem Optimizing symmetric nonnegative matrix factorization with simplicial constraint.
method Frank-Wolfe optimization algorithm for nonconvex problems.
result Proves convergence rate of for -approximate KKT points.
Two new Frank-Wolfe algorithms use subsampling to speed up convergence.
problem Efficiently solving large-scale optimization problems with linear minimization over subsets.
method Randomized variants of Frank-Wolfe algorithms with subsampling.
result Achieves sublinear or linear convergence rates with reduced computational cost.
New Frank-Wolfe method for sparse neural networks.
problem Training sparse neural networks.
method Combines Frank-Wolfe steps and steepest descent steps, with in-face directions and block coordinate steps.
result Significant improvements in training sparse neural networks.
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.
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,…
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 solves convex trace-norm ball problems.
problem Optimizing convex functions over trace-norm balls.
method Rank-k variant of Frank-Wolfe algorithm using top-k singular-vector computation.
result Linear convergence rate for smooth and strongly convex objectives with rank-limited solutions.
Improved Frank-Wolfe for sparse/low-rank problems.
problem Sparse/low-rank optimization problems.
method Primal-Dual Block Frank-Wolfe algorithm.
result Empirically outperforms state-of-the-art methods in classification tasks.
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 .
A new method reduces rank in Frank-Wolfe steps for nuclear norm problems.
problem High rank intermediate iterates in Frank-Wolfe algorithm for nuclear norm problems.
method Rank-drop steps to ensure rank decreases and feasibility.
result Reduced rank of solutions compared to Frank-Wolfe and variants.
Probabilistic line search improves stochastic optimization efficiency.
problem Lack of direct line search methods for stochastic optimization.
method Combines deterministic line search structure with Bayesian optimization concepts.
result Effective removal of learning rate definition for SGD.
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.
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.
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.
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…
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.
A new decentralized Frank-Wolfe algorithm tackles high-dimensional constrained optimization problems.
problem High-dimensional constrained optimization problems in decentralized settings.
method Projection-free optimization approach using Frank-Wolfe algorithm.
result The DeFW algorithm converges with rates for convex, strongly convex, and non-convex objectives.
Develops Frank-Wolfe Augmented Lagrangian for convex optimization.
problem Minimizing functions over intersections of convex sets.
method Frank-Wolfe Augmented Lagrangian (FW-AL) method.
result Sublinear convergence rate for general convex compact sets, linear for polytopes.
Improved Frank-Wolfe algorithm solves saddle point problems efficiently.
problem Solving constrained smooth convex-concave saddle point problems.
method Extends Frank-Wolfe algorithm to use linear minimization oracles.
result First proof of convergence for FW-type saddle point solver over polytopes.
Unified view on matching pursuit and Frank-Wolfe algorithms with improved convergence rates.
problem Improving convergence rates for matching pursuit and Frank-Wolfe algorithms.
method Unified optimization perspective leading to explicit convergence rates.
result Sublinear () convergence for general smooth objectives and linear convergence for strongly convex objectives.
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.
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.
New algorithm estimates barycenters of distributions using Frank-Wolfe.
problem Estimating the average of arbitrary probability distributions.
method Frank-Wolfe optimization for Sinkhorn divergence, incrementally populating support.
result Converges in both discrete and continuous distributions, with proven rates.
The main purpose of the following article is to introduce a \emph{Lie theoretical} approach to the problem of classifying pseudo quaternionic-Kähler (QK) reductions of the pseudo QK symmetric spaces, otherwise called \emph{generalized Wolf spaces}.
We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within the marginal polytope through repeated maximum a posteriori (MAP) calls. This m…
Improved SGD algorithm with faster convergence.
problem Optimization of machine learning models.
method Conditional accelerated lazy stochastic gradient descent.
result Convergence rate of $O\left(\frac{1}{\varepsilon^2}
ight)$, faster than previous methods.
In this paper, we study Clifford-Wolf translations of homogeneous Randers metrics on spheres. It turns out that we can present a complete description of all the Clifford-Wolf translations of all the homogeneous Randers metrics on spheres. The most important point of this paper is that a new phenomena surfaces. Namely, …
An isometry of a Finsler space is called Clifford-Wolf translation (CW-translation) if it moves all points the same distance. A Finsler space is called Clifford-Wolf homogeneous (CW-homogeneous) if for any there is a CW-translation such that . We prove that if is a homogeneous Finsl…
Infinite RBMs use Frank-Wolfe for efficient training and initialization.
problem Training infinite RBMs with sparse solutions.
method Frank-Wolfe algorithm for constrained convex optimization.
result Infinite RBMs can be trained efficiently and initialized effectively.