Related papers: A Nonstochastic Control Approach to Optimization
This text presents an introduction to an emerging paradigm in control of dynamical systems and differentiable reinforcement learning called online nonstochastic control. The new approach applies techniques from online convex optimization…
This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while…
We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
In the online non-stochastic control problem, an agent sequentially selects control inputs for a linear dynamical system when facing unknown and adversarially selected convex costs and disturbances. A common metric for evaluating control…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost…
The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an…
This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous…
Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed…
Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings have catered to a rich source of research…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…
We study how to safely control nonlinear control-affine systems that are corrupted with bounded non-stochastic noise, i.e., noise that is unknown a priori and that is not necessarily governed by a stochastic model. We focus on safety…