Related papers: Efficient Scenario Generation for Heavy-tailed Cha…
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…
The scenario approach is a general data-driven algorithm to chance-constrained optimization. It seeks the optimal solution that is feasible to a carefully chosen number of scenarios. A crucial step in the scenario approach is to compute the…
In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a noisy gradient of its own objective function, and can communicate with its neighbors via a network. To handle this…
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 consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…
Existing neural network-based autonomous systems are shown to be vulnerable against adversarial attacks, therefore sophisticated evaluation on their robustness is of great importance. However, evaluating the robustness only under the…
Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…
We study iterative methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. We propose a machine-learning-based heuristic to determine starting scenarios that provide strong lower bounds. To this end, we…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
We investigate the connections between compression learning and scenario based optimization. We first show how to strengthen, or relax the consistency assumption at the basis of compression learning and study the learning and generalization…
We consider the problem of repetitive scenario design where one has to solve repeatedly a scenario design problem and can adjust the sample size (number of scenarios) to obtain a desired level of risk (constraint violation probability). We…
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…
We propose a data-driven method to establish probabilistic performance guarantees for parametric optimization problems solved via iterative algorithms. Our approach addresses two key challenges: providing convergence guarantees to…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
We treat the so-called scenario approach, a popular probabilistic approximation method for robust minmax optimization problems via independent and indentically distributed (i.i.d) sampling from the uncertainty set, from various…
We study the distributed stochastic optimization (DSO) problem under a heavy-tailed noise condition by utilizing a multi-agent system. Despite the extensive research on DSO algorithms used to solve DSO problems under light-tailed noise…
Existing macroscopic traffic control methods often struggle to strictly regulate rare, safety-critical extreme events under stochastic disturbances. In this paper, we develop a rare chance-constrained optimal control framework for…
In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…
Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…