A Deterministic Nonsmooth Frank Wolfe Algorithm with Coreset Guarantees
We present a new Frank-Wolfe (FW) type algorithm that is applicable to minimization problems with a nonsmooth convex objective. We provide convergence bounds and show that the scheme yields so-called coreset results for various Machine Learning problems including 1-median, Balanced Development, Sparse PCA, Graph Cuts, and the $\ell_1$-norm-regularized Support Vector Machine (SVM) among others. This means that the algorithm provides approximate solutions to these problems in time complexity bounds that are not dependent on the size of the input problem. Our framework, motivated by a growing body of work on sublinear algorithms for various data analysis problems, is entirely deterministic and makes no use of smoothing or proximal operators. Apart from these theoretical results, we show experimentally that the algorithm is very practical and in some cases also offers significant computational advantages on large problem instances. We provide an open source implementation that can be adapted for other problems that fit the overall structure.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Nonsmooth Frank-Wolfe using Uniform Affine Approximations
Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices)…
Boosted Stochastic Frank-Wolfe for Constrained Nonconvex Optimization
The boosted Frank-Wolfe algorithm accelerates the classical Frank-Wolfe algorithm by better aligning the update direction with the negative gradient. Its analysis, however, has been limited to deterministic convex proble…
Nonsmooth Projection-Free Optimization with Functional Constraints
This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank-Wolfe algorithm and its variants a…
Interpretable Neural Networks with Frank-Wolfe: Sparse Relevance Maps and Relevance Orderings
We study the effects of constrained optimization formulations and Frank-Wolfe algorithms for obtaining interpretable neural network predictions. Reformulating the Rate-Distortion Explanations (RDE) method for relevance a…
Revisiting the Approximate Carathéodory Problem via the Frank-Wolfe Algorithm
The approximate Carath\'eodory theorem states that given a compact convex set $\mathcal{C}\subset\mathbb{R}^n$ and $p\in\left[2,+\infty\right[$, each point $x^*\in\mathcal{C}$ can be approximated to $\epsilon$-accuracy i…