Decomposition-Invariant Conditional Gradient for General Polytopes with Line Search
نویسندگان
چکیده
Frank-Wolfe (FW) algorithms with linear convergence rates have recently achieved great efficiency in many applications. Garber and Meshi (2016) designed a new decomposition-invariant pairwise FW variant with favorable dependency on the domain geometry. Unfortunately it applies only to a restricted class of polytopes and cannot achieve theoretical and practical efficiency at the same time. In this paper, we show that by employing an away-step update, similar rates can be generalized to arbitrary polytopes with strong empirical performance. A new “condition number” of the domain is introduced which allows leveraging the sparsity of the solution. We applied the method to a reformulation of SVM, and the linear convergence rate depends, for the first time, on the number of support vectors.
منابع مشابه
Linear-Memory and Decomposition-Invariant Linearly Convergent Conditional Gradient Algorithm for Structured Polytopes
Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a polytope, and ii) the objective is smooth and strongly-convex. However, all of these results suffer from two significant shortcomings: 1. large memory requir...
متن کاملIsometry-Invariant Valuations on Hyperbolic Space
Hyperbolic area is characterized as the unique continuous isometry invariant simple valuation on convex polygons in H. We then show that continuous isometry invariant simple valuations on polytopes in H for n ≥ 1 are determined uniquely by their values at ideal simplices. The proofs exploit a connection between valuation theory in hyperbolic space and an analogous theory on the Euclidean sphere...
متن کاملبخشبندی معنادار مدل سهبعدی اجسام بر اساس استخراج برجستگیها و هسته جسم
3D model segmentation has an important role in 3D model processing programs such as retrieval, compression and watermarking. In this paper, a new 3D model segmentation algorithm is proposed. Cognitive science research introduces 3D object decomposition as a way of object analysis and detection with human. There are two general types of segments which are obtained from decomposition based on thi...
متن کاملA Linearly Convergent Conditional Gradient Algorithm with Applications to Online and Stochastic Optimization
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and admit significantly less efficient algorithms. This motivates the computation...
متن کاملInvariant Empirical Bayes Confidence Interval for Mean Vector of Normal Distribution and its Generalization for Exponential Family
Based on a given Bayesian model of multivariate normal with known variance matrix we will find an empirical Bayes confidence interval for the mean vector components which have normal distribution. We will find this empirical Bayes confidence interval as a conditional form on ancillary statistic. In both cases (i.e. conditional and unconditional empirical Bayes confidence interval), the empiri...
متن کامل