In the boxed algorithm for off$-$policy MC control, you may have been expecting the W update to have involved the importance$-$sampling ratio $,$ but instead it involves $.$ Why is this nevertheless correct?

In the boxed algorithm for off$-$policy MC control, you may have been expecting the W update to have involved the importance$-$sampling ratio $,$ but instead it involves $.$ Why is this nevertheless correct?

In the off$-$policy MC control algorithm, is a deterministic policy. Therefore, for the action actually taken, its probability of being taken is always $1.$

In the off$-$policy MC control algorithm, can be taken out of the fraction since we want to bound the variance.

The algorithm can converge faster by taking out $.$

There is no specific reason for that. This can just simplify the computation since we don't need to know the exact values,but which ones are maximum.