Related papers: Fine-Tuned Convex Approximations of Probabilistic …
With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
This paper proposes a fast decentralized algorithm for solving a consensus optimization problem defined in a directed networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form, and are…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We develop data-driven algorithms for reachability analysis and control of systems with a priori unknown nonlinear dynamics. The resulting algorithms not only are suitable for settings with real-time requirements but also provide provable…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that…
This paper addresses the computation of controlled reach-avoid sets (CRASs) for discrete-time polynomial systems subject to control inputs. A CRAS is a set encompassing initial states from which there exist control inputs driving the system…
A large number of applications such as querying sensor networks, and analyzing protein-protein interaction (PPI) networks, rely on mining uncertain graph and hypergraph databases. In this work we study the following problem: given an…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…
Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…
This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…