Restricted Scope for REU Supplement: Robust Aggregation of Preferences

The focus of this research project is reasoning with a multiplicity of preferences. While the emphases of the main proposal are investigations of conditional preferences, and of preference aggregation, there are many ways to investigate the topic. For this summer REU, we will look at preference-driven planning under uncertainty. For the last two years (his sophomore and junior years), Josiah Hanna has studied academic advising as a decision problem, and has studied planning under uncertainty. His first paper, presented at an ICAPS 2012 workshop, proposed a generator for advising-inspired domains for the International Probabilistic Planning Contest [1]. Last summer, Josiah worked in an operations research lab at LIP6, in Paris, France. Working with Professors Patrice Perny and PaulWeng, Josiah investigated bi-criteria Markov decision processes (MDPs). This work is under review at the Conference on Uncertainty in Artificial Intelligence, and a two-page extended abstract was submitted to the Late Breaking Papers track of AAAI. Markov decision processes are formal mathematical models of decision making that describe a set of states, a finite set of actions that bring about probabilistically-modeled state changes, and utility that can be accrued by being in those states and/or taking actions. We model advising by using transcripts as states, acted on by the actions of taking courses. The choice of courses is (or should be!) guided by student goals and preferences. While the problem of optimal planning in such a model (with a “factored” state space) is PSPACE-hard [2], there are many heuristic algorithms—as long as courses are taken, or considered, one at a time. However, that model of modern academics describes only a small subset of students’ experiences. Josiah will be working to develop heuristic algorithms for concurrent-action MDPs. Multi-criteria optimization is one approach to preference aggregation, and Josiah’s work in that area brings new perspectives to our investigation and understanding of preferences. Josiah will continue his investigation of multi-criteria MDPs. His roles will include algorithm design, implementation, and testing. We hope to expand the work described in our recent conference submission [3], including investigation of multi- (as opposed to bi-) criteria MDPs, and further testing of the proposed algorithm for finding small, representative covers of the set of Lorenz-optimal policies. Finally, if all goes well, we will begin to look at algorithms for finding small, representative subsets of Lorenz-optimal policies for factored MDPs.