Related papers: Heavy Ball Momentum for Conditional Gradient
The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational…
We propose a new method to accelerate the convergence of optimization algorithms. This method simply adds a power coefficient $\gamma\in[0,1)$ to the gradient during optimization. We call this the Powerball method and analyze the…
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…
In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…
Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…
This paper proposes a new variant of Frank-Wolfe (FW), called $k$FW. Standard FW suffers from slow convergence: iterates often zig-zag as update directions oscillate around extreme points of the constraint set. The new variant, $k$FW,…
An extension of the Frank-Wolfe Algorithm (FWA), also known as Conditional Gradient algorithm, is proposed. In its standard form, the FWA allows to solve constrained optimization problems involving $\beta$-smooth cost functions, calling at…
We present a new Frank-Wolfe (FW) type algorithm that is applicable to minimization problems with a nonsmooth convex objective. We provide convergence bounds and show that the scheme yields so-called coreset results for various Machine…
Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the…
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.…
Federated learning is a powerful paradigm for large-scale machine learning, but it faces significant challenges due to unreliable network connections, slow communication, and substantial data heterogeneity across clients. FedAvg and…
In large-scale learning algorithms, the momentum term is usually included in the stochastic sub-gradient method to improve the learning speed because it can navigate ravines efficiently to reach a local minimum. However, step-size and…
In this work, we study the contraction conditions of iterative algorithms for stationary and finite-horizon discrete-time regularized mean-field games (MFGs) with multiple populations, where each population only interacts with the state…
We study trade-offs between convergence rate and robustness to gradient errors in the context of first-order methods. Our focus is on generalized momentum methods (GMMs)--a broad class that includes Nesterov's accelerated gradient,…
The adaptive stochastic gradient descent (SGD) with momentum has been widely adopted in deep learning as well as convex optimization. In practice, the last iterate is commonly used as the final solution to make decisions. However, the…
We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…
The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss…
Federated Reinforcement Learning (FRL) has garnered increasing attention recently. However, due to the intrinsic spatio-temporal non-stationarity of data distributions, the current approaches typically suffer from high interaction and…
Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the…
In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…