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We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference:…

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…

We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

In safety-critical applications, machine learning models should generalize well under worst-case distribution shifts, that is, have a small robust risk. Invariance-based algorithms can provably take advantage of structural assumptions on…

In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…

It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…

Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…

It is a long-standing objective to ease the computation burden incurred by the decision making process. Identification of this mechanism's sensitivity to simplification has tremendous ramifications. Yet, algorithms for decision making under…

In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the…

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…

We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…

Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…

We study the trajectory optimization problem under chance constraints for continuous-time stochastic systems. To address chance constraints imposed on the entire stochastic trajectory, we propose a framework based on the set erosion…