SCORE: Approximating Curvature Information under Self-Concordant Regularization

• URL: http://arxiv.org/abs/2112.07344v3
• Date: Mon, 10 Jul 2023 14:13:17 GMT
• Title: SCORE: Approximating Curvature Information under Self-Concordant Regularization
• Authors: Adeyemi D. Adeoye, Alberto Bemporad
• Abstract summary: We propose a generalized Gauss-Newton with Self-Concordant Regularization (GGN-SCORE) algorithm that updates the minimization speed each time it receives a new input. The proposed algorithm exploits the structure of the second-order information in the Hessian matrix, thereby reducing computational overhead.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Optimization problems that include regularization functions in their objectives are regularly solved in many applications. When one seeks second-order methods for such problems, it may be desirable to exploit specific properties of some of these regularization functions when accounting for curvature information in the solution steps to speed up convergence. In this paper, we propose the SCORE (self-concordant regularization) framework for unconstrained minimization problems which incorporates second-order information in the Newton-decrement framework for convex optimization. We propose the generalized Gauss-Newton with Self-Concordant Regularization (GGN-SCORE) algorithm that updates the minimization variables each time it receives a new input batch. The proposed algorithm exploits the structure of the second-order information in the Hessian matrix, thereby reducing computational overhead. GGN-SCORE demonstrates how to speed up convergence while also improving model generalization for problems that involve regularized minimization under the proposed SCORE framework. Numerical experiments show the efficiency of our method and its fast convergence, which compare favorably against baseline first-order and quasi-Newton methods. Additional experiments involving non-convex (overparameterized) neural network training problems show that the proposed method is promising for non-convex optimization.

Related papers

• Reduced-Space Iteratively Reweighted Second-Order Methods for Nonconvex Sparse Regularization [11.56128809794923]
  This paper explores a specific type of non sparsity-promoting regularization problems, namely those involving $ell_p-$ iterations of local property convergence.
  arXiv  Detail & Related papers  (2024-07-24T12:15:59Z)
• Efficient Low-rank Identification via Accelerated Iteratively Reweighted Nuclear Norm Minimization [8.879403568685499]
  We introduce an adaptive updating strategy for smoothing parameters. This behavior transforms the algorithm into one that effectively solves problems after a few iterations. We prove the global proposed experiment, guaranteeing that every iteration is a critical one.
  arXiv  Detail & Related papers  (2024-06-22T02:37:13Z)
• Faster Riemannian Newton-type Optimization by Subsampling and Cubic Regularization [3.867143522757309]
  This work is on constrained large-scale non-constrained optimization where the constraint set implies a manifold structure. We propose a new second-order saddleian optimization algorithm, aiming at improving convergence and reducing computational cost.
  arXiv  Detail & Related papers  (2023-02-22T00:37:44Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [73.2273449996098]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms. An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Zeroth and First Order Stochastic Frank-Wolfe Algorithms for Constrained Optimization [13.170519806372075]
  Problems of convex optimization with two sets of constraints arise frequently in the context of semidefinite programming. Since projection onto the first set of constraints is difficult, it becomes necessary to explore projection-free algorithms. The efficacy of the proposed algorithms is tested on relevant applications of sparse matrix estimation, clustering via semidefinite relaxation, and uniform sparsest cut problem.
  arXiv  Detail & Related papers  (2021-07-14T08:01:30Z)
• Recent Theoretical Advances in Non-Convex Optimization [56.88981258425256]
  Motivated by recent increased interest in analysis of optimization algorithms for non- optimization in deep networks and other problems in data, we give an overview of recent results of theoretical optimization algorithms for non- optimization.
  arXiv  Detail & Related papers  (2020-12-11T08:28:51Z)
• Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization [98.0595480384208]
  We propose a generalization extraient spaces which converges to a stationary point. The algorithm applies not only to general $p$-normed spaces, but also to general $p$-dimensional vector spaces.
  arXiv  Detail & Related papers  (2020-10-31T21:35:42Z)
• Convergence of adaptive algorithms for weakly convex constrained optimization [59.36386973876765]
  We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope. Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
  arXiv  Detail & Related papers  (2020-06-11T17:43:19Z)
• Effective Dimension Adaptive Sketching Methods for Faster Regularized Least-Squares Optimization [56.05635751529922]
  We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT)
  arXiv  Detail & Related papers  (2020-06-10T15:00:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.