Monitoring With Limited Information

We consider a system with an evolving state that can be stopped at any time by a decision maker (DM), yielding a state-dependent reward. The DM does not observe the state except for a limited number of monitoring times, which he must choose, in conjunction with a suitable stopping policy, to maximize his reward. Dealing … Read more

Pareto Efficiency in Robust Optimization

This paper formalizes and adapts the well known concept of Pareto efficiency in the context of the popular robust optimization (RO) methodology. We argue that the classical RO paradigm need not produce solutions that possess the associated property of Pareto optimality, and illustrate via examples how this could lead to inefficiencies and sub-optimal performance in … Read more

Supermodularity and Affine Policies in Dynamic Robust Optimization

This paper considers robust dynamic optimization problems, where the unknown parameters are modeled as uncertainty sets. We seek to bridge two classical paradigms for solving such problems, namely (1) Dynamic Programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We provide a set … Read more

A Hierarchy of Near-Optimal Policies for Multi-stage Adaptive Optimization

In this paper, we propose a new tractable framework for dealing with multi-stage decision problems affected by uncertainty, applicable to robust optimization and stochastic programming. We introduce a hierarchy of polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The approach yields a hierarchy parameterized by … Read more