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To solve discrete Markov decision models with a large number of dimensions isalways difficult (and at times, impossible), because size of state space andcomputation cost increases exponentially with the number of dimensions. Thisphenomenon is called "The Curse of Dimensionality," and it prevents us fromusing models with many state variables. To overcome this problem, we propose anew approximation method, named statistical least square temporal difference(SLSTD) method, that can solve discrete Markov decision models with large statespace. SLSTD method approximate the value function on the whole state space atonce, and obtain optimal approximation weight by minimizing temporal residualsof the Bellman equation. Furthermore, a stochastic approximation method enablesus to optimize the problem with low computational cost. SLSTD method can solveDMD models with large state space more easily than other existing methods, andin some cases, reduces the computation time by over 99 percent. We also showthe parameter estimated by SLSTD is consistent and asymptotically normallydistributed.

Approximation method for discrete Markov decision models with a large state space