Data-driven satisficing measure and ranking

We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by Conditional value-at-risk. Starting from offline optimization, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimization case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations).Comment: 26 Pages, 6 Figure

Design of Cooperative Networks

In this paper we analyse several approaches to the design of Cooperative Algorithms for solving a general problem: That of computing the values of some property over a spatial domain, when these values are constrained (but not uniquely determined) by some observations, and by some a priori knowledge about the nature of the solution (smoothness, for example). Specifically, we discuss the use of: Variational techniques; stochastic approximation methods for global optimization, and linear threshold networks. Finally, we present a new approach, based on the interconnection of Winner-take-all networks, for which it is possible to establish precise convergence results, including bounds on the rate of convergence.MIT Artificial Intelligence Laborator