Related papers: On the Sample Size of Random Convex Programs with …
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…
We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…
Solving chance-constrained stochastic optimal control problems is a significant challenge in control. This is because no analytical solutions exist for up to a handful of special cases. A common and computationally efficient approach for…
We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
Foundation models often generate unreliable answers, while heuristic uncertainty estimators fail to fully distinguish correct from incorrect outputs, causing users to accept erroneous answers without any statistical guarantee. We address…
Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
In many synthesis problems, it can be essential to generate implementations which not only satisfy functional constraints but are also randomized to improve variety, robustness, or unpredictability. The recently-proposed framework of…
Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the $\ell_1$ minimization method for…
We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…