Mean field for Markov Decision Processes: from Discrete to Continuous Optimization - Computer Science > Artificial IntelligenceReportar como inadecuado




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Abstract: We study the convergence of Markov Decision Processes made of a large numberof objects to optimization problems on ordinary differential equations ODE.We show that the optimal reward of such a Markov Decision Process, satisfying aBellman equation, converges to the solution of a continuousHamilton-Jacobi-Bellman HJB equation based on the mean field approximation ofthe Markov Decision Process. We give bounds on the difference of the rewards,and a constructive algorithm for deriving an approximating solution to theMarkov Decision Process from a solution of the HJB equations. We illustrate themethod on three examples pertaining respectively to investment strategies,population dynamics control and scheduling in queues are developed. They areused to illustrate and justify the construction of the controlled ODE and toshow the gain obtained by solving a continuous HJB equation rather than a largediscrete Bellman equation.



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Fuente: https://arxiv.org/







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