Typical NP-complete/hard problems in machine learning
Many theoretical problems in ML are NP-hard.


I think the famous AlphaGo is trying to solve a NP-hard problem. 
Contextual bandit problem and its combinatorial variants are np-hard. 
In social network analysis, the famous influence maximization problem is a NP-hard problem. 
There are many others. You can search in google. Also you can find related papers in two famous ML conferences: NIPS and ICML.