Evaluation of the Rate of Convergence in the PIA
2017
Folklore says that Howard's Policy Improvement Algorithm converges extraordinarily fast, even for controlled diffusion settings.
In a previous paper, we proved that approximations of the solution of a particular parabolic partial differential equation obtained via the policy improvement algorithm show a quadratic local convergence.
In this paper, we show that we obtain the same rate of convergence of the algorithm in a more general setup. This provides some explanation as to why the algorithm converges fast.
We provide an example by solving a semilinear elliptic partial differential equation numerically by applying the algorithm and check how the approximations converge to the analytic solution.
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