Q$2\mathrm{.}2$ Expected Regret and Pseudo$-$Regret

$1$ Point

Grading comment:

Select all of the definitions which are true.

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Choice $1$ of $10$: The expected regret is the expectation of the regret over the randomness in the payout, conditioned on the sequence of choices made.

Choice $2$ of $10$: The expected regret is the expectation of the regret over the randomness in the payout and the sequence of choices made.

Choice $3$ of $10$: The expected regret is $$i$=1$t$($maxa in AXia$$XiAi$)$i$=1$t$($a in Amax$$Xia$$XiAi$).$

Choice $4$ of $10$: The expected regret is $$i$=1$t$($maxa in AXia$$E$[$XiAi$])$i$=1$t$($a in Amax$$Xia$$E$[$XiAi$]).$

Choice $5$ of $10$: The expected regret is $$i$=1$t$($maxa in A$\backslash$mu a$$E$[$XiAi$])$i$=1$t$($a in Amax$\backslash$mu a$$E$[$XiAi$])$

Choice $6$ of $10$: The pseudo$-$regret is the expectation of the regret over the randomness in the payout, conditioned on the sequence of choices made.

Choice $7$ of $10$: The pseudo$-$regret is the expectation of the regret over the randomness in the payout and the sequence of choices made.

Choice $8$ of $10$: The pseudo$-$regret is $$i$=1$t$($maxa in AXia$$XiAi$)$i$=1$t$($a in Amax$$Xia$$XiAi$).$

Choice $9$ of $10$: The pseudo$-$regret is $$i$=1$t$($maxa in AXia$$E$[$XiAi$])$i$=1$t$($a in Amax$$Xia$$E$[$XiAi$]).$

Choice $10$ of $10$: The pseudo$-$regret is $$i$=1$t$($maxa in A$\backslash$mu a$$E$[$XiAi$])$i$=1$t$($a in Amax$\backslash$mu a$$E$[$XiAi$])$