Proto-Value Functions: A Unified Framework for Learning Task-Specific Behaviors and Task-Independent Representations

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This project addresses a longstanding puzzle in artificial intelligence (AI): how can agents transform their temporal experience into multiscale task-independent representations that can effectively guide long-term task-specific behavior? The project will investigate a nonparametric framework combining task-independent learning with task-specific learning. Algorithmically, the framework comprises of four phases. Initially, agents learn a discrete manifold representation of a given environment, which can be viewed as a topological graph representing the states reachable through single or multi-step actions. Next, the graph is analyzed using spectral clustering techniques to reveal "bottlenecks," symmetries, and other geometric invariants. In the third phase, an orthonormal set of task-independent basis functions called proto-value functions are extracted from the environment's topology: These basis functions capture large-scale geometric invariants that all value functions on the state space must adhere to. In the final phase, proto-value functions are combined with rewards to approximate task-specific value functions.The proposed framework unifies two previously disparate lines of research in AI: learning of behavior using value functions, pioneered by Arthur Samuel, and the learning of representations based on global state space analysis, pioneered by Saul Amarel. The theoretical basis for the framework draws upon links between discrete and continuous mathematics: Riemannian manifolds and the spectral theory of graphs; elliptic differential equations and abstract harmonic analysis on graphs. Specifically, the Hilbert space of smooth functions on a Riemannian manifold has a discrete spectrum based on the eigenfunctions of the Laplace-Beltrami operator. The applications of this theory to Markov decision processes will be explored, in particular the ability of Laplacian eigenfunctions or proto-value functions to both capture large-scale geometric structure and as well as approximate task-specific value functions. A novel class of algorithms termed Representation Policy Iteration (RPI) will be investigated, which interleave representation learning and behavior learning. The research thus also addresses a longstanding question not resolved in much previous work on approximation methods for solving large Markov decision processes: how can basis functions be generated automatically? The research will investigate the scalability of the proposed framework to larger problems, including both discrete factored state spaces as well as continuous state spaces. The testbeds include simulated discrete and continuous benchmark problems, simulated and real robot testbeds, and an information extraction task of maintaining the Reinforcement Learning Repository (RLR), the world's largest collection of documents and data relating to reinforcement learning.Broader impacts of this project include algorithmic and theoretical insights leading to a unified approach to learning behavior and representation, as well as applications to real-world problems such as humanoid robotics and web repository maintenance. Additionally, this project will give valuable research experience to women graduate students and to undergraduate students from local four year colleges.