$($a$)$ Why AlphaGo use a separate policy network and a separate value network? $[1\mathrm{.}0$ M$]$

$($b$)$ How does the MCTS ensure an action with the highest value is found in real$-$time? If the

best action can be selected only by MCTS$,$ why is any prior learning of Q$($s$,$a$)$ required?

$[2\mathrm{.}0$ M$]$

$($c$)$ We have learned that Supervised Learning that learns with samples from a given

distribution does not capture the online nature of interactions as required for

reinforcement learning quite well.

$($i$)$ Why does AlphaGo use supervised learning to learn the initial policy $($ and even

further$)?[1\mathrm{.}5$ M$]$

$($ii$)$ In what ways the shortcomings of supervised learning are mitigated in AlphaGo?

$[2\mathrm{.}0$ M$]$

$($d$)$ How does DQN handle the challenges referred to in the c part of this question?