Related papers: Accelerated Gradient Descent via Long Steps

Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…

The gradient descent (GD) method -- is a fundamental and likely the most popular optimization algorithm in machine learning (ML), with a history traced back to a paper in 1847 (Cauchy, 1847). It was studied under various assumptions,…

The convergence behavior of gradient methods for minimizing convex differentiable functions is one of the core questions in convex optimization. This paper shows that their well-known complexities can be achieved under conditions weaker…

Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…

We develop new sub-optimality bounds for gradient descent (GD) that depend on the conditioning of the objective along the path of optimization rather than on global, worst-case constants. Key to our proofs is directional smoothness, a…

We present a coupled system of ODEs which, when discretized with a constant time step/learning rate, recovers Nesterov's accelerated gradient descent algorithm. The same ODEs, when discretized with a decreasing learning rate, leads to novel…

Quasi-Newton methods are widely used for solving convex optimization problems due to their ease of implementation, practical efficiency, and strong local convergence guarantees. However, their global convergence is typically established…

We propose an efficient distributed randomized coordinate descent method for minimizing regularized non-strongly convex loss functions. The method attains the optimal $O(1/k^2)$ convergence rate, where $k$ is the iteration counter. The core…

There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…

This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the…

We consider gradient descent with constant stepsizes and derive exact worst-case convergence rates on the minimum gradient norm of the iterates. Our analysis covers all possible stepsizes and arbitrary upper/lower bounds on the curvature of…

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…

Gradient descent is slow to converge for ill-conditioned problems and non-convex problems. An important technique for acceleration is step-size adaptation. The first part of this paper contains a detailed review of step-size adaptation…

We consider the gradient method with variable step size for minimizing functions that are definable in o-minimal structures on the real field and differentiable with locally Lipschitz gradients. We prove that global convergence holds if…

Epoch gradient descent method (a.k.a. Epoch-GD) proposed by Hazan and Kale (2011) was deemed a breakthrough for stochastic strongly convex minimization, which achieves the optimal convergence rate of $O(1/T)$ with $T$ iterative updates for…

We aim to make stochastic gradient descent (SGD) adaptive to (i) the noise $\sigma^2$ in the stochastic gradients and (ii) problem-dependent constants. When minimizing smooth, strongly-convex functions with condition number $\kappa$, we…

We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly…

Adaptive gradient methods are typically used for training over-parameterized models. To better understand their behaviour, we study a simplistic setting -- smooth, convex losses with models over-parameterized enough to interpolate the data.…

Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…