Empirical cost distribution: A scenario approach to the construction of probability boxes with application to channel equalization

Abstract

Based on recent results on randomized min-max convex problems, we present a technique for building probability boxes that envelop the probability distribution of the costs incurred by a sample-based solution. The proposed technique is data-based in that the probability boxes are built based on the same data that are used to obtain the solution. The construction is distribution-free, and no specific assumption is made about the probability distribution of the data. For concreteness, the proposed technique is presented on a channel equalization problem where a finite-impulse response equalizer is designed to minimize distortion. The presence of uncertainty affecting the channel is described by a sample of uncertainty instances, and the equalizer is chosen according to a min-max logic over this sample. A probability box, built according to the proposed technique, characterizes the performance of this equalizer when it is applied to other uncertain channel instances than those seen in the sample.

Application of Scenario Approach to Optimal Choice of Feedback Coefficients in Trading Strategy Using PI-Controller

“…Figure 1 was borrowed from the presentation of EECI International Graduate School (graduate course on the Scenario approach, Care et al [5]). It shows schematically the main principal of scenario approach.…”