Topological Foundations Of Reinforcement Learning

Abstract

The goal of this work is to serve as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. By studying these spaces from a mathematical perspective, we expect to gain more insight into how to build better algorithms to solve decision problems. Therefore, we focus on presenting the connection between the Banach fixed point theorem and the convergence of reinforcement learning algorithms, and we illustrate how the insights gained from this can practically help in designing more efficient algorithms. Before doing so, however, we first introduce relevant concepts such as metric spaces, normed spaces and Banach spaces for better understanding, before expressing the entire reinforcement learning problem in terms of Markov decision processes. This allows us to properly introduce the Banach contraction principle in a language suitable for reinforcement learning, and to write the Bellman equations in terms of operators on Banach spaces to s

Stats

• citations0
• S2 citations—
• github stars0
• HF likes0
• heat score0.00
• arxiv keykadurha2024topological

Related papers

• On The Geometry Of Reinforcement Learning In Continuous State And Action Spaces (2022)0.00
• Taming "data-hungry" Reinforcement Learning? Stability In Continuous State-action Spaces (2024)2.26
• Metrics And Continuity In Reinforcement Learning (2021)0.00
• Reinforcement Learning Under Latent Dynamics: Toward Statistical And Algorithmic Modularity (2024)0.00
• On The Convergence And Stability Of Upside-down Reinforcement Learning, Goal-conditioned Supervised Learning, And Online Decision Transformers (2025)0.00
• Sample Efficient Reinforcement Learning In Continuous State Spaces: A Perspective Beyond Linearity (2021)0.00
• Asymptotically Optimal Reinforcement Learning In Block Markov Decision Processes (2025)0.00
• Directed Exploration In Reinforcement Learning From Linear Temporal Logic (2024)0.00