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tfg_rosell_esau_keila_ruth.pdf (628.57 KB)

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Bachelor thesis

Publication date

2022-01-23

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cc-by-nc-nd (c) Keila Ruth Rosell Esau, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/186821

Optimización con programación dinámica

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: José Manuel Corcuera Valverde

Subject

Equacions de Hamilton-Jacobi, Treballs de fi de grau, Programació dinàmica, Optimització matemàtica, Processos de Markov

Subject (English)

Hamilton-Jacobi equations, Bachelor's theses, Dynamic programming, Mathematical optimization, Markov processes

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

ROSELL ESAU, Keila Ruth. Optimización con programación dinámica. [consulted: 18 of August of 2026]. Available at: https://hdl.handle.net/2445/186821

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