Monte Carlo control

In Monte Carlo prediction, we have seen how to estimate the value function. In Monte Carlo control, we will see how to optimize the value function, that is, how to make the value function more accurate than the estimation. In the control methods, we follow a new type of iteration called generalized policy iteration, where policy evaluation and policy improvement interact with each other. It basically runs as a loop between policy evaluation and improvement, that is, the policy is always improved with respect to the value function, and the value function is always improved according to the policy. It keeps on doing this. When there is no change, then we can say that the policy and value function have attained convergence, that is, we found the optimal value function and optimal policy:

Now we will see a different Monte Carlo control algorithm as follows.

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