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Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural…
Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts…
We systematically develop a learning-based treatment of stochastic optimal control (SOC), relying on direct optimization of parametric control policies. We propose a derivation of adjoint sensitivity results for stochastic differential…
This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties…
We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton's method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the…
We consider a gradient approximation scheme that is based on applying needle shaped inputs. By using ideas known from the classic proof of the Pontryagin Maximum Principle we derive an approximation that reveals that the considered system…
This paper introduces an event-triggered source seeking control (ET-SSC) for autonomous vehicles modeled as the nonholonomic unicycle. The classical source seeking control is enhanced with static-triggering conditions to enable aperiodic…
Gradient optimization algorithms using epochs, that is those based on stochastic gradient descent without replacement (SGDo), are predominantly used to train machine learning models in practice. However, the mathematical theory of SGDo and…
This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient…
Quasi-Newton methods are widely used in practise for convex loss minimization problems. These methods exhibit good empirical performance on a wide variety of tasks and enjoy super-linear convergence to the optimal solution. For large-scale…
Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a number of applications. Introducing stochasticity is key to…
The incremental gradient method is a prominent algorithm for minimizing a finite sum of smooth convex functions, used in many contexts including large-scale data processing applications and distributed optimization over networks. It is a…
In this paper we propose stochastic gradient-free methods and accelerated methods with momentum for solving stochastic optimization problems. All these methods rely on stochastic directions rather than stochastic gradients. We analyze the…
Nonconvex optimization underlies many modern machine learning and control tasks, where saddle points pose the dominant obstacle to reliable convergence in high-dimensional settings. Escaping these saddle points deterministically using…
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue…
Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation…
In this paper, we propose and practically evaluate a class of gradient-free control functions ensuring the motion of a unicycle-type system towards the extremum point of a time-varying cost function. We prove that the unicycle is able to…
The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dynamics escape strict local minima and…
Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In this article, we study these types of methods through the…
Recent works in high-dimensional model-predictive control and model-based reinforcement learning with learned dynamics and reward models have resorted to population-based optimization methods, such as the Cross-Entropy Method (CEM), for…