Related papers: Solving Chance Constrained Optimization under Non-…

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…

Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making…

This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents…

Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…

We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…

We present a distributionally robust approach for collision avoidance by incorporating contextual information. Specifically, we embed the conditional distribution of future trajectory of the obstacle conditioned on the motion of the ego…

Probabilistic predictions are probability distributions over the set of possible outcomes. Such predictions quantify the uncertainty in the outcome, making them essential for effective decision making. By combining multiple predictions, the…

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…

In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…

Many commodity sensors that measure the robot and dynamic obstacle's state have non-Gaussian noise characteristics. Yet, many current approaches treat the underlying-uncertainty in motion and perception as Gaussian, primarily to ensure…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

We present algorithms for performing data-driven stochastic reachability as an addition to SReachTools, an open-source stochastic reachability toolbox. Our method leverages a class of machine learning techniques known as kernel embeddings…

We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…

We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least…

We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…

In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kernel mean embedding. Specifically, we formulate the…

This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…

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 address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…