# Multi-armed Bandits

Could someone explains to me the notation of this function, I mean I understand that we take the average of sum of the rewards for some particular action, however the notation seems strange to me for example what is t-1 at the top of the sigma notation, and what is this 1 there what does that suppose to mean

• $i$ runs from $1$ to $t-1$ because it is "prior to $t$" Commented Jul 17, 2021 at 15:16
• $\mathbb 1_{A_i=a}$ is $1$ when $A_i=a$ and $0$ when $A_i\not=a$ Commented Jul 17, 2021 at 15:17
• @Henry That sure looks like an answer to me!
– Dave
Commented Jul 17, 2021 at 15:26
• Ok, I see now, so it is like if we say, consider only "the number of times a taken prior to t" and if we there is another action it should be zero. Ok thank you@Henry Commented Jul 17, 2021 at 15:31
• Why is sigma-algebra tagged? Where's the measure theory in this question that requires it? Commented Jul 17, 2021 at 15:35

• $$i$$ runs from $$1$$ to $$t-1$$ because it is "prior to $$t$$"
• $$\mathbf{1}_{A_i=a}$$ is $$1$$ when $$A_i=a$$ and $$0$$ when $$A_i\not = a$$