Reinforcement Learning

Abstract:

On this page, we will cover reinforcement learning from A to Z. First, we explore the deep connection between classical mechanics and modern AI's reinforcement learning. It traces the evolution from Newton's laws, originally formulated to describe motion, to the Hamilton-Jacobi formalism, which optimizes paths in nature. This formalism was later extended by Richard Bellman, leading to the Hamilton-Jacobi-Bellman equation, a cornerstone of reinforcement learning. By discreti zing this equation and introducing probabilistic elements, AI systems learn optimal strategies. This forms the basis of some of the most advanced AI models like DeepSeek-R1, AlphaGo, and ChatGPT.

Next, we cover different methods of implementing the Bellman equation and the pros and cons of each of them: 1. Dynamic Programming, 2. Monte Carlo Methods, and 3. Temporal-Difference Learning. We also provide code implementations for each method through solving hands-on examples.