Topological Foundations of Reinforcement Learning

Applying algebraic topology to understand the structure of RL state, action, and policy spaces.

This project explores how topological structures underlie the fundamental objects in reinforcement learning. By viewing state spaces, action spaces, and policy spaces through the lens of algebraic topology, we uncover geometric and topological properties that inform the design of more robust RL algorithms.

Key Contributions

  • Formal topological characterization of RL state and action spaces
  • Connections between fixed point theory and convergence of RL algorithms
  • Topological analysis of policy spaces and their deformation properties

References