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Motivated from Bertsekas' recent study on policy iteration (PI) for solvingthe problems of infinite-horizon discounted Markov decision processes (MDPs) inan on-line setting, we develop an off-line PI integrated with a multi-policyimprovement method of policy switching and then adapt its asynchronous variantinto on-line PI algorithm that generates a sequence of policies over time. Thecurrent policy is updated into the next policy by switching the action only atthe current state while ensuring the monotonicity of the value functions of thepolicies in the sequence. Depending on MDP's state-transition structure, thesequence converges in a finite time to an optimal policy for an associatedlocal MDP. When MDP is communicating, the sequence converges to an optimalpolicy for the original MDP.

On-line Policy Iteration with Policy Switching for Markov Decision Processes