Fundamental Limits of Learning Concepts and Models for Complex Systems
Abstract
The goal of this project is to develop a holistic view and unified mathematical framework for understanding the fundamental limits of learning in the studies of complex systems, including those studied in material science, genetics and bioinformatics, neuroscience, evolutionary biology and ecology, and robot autonomy. These systems consists of a large number of hierarchically organized elements, and exhibit complex and emerging behaviors and equilibrium through local interactions. The most complex system, like the robot autonomy consists of physical environments and social agents. The latter can make plans to act on the environments and have perceptual capabilities to perceive the environments, understand the causal effects of actions, and even infer the minds and intents of other agents through communications. Modeling such complex systems is the goal of multiple scientific disciplines, and learning these models from data is the concern of statistical and machine learning. In this framework, we propose to develop a new paradigm that integrates both inductive and deductive learning in a closed loop. ¥Inductive learning is example-based and data-driven, and is good for learning the concepts, relations, and parameters in some predefined hypothesis spaces for specific tasks; ¥Deductive learning is utility-based and goal-driven. It can explain system behaviors using its utility functions and causal chains. It can create new concepts and invent object categories and tools, which are then taught to others agents by inductive learning. By integrating the inductive and deductive learning, we will be able to learn more advanced models in a series of advanced hypothesis spaces. Thus our framework unifies two other dimensions: ¥Mixing supervised, semi-supervised and unsupervised learning in a continuous spectrum. ¥Mixing observational and experimental data in a continuous spectrum. We will also Develop new performance measures and bounds to i) quantitatively bound the limits of learning, ii) derive the learning rates for various machine learning paradigms, and iii) develop the conditions of generalization or transportability.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1610579
Entities
People
- S. Zhu
Organizations
- Army Contracting Command
- Defense Advanced Research Projects Agency
- University of California, Los Angeles