Related papers: Optimization with Temporal and Logical Specificati…

High-order methods for convex and nonconvex optimization, particularly $p$th-order Adaptive Regularization Methods (AR$p$), have attracted significant research interest by naturally incorporating high-order Taylor models into adaptive…

The article discusses distributed gradient-descent algorithms for computing local and global minima in nonconvex optimization. For local optimization, we focus on distributed stochastic gradient descent (D-SGD)--a simple network-based…

This work provides test error bounds for iterative fixed point methods on linear predictors -- specifically, stochastic and batch mirror descent (MD), and stochastic temporal difference learning (TD) -- with two core contributions: (a) a…

Stiff dynamical systems present a challenge for machine-learning reduced-order models (ML-ROMs), as explicit time integration becomes unstable in stiff regimes while implicit integration within learning loops is computationally expensive…

For the purpose of finding benchmark quality solutions to time dependent Sn transport problems, we develop a numerical method in a Discontinuous Galerkin (DG) framework that utilizes time dependent cell edges, which we call a moving mesh,…

This paper presents a motion planning and risk analysis framework for enhancing human-robot collaboration with a Multi-Rotor Aerial Vehicle. The proposed method employs Signal Temporal Logic to encode key mission objectives, including…

The wide availability of data coupled with the computational advances in artificial intelligence and machine learning promise to enable many future technologies such as autonomous driving. While there has been a variety of successful…

In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical…

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…

The Downhill Simplex Method (DSM) is a fast-converging derivative-free optimization technique for nonlinear systems. However, the optimization process is often subject to premature convergence due to degenerated simplices or noise-induced…

First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning…

Real-world robotic systems must comply with safety requirements in the presence of uncertainty. To define and measure requirement adherence, Signal Temporal Logic (STL) offers a mathematically rigorous and expressive language. However,…

Continuous-time control of multiple quadrotors in constrained environments under signal temporal logic (STL) specifications is critical due to their nonlinear dynamics, safety constraints, and the requirement to ensure continuous-time…

This study proposes a novel planning framework based on a model predictive control formulation that incorporates signal temporal logic (STL) specifications for task completion guarantees and robustness quantification. This marks the…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Many machine learning tasks can be formulated as Regularized Empirical Risk Minimization (R-ERM), and solved by optimization algorithms such as gradient descent (GD), stochastic gradient descent (SGD), and stochastic variance reduction…

We consider randomized block coordinate stochastic mirror descent (RBSMD) methods for solving high-dimensional stochastic optimization problems with strongly convex objective functions. Our goal is to develop RBSMD schemes that achieve a…

As machine learning (ML) systems become pervasive, safeguarding their security is critical. However, recently it has been demonstrated that motivated adversaries are able to mislead ML systems by perturbing test data using semantic…

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…

Scientific machine learning (SciML) is a field of increasing interest in several different application fields. In an optimization context, SciML-based tools have enabled the development of more efficient optimization methods. However,…