Seminar by Prof. Angelos Georghiou, McGill University
2019-07-03 15:00 - 16:30 | ODY 0 03 https://plan.epfl.ch/?room=ODY003
Prof. Angelos Georghiou, McGill University
Robust Optimization with Decision-Dependent Information Discovery

Abstract

Robust optimization is a popular paradigm for modeling and solving sequential decision-making problems affected by uncertainty. Most approaches assume that the uncertain parameters can be observed for free and that the sequence in which they are revealed is independent of the decision-maker’s actions. Yet, these assumptions fail to hold in many applications where the time of information discovery is decision-dependent and uncertain parameters only become observable after a costly investment.
In this paper, we consider two-stage robust optimization problems in which (part of) the decision variables control the time of information discovery. Thus, information available at any given time is decision-dependent and can be discovered by making strategic exploratory investments in previous stages. We propose a novel dynamic formulation of the problem. We prove correctness of this formulation and leverage our new model to provide a solution method inspired from the K-adaptability approximation approach, whereby K candidate strategies for each decision stage are chosen here-and-now and, at the beginning of each period, the best of these strategies is selected after the portion of the uncertain parameters that was chosen to be observed is revealed. We reformulate the problem as an MILP solvable with off-the-shelf solvers
and demonstrate its effectiveness on both synthetic and real data instances of the active preference elicitation problem used to learn the moral priorities of policy-makers in charge of allocating housing resources to the homeless.
