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Related papers: Variance Reduced methods for Non-convex Compositio…

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We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…

Optimization and Control · Mathematics 2016-08-26 Zeyuan Allen-Zhu , Elad Hazan

We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…

Optimization and Control · Mathematics 2020-12-22 Andrzej Ruszczynski

In this paper, we consider the problem of minimizing the average of a large number of nonsmooth and convex functions. Such problems often arise in typical machine learning problems as empirical risk minimization, but are computationally…

Machine Learning · Statistics 2018-05-21 Wenjie Huang

We study a class of stochastic nonconvex optimization in the form of $\min_{x\in\mathcal{X}} F(x):=\mathbb{E}_\xi [f(\phi(x,\xi))]$, i.e., $F$ is a composition of a convex function $f$ and a random function $\phi$. Leveraging an (implicit)…

Optimization and Control · Mathematics 2024-07-16 Xin Chen , Niao He , Yifan Hu , Zikun Ye

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…

Optimization and Control · Mathematics 2024-06-07 Wei Jiang , Sifan Yang , Wenhao Yang , Yibo Wang , Yuanyu Wan , Lijun Zhang

In this paper, we proposed a new technique, {\em variance controlled stochastic gradient} (VCSG), to improve the performance of the stochastic variance reduced gradient (SVRG) algorithm. To avoid over-reducing the variance of gradient by…

Machine Learning · Computer Science 2021-02-22 Jia Bi , Steve R. Gunn

In this paper, we study the performance of a large family of SGD variants in the smooth nonconvex regime. To this end, we propose a generic and flexible assumption capable of accurate modeling of the second moment of the stochastic…

Optimization and Control · Mathematics 2020-06-15 Zhize Li , Peter Richtárik

We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…

Optimization and Control · Mathematics 2026-02-03 Ruyu Wang , Chao Zhang

This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…

Optimization and Control · Mathematics 2025-01-14 Raghu Bollapragada , Cem Karamanli

This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and…

Optimization and Control · Mathematics 2024-01-10 I. Necoara , F. Chorobura

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

Optimization and Control · Mathematics 2016-05-24 Sashank J. Reddi , Suvrit Sra , Barnabas Poczos , Alex Smola

Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of…

Machine Learning · Statistics 2020-01-28 Huizhuo Yuan , Xiangru Lian , Ji Liu

We consider decentralized time-varying stochastic optimization problems where each of the functions held by the nodes has a finite sum structure. Such problems can be efficiently solved using variance reduction techniques. Our aim is to…

The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…

Machine Learning · Computer Science 2026-01-27 Naoki Sato , Hideaki Iiduka

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the…

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

Optimization and Control · Mathematics 2025-11-14 Ilyas Fatkhullin , Niao He , Guanghui Lan , Florian Wolf

This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…

Optimization and Control · Mathematics 2024-10-24 Wei Jiang , Sifan Yang , Yibo Wang , Lijun Zhang

The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale…

Optimization and Control · Mathematics 2024-03-06 Trang H. Tran , Quoc Tran-Dinh , Lam M. Nguyen

This work considers optimization of composition of functions in a nested form over Riemannian manifolds where each function contains an expectation. This type of problems is gaining popularity in applications such as policy evaluation in…

Optimization and Control · Mathematics 2024-03-20 Dewei Zhang , Sam Davanloo Tajbakhsh

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

Optimization and Control · Mathematics 2020-05-05 Quoc Tran-Dinh , Nhan H. Pham , Dzung T. Phan , Lam M. Nguyen