Research Summaries

Back Distributional Stability and Error Estimates in Constrained Learning, Optimization under Uncertainty, and Defense Applications

Fiscal Year 2019
Division Graduate School of Operational & Information Sciences
Department Operations Research
Investigator(s) Royset, Johannes O.
Norton, Matthew D.
Sponsor Air Force Office of Scientific Research (Air Force)
Summary After more than 60 years of active research on optimization problems with uncertain parameters and data, accompanied by the rapid development of statistical learning methods over 25 years, it remains challenging to reliably extrapolate an approximate solution when the true parameter or data distribution is unknown and we are in possession of an empirical, perturbed, or misspecified probability distribution. Consequently, analysts are often left with heuristic methods for constructing approximate solutions and these are accompanied by only empirical verification methods such as the use of cross-validation, which at best produce mere indications of the quality of a solution or estimate. Their ability to generalize to an unknown distribution is limited. We propose to develop a new nonasymptotic theory and supporting algorithms for assessing the quality of an approximate solution in constrained learning and optimization under uncertainty. The advances will be demonstrated on defense applications such as military manpower data (currently available and approved for use at the Naval Postgraduate School) and other DoD applications.
Keywords Manpower Optimization algorithms statistical learning
Publications Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal
Data Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal