Related papers: Optimization under rare events: scaling laws for l…

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…

Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…

This paper studies the optimization of Markov decision processes (MDPs) from a risk-seeking perspective, where the risk is measured by conditional value-at-risk (CVaR). The objective is to find a policy that maximizes the long-run CVaR of…

The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed stochastic processes. Our changes-of-measure are parameterized by a family of distributions admitting a mixture…

We consider continuous-time stochastic optimal control problems featuring Conditional Value-at-Risk (CVaR) in the objective. The major difficulty in these problems arises from time-inconsistency, which prevents us from directly using…

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…

Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…

Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…

Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…

The "scenario approach" provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled…

Options are generally learned by using an inaccurate environment model (or simulator), which contains uncertain model parameters. While there are several methods to learn options that are robust against the uncertainty of model parameters,…

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…

Financial portfolios are often optimized for maximum profit while subject to a constraint formulated in terms of the Conditional Value-at-Risk (CVaR). This amounts to solving a linear problem. However, in its original formulation this…

We introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification…

The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…

Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…

Extreme value theory is concerned with probabilistic and statistical questions related to very high or very low values in sequences of random variables and in stochastic processes. The subject has a rich mathematical theory and also a long…

An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo…

Data in the real-world classification problems are always imbalanced or long-tailed, wherein the majority classes have the most of the samples that dominate the model training. In such setting, the naive model tends to have poor performance…

We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…