This EArly-Grant for Exploratory Research (EAGER) award provides support for the development of new theory and methods for optimization of dynamic resource allocation problems. Its objective is to provide an enhanced but tractable framework for these problems, expanding the applicability of existing methodology to broader, more realistic applications. This research has the potential to be transformative in the theoretical field (opening up new lines of research ) and in applications across diverse domains, such as defense (e.g., goal-oriented deployment of heterogeneous assets, minimizing cost of failure), medicine (clinical trials with failures and cumulative costs), education, health monitoring, and computer science (dynamic operation of multi-modal sensor networks).
Dynamic resource allocation problems have been traditionally approached within the multi armed bandit framework, under the following restrictions. At each period over a time horizon, a controller activates one project of a finite collection of independent projects, advancing the state of the selected project while the others remain frozen. Rewards, collected from each activated project, are discounted at a constant rate, either modeling risk or accounting for compounding interest. There is a uniformity of the time-scale as well as a structural symmetry among the projects. The primary objectives of this research project are: i) To break the uniform time-scale restriction. ii) To break the structural symmetry among the projects. To achieve these goals we plan to investigate project dependent "halting events." These halting events allow the modeling of projects that operate at different rates, as well as "singling out" projects - generating rewards from successful projects and incurring costs for unsuccessful ones. A main challenge is to model the expanded frameworks in a way that makes it possible to obtain insight into the structure of optimal solutions. A second challenge is to develop efficient computational methods for these inherently large scale data and optimization problems.
