Research Summaries

Back Context-Rich Predictors for Self-Reflective Autonomy: Variational Foundations

Fiscal Year 2017
Division Graduate School of Operational & Information Sciences
Department Operations Research
Investigator(s) Royset, Johannes O.
Sponsor Office of Naval Research (Navy)
Summary We offer to develop new mathematical tools that will improve the predictive capability of autonomous systems and their ability to self-reflect on such capabilities. Specifically, we will develop and analyze a new class of variational-based nonparametric estimators and filters (context-rich predictors) that account for sensor data, experiences, contextual information, and uncertainty in such information. We will also develop variational theory and protocols for assessing, selecting, constructing, and instantiating context-rich predictors based on sensor data, experiences, and contextual information, and thereby support the development of self-reflective autonomy. The approach strains existing mathematics of statistics and learning in three directions. First, the infinite-dimensionality associated with nonparametric models gives rise to the need for approximations and even concerns about existence of estimators. Second, constraints arising from contextual information and minimax formulations introduced to enhance robustness cause nonsmoothness not easily handled by calculus of variation and classical analysis. Third, nonconvexity is unavoidable in some formulations causing further complications in subdifferentiation and approximation.
For the first time, we bring to bear the full weight of variational analysis to address these challenges. We will develop approximation theory for optimization problems based on epi-convergence that will permit modeling of contextual information in a large variety of ways. We will construct approximation theory for minimax formulations using lopsided convergence and thereby capture the uncertainty about the quality, accuracy, and applicability of contextual information. Novel formulations based on semicontinuous functions will yield modeling flexibility and fundamental advantages such as those related to compactness and converges of modes of probability density functions under approximations. Our approach to self-reflective autonomy does not rely on a large database of prior estimates and their data driven assessment. Instead, we aim to develop a variational theory of optimality of predictors and data-free or data-light error estimates based on quantification of epi- and lopsided-convergence. In a nearly unsupervised manner, these error estimates quantify the quality of a predictor in a given setting using deep understanding of approximations implicitly introduced by the underlying formulation and their relations to the complexity of the environment, amount of sensor data, and uncertainty in contextual information.
Keywords Autonomous systems Statistics information fusion
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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