The goal of this course is giving the student a background in the methodologies in the advanced design of mechanisms using non-lineal convex optimization and game theory. The program will cover from basic concepts related to convexity, convex optimization problems, Game Theory, Nash Equilibria, to applications of these methodologies to networking such as resource allocation, back-pressure models, power-control models compressive sensing, game theory in wireless networks, pricing models in networks, game theory in routing problems or incentives in P2P systems.
Horas semanales
Teoría
4
Problemas
0
Laboratorio
0
Aprendizaje dirigido
0
Aprendizaje autónomo
7
Competencias
Competencias Técnicas de cada especialidad
Computer networks and distributed systems
CEE2.1 - Capacidad para entender los modelos, problemas y algoritmos relacionados con los sistemas distribuidos, así como poder diseñar y evaluar algoritmos y sistemas que traten la problemática de la distribución y ofrezcan servicios distribuidos
CEE2.2 - Capacidad de entender los modelos, problemas y algoritmos relacionados con las redes de computadores, así como poder diseñar y evaluar algoritmos, protocolos y sistemas que traten la problemática de la redes de comunicación entre computadores.
CEE2.3 - Capacidad de entender los modelos, problemas y herramientas matemáticas que permiten analizar, diseñar y evaluar redes de computadores y sistemas distribuidos.
Competencias Transversales
Razonamiento
CTR6 - Capacidad de razonamiento crítico, lógico y matemático. Capacidad para resolver problemas dentro de su área de estudio. Capacidad de abstracción: capacidad de crear y utilizar modelos que reflejen situaciones reales. Capacidad de diseñar y realizar experimentos sencillos, y analizar e interpretar sus resultados. Capacidad de análisis, síntesis y evaluación.
Objetivos
Capacity to formulate a convex optimization problem
Competencias relacionadas:
CTR6,
CEE2.3,
Capacity to apply convex optimization to networking problems.
Competencias relacionadas:
CTR6,
CEE2.1,
CEE2.2,
CEE2.3,
Capacity to understand what game theory is and how a game is solved.
Competencias relacionadas:
CTR6,
CEE2.3,
Capacity to apply game theory to networking problems
Competencias relacionadas:
CTR6,
CEE2.3,
Contenidos
Convex Optimization basics
Convex sets, convex functions, convex optimization problems (COP) and duality (Lagrange dual function, KKT optimality conditions), methods for solving COP's (General Descent Methods, Interior Point Methods)
Convex Optimization Applications to networking
Exxamples on Resource allocation in networks, back-pressure, Power control, Publish-subscribe in DTN, Compressive Sensing.
Game Theory basics
Strategic and Extensive Forms of a Game, Non cooperative Games (Nash pure and mixed equilibria, correlated equilibria), Cooperative Games (core of a game, Shapley values, Nash Arbitration scheme), cost-sharing (Braess Paradox, Price of Anarchy and Stability), Auctions.
Game Theory Applications to Networking
Wireless Networking games, Energy-Efficient Power Control games, pricing, P2P games
During the initial sessions of each topic, the main results will be explained in the blackboard. the student will solve some exercises to prove their skills in the topic. Finally, there will be some sessions devoted to discuss in the classroom models taken from research papers that apply the related topics.
Método de evaluación
The evaluation is based on different activities
- Short projects and presentations in which the student has to deliver and defend the obtained results (P)
- A final exam (FE)
Each of the activities will be evaluated (0=
The final mark for the course (FM) will be:
FM= 0.60xP+0.4xFE
Where P=(1/N) x Sum (Pi) with i=1,...N
with Pi the projects and oral presentation mark. There will be a minimum of 2 practical projects and 1 oral presentation.