Five Miracles of Mirror Descent, Lecture 2/9

[@honey-py9pj]

In 9:49 it is stated that opt is a vector that has everywhere 0 expect from one coordinate , let's say the i-th. Why exactly?To find this we take the gradient of cumulative losses for a fixed probability distribution p , right? And then?

[@avi111986]

I'm not sure about Approach 1 suggested around 4:00 . How does he perform GD on the function < l_t, p >, when l_t is not known in advance? If l_t is known to the player at the beginning of time t why not just choose some expert with 0 loss? I'm probably missing something in the problem description. Can someone please help me out here?

[@SebastienBubeck]

The suggestion is to get p_{t+1} from p_t by a step of gradient descent on the function < l_t, p >. In particular, this operation can be performed at the beginning of round t+1 (when you need p_{t+1}), and thus at a time when l_t is known to the player.

[@scose]

Is there a written reference for this Riemannian interpretation of mirror descent? It seems different from the interpretation in your work "Convex Optimization: Algorithms and Complexity", which doesn't mention manifolds.

[@SebastienBubeck]

Unfortunately I have not written it yet, but I have plans to do it at some point in the future... For the moment you can take a look at this paper arxiv.org/abs/2004.01025 , although they have a different interpretation than mine.

[@scose]

@@SebastienBubeck Thank you!

[@christianholtz5182]

Hi, me again. I start a company called 5k education. Book learning, watch lectures on tv with 3 friends, testing. 2 degrees for 5k (since most fail, see executive function).

[@cpthddk]

Cameraman kind of sucks on this one... I feel like they didn't get that the content was important, not seb's hot bod