Optimización con programación dinámica

Abstract

[en] In this thesis we study the optimization method called Dynamic Programming and how it is implemented to solve sequential problems, that is, those problems in which the solution is to make a series of decisions in many different stages in order to maximize a reward, according to a purpose. Different approaches are analyzed, depending on whether all the data is known for the problem, in the deterministic case, or if the data is determined by a probability distribution, in the stochastic case. A distinction will also be made for cases where time evolves in a discrete way or if it does so continuously. For each case we will develop the Hamilton-Jacobi-Bellman equation, which is a central element of the dynamic programming algorithms and is useful in finding and comparing different strategies for the decision-making agent. Finally, dynamic programming is applied to reinforcement learning, which is an area of artificial intelligence that is focused on determining what actions a software agent must choose in a given environment, in order to find the highest reward.