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Deep Neural Networks (DNNs) generalization is known to be closely related to the flatness of minima, leading to the development of Sharpness-Aware Minimization (SAM) for seeking flatter minima and better generalization. In this paper, we…

The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant…

The convergence of deterministic policy gradient under the Hadamard parameterization is studied in the tabular setting and the linear convergence of the algorithm is established. To this end, we first show that the error decreases at an…

Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…

The majorization-minimization (MM) principle is an extremely general framework for deriving optimization algorithms. It includes the expectation-maximization (EM) algorithm, proximal gradient algorithm, concave-convex procedure, quadratic…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can…

The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…

This paper proposes a theoretical framework to evaluate and compare the performance of stochastic gradient algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have…

In most state-of-the-art image restoration methods, the sum of a data-fidelity and a regularization term is optimized using an iterative algorithm such as ADMM (alternating direction method of multipliers). In recent years, the possibility…

Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…

Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…

In this paper, we propose an interior-point method for linearly constrained optimization problems (possibly nonconvex). The method - which we call the Hessian barrier algorithm (HBA) - combines a forward Euler discretization of Hessian…

There is a significant gap between our theoretical understanding of optimization algorithms used in deep learning and their practical performance. Theoretical development usually focuses on proving convergence guarantees under a variety of…

Decentralized optimization is a common paradigm used in distributed signal processing and sensing as well as privacy-preserving and large-scale machine learning. It is assumed that several computational entities locally hold objective…

We empirically demonstrate that full-batch gradient descent on neural network training objectives typically operates in a regime we call the Edge of Stability. In this regime, the maximum eigenvalue of the training loss Hessian hovers just…

The paper derives analytical expressions for the asymptotic average updating direction of the adaptive moment generation (ADAM) algorithm when applied to recursive identification of nonlinear systems. It is proved that the standard…

Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…

In this work, we study an optimizer, Grad-Avg to optimize error functions. We establish the convergence of the sequence of iterates of Grad-Avg mathematically to a minimizer (under boundedness assumption). We apply Grad-Avg along with some…

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving…