Before revision:  For settings with large state spaces, we also define a regularized problem, propose a faster, approximate algorithm , and provide bounds on the computational complexityof each iteration. Finally, we validate our theoretical results empirically  , demonstrating that the approximate algorithm exhibits faster overall runtime with low error in a simulation study .
After revision:  For settings with large state spaces, we also define a regularized problem, propose a faster, approximate algorithm , and provide bounds on its per-iteration complexity. We establish a stability result for both the regularized and unregularized algorithms, from which a statistical consistency result follows as a corollary. We validate our theoretical results empirically , demonstrating that the approximate algorithm exhibits faster overall runtime with low error in a simulation study .