Dear Gabin,
Your approach looks reasonable! Regarding the last term: try to write down each
explicitly as a sum of products (regret when choosing arm
times the probability of arm
looking the best). Moreover, note that the latter probability can be upper bounded by the prob. that arm
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
Your approach looks reasonable! Regarding the last term: try to write down each
![\mathbb{E}[X_{i}^t*}] \mathbb{E}[X_{i}^t*}]](https://moodlearchive.epfl.ch/2022-2023/filter/tex/pix.php/30044841db66c38e88625209056f702d.gif)
![1 \leq t \leq k 1 \leq t \leq k](https://moodlearchive.epfl.ch/2022-2023/filter/tex/pix.php/a07de5bc93cb63c49b9dd9ff95f82845.gif)
![t^* t^*](https://moodlearchive.epfl.ch/2022-2023/filter/tex/pix.php/ae25b720797349452f3f62982e4575a6.gif)
![t^* t^*](https://moodlearchive.epfl.ch/2022-2023/filter/tex/pix.php/ae25b720797349452f3f62982e4575a6.gif)
You might also want to take a look at my recent post in the discussion forum.
Best,
Thomas