Discussion Forum

Dear Gabin,

Your approach looks reasonable! Regarding the last term: try to write down each $\mathbb{E}[X_{i}^t*}]$ explicitly as a sum of products (regret when choosing arm $1 \leq t \leq k$ times the probability of arm $t^*$ looking the best). Moreover, note that the latter probability can be upper bounded by the prob. that arm $t^*$ looks better than just the optimal arm (arm 1 by convention).

You might also want to take a look at my recent post in the discussion forum.

Best,
Thomas