Related papers: Minimizing risk measures with applications in netw…
We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend…
In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…
Enforcing safety in the presence of stochastic uncertainty is a challenging problem. Traditionally, researchers have proposed safety in the statistical mean as a safety measure in this case. However, ensuring safety in the statistical mean…
We consider three shortest path problems in directed graphs with random arc lengths. For the first and the second problems, a risk measure is involved. While the first problem consists in finding a path minimizing this risk measure, the…
Infrastructure networks are increasingly vulnerable to natural hazards and design flaws, making resilience assessment essential. This paper presents a scenario-based framework to evaluate network vulnerability by combining local measures…
This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or PDEs) under uncertainty. As an example, we focus on the so-called Conditional…
Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains. We develop a new formula for the gradient of the CVaR in the form of a conditional expectation. Based on this formula, we…
In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a…
We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
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…
Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, with the latter being adjusted after…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…
The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the…
We study the problem of incorporating risk while making combinatorial decisions under uncertainty. We formulate a discrete submodular maximization problem for selecting a set using Conditional-Value-at-Risk (CVaR), a risk metric commonly…
Bilevel optimization with traffic equilibrium constraints plays an important role in transportation planning and management problems such as traffic control, transport network design, and congestion pricing. In this paper, we consider a…
In safety-critical decision-making, the environment may evolve over time, and the learner adjusts its risk level accordingly. This work investigates risk-averse online optimization in dynamic environments with varying risk levels, employing…
Mainstream approximate action-value iteration reinforcement learning (RL) algorithms suffer from overestimation bias, leading to suboptimal policies in high-variance stochastic environments. Quantile-based action-value iteration methods…
The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a nonstandard optimal control…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…