Q$1$: Variance

The goal of this question is to study the variance of different algorithms for adversarial multiarmed

bandits problem experimentally. Consider the EXP$3$ and EXP$3-$IX algorithms that

were discussed in class for this problem. Let the number of arms be $10.$ At each iteration,

generate a $10$ dimensional loss vector where each component is chosen iid from a Beta

distribution with both parameters equal to $5$ for all arms except the $10$th arm. For the $10$th

arm, let the parameters be $\backslash$alpha $=5,\backslash$beta $=10.$ Implement both the algorithms and run it for

$1000$ times for $10,000$ iterations each and plot the $($pseudo$)$ regrets along with error bars.

Comment on the variance of these two algorithms. $($Bonus: what happens to the variance

when you play around with the shape parameters?$)$