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2022

On solutions of the distributional Bellman equation

Gerstenberg, Julian, Neininger, Ralph, Spiegel, Denis

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In distributional reinforcement learning not only expected returns but the complete return distributions of a policy are taken into account.

The return distribution for a fixed policy is given as the solution of an associated distributional Bellman equation.
In this note we consider general distributional Bellman equations and study existence and uniqueness of their solutions as well as tail properties of return distributions.
We give necessary and sufficient conditions for existence and uniqueness of return distributions and identify cases of regular variation.

On solutions of the distributional Bellman equation · Around

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