Related papers: Extremum Seeking is Stable for Scalar Maps that ar…
Stochastic gradients for deep neural networks exhibit strong correlations along the optimization trajectory, and are often aligned with a small set of Hessian eigenvectors associated with outlier eigenvalues. Recent work shows that…
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…
During neural network training, the sharpness of the Hessian matrix of the training loss rises until training is on the edge of stability. As a result, even nonstochastic gradient descent does not accurately model the underlying dynamical…
This paper studies a stochastic extremum seeking method to steer a nonholonomic vehicle to the unknown source of a static spatially distributed filed in a plane. The key challenge lies in the lack of vehicle's position information and the…
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…
The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the…
In this paper, we propose objective-function-free (OFF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using…
Sharpness-Aware Minimization (SAM) aims to improve generalization by minimizing a worst-case perturbed loss over a small neighborhood of model parameters. However, during training, its optimization behavior does not always align with…
While momentum-based optimization algorithms are commonly used in the notoriously non-convex optimization problems of deep learning, their analysis has historically been restricted to the convex and strongly convex setting. In this article,…
Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…
This paper aims at investigating the problem of fast convergence to the Nash equilibrium (NE) for N-Player noncooperative differential games. The proposed method is such that the players attain their NE point without steady-state…
This paper introduces a novel Homogeneous Second-order Descent Ascent (HSDA) algorithm for nonconvex-strongly concave minimax optimization problems. At each iteration, HSDA uniquely computes a search direction by solving a homogenized…
Verifying the Second-Order Sufficient Condition (SOSC), thus ensuring a stationary point locally minimizes a given objective function (subject to certain constraints), is an essential component of non-convex computational optimization and…
In this paper we validate, including experimentally, the effectiveness of a recent theoretical developments made by our group on control-affine Extremum Seeking Control (ESC) systems. In particular, our validation is concerned with the…
We develop an exact coordinate descent algorithm for high-dimensional regularized Huber regression. In contrast to composite gradient descent methods, our algorithm fully exploits the advantages of coordinate descent when the underlying…
In this paper, we consider a strongly convex finite-sum minimization problem over a decentralized network and propose a communication-efficient decentralized Newton's method for solving it. We first apply dynamic average consensus (DAC) so…
Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE's performance. However,…
Our recently developed "unbiased" extremum seeking (uES) algorithms ensure perfect convergence to the optimum at a user-assigned exponential rate or, more powerfully, within a user-prescribed time. Unlike classical approach, these…
The convergence rate of stochastic gradient search is analyzed in this paper. Using arguments based on differential geometry and Lojasiewicz inequalities, tight bounds on the convergence rate of general stochastic gradient algorithms are…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…