Related papers: Sampling methods for multistage robust convex opti…
Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial or worst-case inputs, but researchers…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…
We consider a risk-averse stochastic capacity planning problem under uncertain demand in each period. Using a scenario tree representation of the uncertainty, we formulate a multistage stochastic integer program to adjust the capacity…
This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…
We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications.…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
Scenario reduction algorithms can be an effective means to provide a tractable description of the uncertainty in optimal control problems. However, they might significantly compromise the performance of the controlled system. In this paper,…
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…
For multi-limbed robots, motion planning with posture and force constraints tends to be a difficult optimization problem due to nonlinearities, which also present extended solve times. We propose a multi-stage optimization framework with…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
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…
We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
Efficient sampling from constraint manifolds, and thereby generating a diverse set of solutions for feasibility problems, is a fundamental challenge. We consider the case where a problem is factored, that is, the underlying nonlinear…
Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be efficient in solving high dimensional problems. Even though…