A Comparative Study of Dynamic Programming and Reinforcement Learning in Finite Horizon Dynamic Pricing

This paper provides a systematic comparison between Fitted Dynamic Programming (DP), where demand is estimated from data, and Reinforcement Learning (RL) methods in finite-horizon dynamic pricing problems. We analyze their performance across environments of increasing structural complexity, ranging from a single typology benchmark to multi-typology settings with heterogeneous demand and inter-temporal revenue constraints. Unlike simplified comparisons that restrict DP to low-dimensional settings, we apply dynamic programming in richer, multi-dimensional environments with multiple product types and constraints. We evaluate revenue performance, stability, constraint satisfaction behavior, and computational scaling, highlighting the trade-offs between explicit expectation-based optimization and trajectory-based learning.