  To solve discrete Markov decision models with a large number of dimensions is
always difficult (and at times, impossible), because size of state space and
computation cost increases exponentially with the number of dimensions. This
phenomenon is called "The Curse of Dimensionality," and it prevents us from
using models with many state variables. To overcome this problem, we propose a
new approximation method, named statistical least square temporal difference
(SLSTD) method, that can solve discrete Markov decision models with large state
space. SLSTD method approximate the value function on the whole state space at
once, and obtain optimal approximation weight by minimizing temporal residuals
of the Bellman equation. Furthermore, a stochastic approximation method enables
us to optimize the problem with low computational cost. SLSTD method can solve
DMD models with large state space more easily than other existing methods, and
in some cases, reduces the computation time by over 99 percent. We also show
the parameter estimated by SLSTD is consistent and asymptotically normally
distributed.
