Related papers: Worst-case search in constrained uncertainty space…

In this paper, we present an approach for designing correct-by-design controllers for cyber-physical systems composed of multiple dynamically interconnected uncertain systems. We consider networked discrete-time uncertain nonlinear systems…

Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…

This paper presents a strictly convex chance-constrained stochastic control framework that accounts for uncertainty in control specifications such as reference trajectories and operational constraints. By jointly optimizing control inputs…

Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer limited insight into the nonconvex optimization landscape and…

We propose a method for learning constraints represented as Gaussian processes (GPs) from locally-optimal demonstrations. Our approach uses the Karush-Kuhn-Tucker (KKT) optimality conditions to determine where on the demonstrations the…

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the…

This paper studies the well-posedness and regularity of safe stabilizing optimization-based controllers for control-affine systems in the presence of model uncertainty. When the system dynamics contain unknown parameters, a finite set of…

Robust control seeks stabilizing policies that perform reliably under adversarial disturbances, with $\mathcal{H}_\infty$ control as a classical formulation. It is known that policy optimization of robust $\mathcal{H}_\infty$ control…

We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…

This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…

Objective: To obtain explainable guarantees in the online synthesis of optimal controllers for high-integrity cyber-physical systems, we re-investigate the use of exhaustive search as an alternative to reinforcement learning. Approach: We…

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…

This paper offers a critical view of the "worst-case" approach that is the cornerstone of robust control design. It is our contention that a blind acceptance of worst-case scenarios may lead to designs that are actually more dangerous than…

In distributed stochastic optimization, where parallel and asynchronous methods are employed, we establish optimal time complexities under virtually any computation behavior of workers/devices/CPUs/GPUs, capturing potential disconnections…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

The purpose of this paper is to formulate and solve a H-infinity controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes…

We study the worst-case complexity of a non-monotone line search framework that covers a wide variety of known techniques published in the literature. In this framework, the non-monotonicity is controlled by a sequence of nonnegative…

Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…

Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods. This basic operation typically consists in solving an intermediary (hopefully simpler) optimization…