Related papers: Decision-Scaled Scenario Approach for Rare Chance-…
Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…
Algorithms for rare event complex systems simulations are proposed. Compressed Sensing (CS) has {\it revolutionized} our understanding of limits in signal recovery and has forced us to re-define Shannon-Nyquist sampling theorem for sparse…
Scenario generation is an effective data-driven method for solving chance-constrained optimization while ensuring desired risk guarantees with a finite number of samples. Crucial challenges in deploying this technique in the real world…
We propose a flexible scenario-based regularized Sample Average Approximation (SBR-SAA) framework for stochastic optimization. This work is motivated by challenges in standard Wasserstein Distributionally Robust Optimization (WDRO), where…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…
Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of…
Estimating rare events in complex systems is a key challenge in reliability analysis. The challenge grows in multimodal problems, where traditional methods often rely on a small set of design points and risk overlooking critical failure…
Rare event simulation and estimation for systems in equilibrium are among the most challenging topics in molecular dynamics. As was shown by Jarzynski and others, nonequilibrium forcing can theoretically be used to obtain equilibrium rare…
We study rare-event simulation for a class of problems where the target hitting sets of interest are defined via modern machine learning tools such as neural networks and random forests. This problem is motivated from fast emerging studies…
The scenario approach provides a powerful data-driven framework for designing solutions under uncertainty with rigorous probabilistic robustness guarantees. Existing theory, however, primarily addresses assessing robustness with respect to…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the…
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…
This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…