Mathematical methods of reinforcement learning
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates for value and policy iteration, and temporal-difference schemes. We then develop the optimization perspective: stochastic approximation and martingale methods, convex duality and the role of regularization linking mirror/proximal methods. Function approximation is treated thro...
| Authors | Denis Belomestny, Alexander Gasnikov, Egor Gladin et al. |
|---|---|
| Primary category | math.OC |
| Published | 8 July 2026 |
| Last updated at source | 8 July 2026 |
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