相关论文: Objective acceleration for unconstrained optimizat…

The Regularized Nonlinear Acceleration (RNA) algorithm is an acceleration method capable of improving the rate of convergence of many optimization schemes such as gradient descend, SAGA or SVRG. Until now, its analysis is limited to convex…

The recent breakthroughs and prohibitive complexities of Deep Neural Networks (DNNs) have excited extensive interest in domain-specific DNN accelerators, among which optical DNN accelerators are particularly promising thanks to their…

Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational…

We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise…

This paper establishes the theoretical foundations of the online scaled gradient methods (OSGM), a framework that utilizes online learning to adapt stepsizes and provably accelerate first-order methods. OSGM quantifies the effectiveness of…

Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…

Anderson acceleration (or Anderson mixing) is an efficient acceleration method for fixed point iterations $x_{t+1}=G(x_t)$, e.g., gradient descent can be viewed as iteratively applying the operation $G(x) \triangleq x-\alpha\nabla f(x)$. It…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings.…

In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…

Line search (or backtracking) procedures have been widely employed into first-order methods for solving convex optimization problems, especially those with unknown problem parameters (e.g., Lipschitz constant). In this paper, we show that…

First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…

Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…

We study distributed optimization to minimize a global objective that is a sum of smooth and strongly-convex local cost functions. Recently, several algorithms over undirected and directed graphs have been proposed that use a gradient…

Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…

This paper presents a new regularization approach -- termed OpReg-Boost -- to boost the convergence and lessen the asymptotic error of online optimization and learning algorithms. In particular, the paper considers online algorithms for…

We study realizable continual linear regression under random task orderings, a common setting for developing continual learning theory. In this setup, the worst-case expected loss after $k$ learning iterations admits a lower bound of…

We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical…

Gradient boosting of prediction rules is an efficient approach to learn potentially interpretable yet accurate probabilistic models. However, actual interpretability requires to limit the number and size of the generated rules, and existing…

We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…