A Novel Unified Parametric Assumption for Nonconvex Optimization

• URL: http://arxiv.org/abs/2502.12329v1
• Date: Mon, 17 Feb 2025 21:25:31 GMT
• Title: A Novel Unified Parametric Assumption for Nonconvex Optimization
• Authors: Artem Riabinin, Ahmed Khaled, Peter Richtárik,
• Abstract summary: Non optimization is central to machine learning, but the general framework non convexity enables weak convergence guarantees too pessimistic compared to the other hand. We introduce a novel unified assumption in non convex algorithms.
• Score: 53.943470475510196
• License:
• Abstract: Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables efficient optimization, it is of limited applicability to many practical problems. To bridge this gap and better understand the practical success of optimization algorithms in nonconvex settings, we introduce a novel unified parametric assumption. Our assumption is general enough to encompass a broad class of nonconvex functions while also being specific enough to enable the derivation of a unified convergence theorem for gradient-based methods. Notably, by tuning the parameters of our assumption, we demonstrate its versatility in recovering several existing function classes as special cases and in identifying functions amenable to efficient optimization. We derive our convergence theorem for both deterministic and stochastic optimization, and conduct experiments to verify that our assumption can hold practically over optimization trajectories.

Related papers

• A Generalization Result for Convergence in Learning-to-Optimize [4.112909937203119]
  Conventional convergence guarantees in optimization are based on geometric arguments, which cannot be applied to algorithms. We are the first to prove the best of our knowledge, we are the first to prove the best of our knowledge, we are the first to prove the best of our knowledge, we are the first to prove the best of our knowledge, we are the first to prove the best of our knowledge, we are the first to prove the best of our knowledge, we are the first to prove the best of our knowledge, we are the first to prove the best of our knowledge, we are the first to prove the best of our
  arXiv  Detail & Related papers  (2024-10-10T08:17:04Z)
• Pseudo-Bayesian Optimization [7.556071491014536]
  We study an axiomatic framework that elicits the minimal requirements to guarantee black-box optimization convergence. We show how using simple local regression, and a suitable "randomized prior" construction to quantify uncertainty, not only guarantees convergence but also consistently outperforms state-of-the-art benchmarks.
  arXiv  Detail & Related papers  (2023-10-15T07:55:28Z)
• Non-Convex Optimization with Certificates and Fast Rates Through Kernel Sums of Squares [68.8204255655161]
  We consider potentially non- optimized approximation problems. In this paper, we propose an algorithm that achieves close to optimal a priori computational guarantees.
  arXiv  Detail & Related papers  (2022-04-11T09:37:04Z)
• Optimization on manifolds: A symplectic approach [127.54402681305629]
  We propose a dissipative extension of Dirac's theory of constrained Hamiltonian systems as a general framework for solving optimization problems. Our class of (accelerated) algorithms are not only simple and efficient but also applicable to a broad range of contexts.
  arXiv  Detail & Related papers  (2021-07-23T13:43:34Z)
• Implicit Rate-Constrained Optimization of Non-decomposable Objectives [37.43791617018009]
  We consider a family of constrained optimization problems arising in machine learning. Our key idea is to formulate a rate-constrained optimization that expresses the threshold parameter as a function of the model parameters. We show how the resulting optimization problem can be solved using standard gradient based methods.
  arXiv  Detail & Related papers  (2021-07-23T00:04:39Z)
• Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework [100.36569795440889]
  This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information. We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
  arXiv  Detail & Related papers  (2020-12-21T17:29:58Z)
• 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)
• Bilevel Optimization: Convergence Analysis and Enhanced Design [63.64636047748605]
  Bilevel optimization is a tool for many machine learning problems. We propose a novel stoc-efficientgradient estimator named stoc-BiO.
  arXiv  Detail & Related papers  (2020-10-15T18:09:48Z)

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.