Corcuera Valverde, José ManuelRosell Esau, Keila Ruth2022-06-202022-06-202022-01-23https://hdl.handle.net/2445/186821Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: José Manuel Corcuera Valverde[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.48 p.application/pdfspacc-by-nc-nd (c) Keila Ruth Rosell Esau, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Equacions de Hamilton-JacobiTreballs de fi de grauProgramació dinàmicaOptimització matemàticaProcessos de MarkovHamilton-Jacobi equationsBachelor's thesesDynamic programmingMathematical optimizationMarkov processesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess