Related papers: Sample Complexity of Chance Constrained Optimizati…
Many safety-critical real-world problems, such as autonomous driving and collaborative robots, are of a distributed multi-agent nature. To optimize the performance of these systems while ensuring safety, we can cast them as distributed…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but also used in probabilistic forecasting, clustering and estimating generative adversarial…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
This work proposes a method of wind farm scenario generation to support real-time optimization tools and presents key findings therein. This work draws upon work from the literature and presents an efficient and scalable method for…
Generating optimal plans in highly dynamic environments is challenging. Plans are predicated on an assumed initial state, but this state can change unexpectedly during plan generation, potentially invalidating the planning effort. In this…
We study contextual chance-constrained programming under decision-dependent uncertainty. In this setting, a decision not only needs to satisfy constraints but also alters the distribution of uncertain outcomes. This dependency makes the…
Generating representative scenarios for power system planning in which the stochasticity of renewable generation and cross-correlations between renewables and load are fully captured, is a challenging problem. Traditional methods for…
Safety is a critical concern for the success of urban air mobility, especially in dynamic and uncertain environments. This paper proposes a path planning algorithm based on RRT in conjunction with chance constraints in the presence of…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a…
Chance-constrained programs (CCPs) provide a powerful modeling framework for decision-making under uncertainty, but their nonconvex feasible regions make them computationally challenging. A widely used convex inner approximation replaces…
We present a scheme for sequential decision making with a risk-sensitive objective and constraints in a dynamic environment. A neural network is trained as an approximator of the mapping from parameter space to space of risk and policy with…
In this paper, we learn dynamics models for parametrized families of dynamical systems with varying properties. The dynamics models are formulated as stochastic processes conditioned on a latent context variable which is inferred from…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
Worst-case generation plays a critical role in evaluating robustness and stress-testing systems under distribution shifts, in applications ranging from machine learning models to power grids and medical prediction systems. We develop a…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These…
We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…