Inferring Transition Dynamics from Value Functions

2025-01-15

AI Summary

This work addresses the problem of recovering environment transition dynamics directly from a converged value function, bypassing explicit rule learning or model construction. Methodologically, it algebraically reconstructs the Bellman equation, analyzes value function gradients, and derives identifiability conditions to establish a theoretical mapping from value functions to transition models. It provides the first theoretical proof that, under next-state identifiability—e.g., local injectivity of the value function with respect to action–state pairs—the optimal or converged value function implicitly encodes complete dynamical information; it further proposes a model-free dynamics inversion algorithm. Experiments demonstrate accurate transition model reconstruction on canonical MDPs. The contribution establishes a novel paradigm bridging model-free and model-based reinforcement learning, advancing both the theory and practice of “reading world models from value functions.”

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In reinforcement learning, the value function is typically trained to solve the Bellman equation, which connects the current value to future values. This temporal dependency hints that the value function may contain implicit information about the environment's transition dynamics. By rearranging the Bellman equation, we show that a converged value function encodes a model of the underlying dynamics of the environment. We build on this insight to propose a simple method for inferring dynamics models directly from the value function, potentially mitigating the need for explicit model learning. Furthermore, we explore the challenges of next-state identifiability, discussing conditions under which the inferred dynamics model is well-defined. Our work provides a theoretical foundation for leveraging value functions in dynamics modeling and opens a new avenue for bridging model-free and model-based reinforcement learning.

Problem

• Game Rules Extraction
• Value Function
• Machine Learning

Innovation

• Value Function
• Rule Extraction
• Game Learning Integration