Related papers: Decentralized Relaxed Smooth Optimization with Gra…
In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use…
Stochastic distributed optimization methods that solve an optimization problem over a multi-agent network have played an important role in a variety of large-scale signal processing and machine leaning applications. Among the existing…
In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f(x)$ over a closed convex subset $\mathcal{X}$ of $\mathbb{R}^n$, with additional nonsmooth nonconvex constraints $c(x) = 0$. We develop a unified…
The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In…
$L^1$ based optimization is widely used in image denoising, machine learning and related applications. One of the main features of such approach is that it naturally provide a sparse structure in the numerical solutions. In this paper, we…
This work considers the problem of decentralized online learning, where the goal is to track the optimum of the sum of time-varying functions, distributed across several nodes in a network. The local availability of the functions and their…
Optimization problem, which is aimed at finding the global minimal value of a given cost function, is one of the central problem in science and engineering. Various numerical methods have been proposed to solve this problem, among which the…
We develop a general framework unifying several gradient-based stochastic optimization methods for empirical risk minimization problems both in centralized and distributed scenarios. The framework hinges on the introduction of an augmented…
We study convergence properties of Stochastic Gradient Descent (SGD) for convex objectives without assumptions on smoothness or strict convexity. We consider the question of establishing that with high probability the objective evaluated at…
We present an analysis for the performance of decentralized consensus-based gradient (DCG) methods for solving optimization problems over a cluster network of nodes. This type of network is composed of a number of densely connected clusters…
Gradient descent algorithm is the most utilized method when optimizing machine learning issues. However, there exists many local minimums and saddle points in the loss function, especially for high dimensional non-convex optimization…
We study the convergence of the shuffling gradient method, a popular algorithm employed to minimize the finite-sum function with regularization, in which functions are passed to apply (Proximal) Gradient Descent (GD) one by one whose order…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
Adaptive gradient methods, especially Adam-type methods (such as Adam, AMSGrad, and AdaBound), have been proposed to speed up the training process with an element-wise scaling term on learning rates. However, they often generalize poorly…
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…
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…
We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i)…
Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or ``stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
We study high-probability (HP) convergence guarantees in decentralized stochastic optimization, where multiple agents collaborate to jointly train a model over a network. Existing HP results in decentralized settings almost exclusively…