Correct learning algorithm for grouped examples I need to learn which item will be (most probably) picked from a group. The data I have consists of groups by 10 items and which one was picked(or if neither was picked).

My current approach is to ignore the groups and to use flat list with all items classified as picked or not picked and use some classification algorithm, but I wanted to know if there is a way to use the knowledge that the item was picked from that specific group.
Let $M$ be the size of each group. You want to learn the function $f$ that takes $M$ vectors $v_{i}$, $i \in [1,M]$  and yields a vector $\hat{v}$ that can be 0 or one of the $v_{i}$.
You can train a DNN to learn $f$ by organizing your training data as follows:

Input              Label
[batchSize, M, 1]  [batchSize,1]


Optimize on the reduced RMS error between the predicted vectors and the label vectors. The group information will then be learned by your DNN.