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Multi-agent planning and reinforcement learning can be challenging when agents cannot see the state of the world or communicate with each other due to communication costs, latency, or noise. Partially Observable Stochastic Games (POSGs)…
We introduce a new framework for unifying and systematizing the performance analysis of first-order black-box optimization algorithms for unconstrained convex minimization. The low-cost iteration complexity enjoyed by first-order algorithms…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
In this paper, we study ordinary differential equations (ODE) coupled with solutions of a stochastic nonsmooth convex optimization problem (SNCOP). We use the regularization approach, the sample average approximation and the time-stepping…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
Memory is a key computational bottleneck when solving large-scale convex optimization problems such as semidefinite programs (SDPs). In this paper, we focus on the regime in which storing an $n\times n$ matrix decision variable is…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
We prove lower bounds for higher-order methods in smooth non-convex finite-sum optimization. Our contribution is threefold: We first show that a deterministic algorithm cannot profit from the finite-sum structure of the objective, and that…
We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and additionally allow convex or inexpensive constraints. An…
We present a finite-horizon optimization algorithm that extends the established concept of Dual Dynamic Programming (DDP) in two ways. First, in contrast to the linear costs, dynamics, and constraints of standard DDP, we consider problems…
We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…
A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets of polynomial dynamical systems by…