Algo Carè

Scenario Min-Max Optimization and the Risk of Empirical Costs

We consider convex optimization problems in the presence of stochastic uncertainty. The min-max sample-based solution is the solution obtained by minimizing the max of the cost functions corresponding to a finite sample of the uncertainty parameter. The empirical costs are instead the cost values that the solution incurs for the various parameter realizations that have been sampled. Our goal is to evaluate the risks associated with the empirical costs, where the risk associated with a cost is the probability that the cost is exceeded when a new realization of the uncertainty parameter is seen. This task is accomplished without resorting to uncertainty realizations other than those used in optimization. The theoretical result proved in this paper is that these risks form a random vector whose probability distribution is an ordered Dirichlet distribution, irrespective of the probability measure of the stochastic uncertainty parameter. This result provides a distribution-free characterization of the risks as...

Random Convex Programs with

Random convex programs are convex optimization problems that are robust with respect to a finite number of randomly sampled instances of an uncertain variable

L_1

\delta

-Regularization: Sparsity and Generalization

. This paper studies random convex programs in which there is uncertainty in the objective function. Specifically, let

A randomised approach to flood control using Value-at-Risk

L(x,\delta)

Sign-Perturbed Sums (SPS) with asymmetric noise: Robustness analysis and robustification techniques

be a loss function that is convex in

Sign-Perturbed Sums (SPS) with instrumental variables for the identification of ARX systems

x

Finite-Sample System Identification: An Overview and a New Correlation Method

, the optimization variable, while it has an arbitrary dependence on the random variable

A randomised approach to Multiple Chance-Constrained Problems: An application to flood avoidance

\delta

Control of rivers with flood avoidance

representing uncertainty in the optimization problem. After sampling