There are ideas floating around for this. One example is that a third party would insure the transaction after a small amount of time but before the first confirmation. If the transaction turned out to be bad and you did not get your BTC then the third party insurance would pay you the BTC you lost due to the fact the transaction never confirmed. There would be a fee for this insurance and the better insurance companies would have methods to reduce their claims by studying the transaction to make sure it has a very good chance of getting confirmed.
Is that along the lines of what you are talking about?
Yes, absolutely I was talking about that, and as Danny has pointed out I misunderstood what confirmation means in this context. More precisely, I understood that the confirmation is possible only in after 10 minutes as the transaction must be included in a new block, so I should talk about speeding up transaction acceptance instead of speeding up confirmation.
Thanks for the replies, all of you provided me with really useful info. Probably I should not make any comments when experienced hero members having brain storming about possible solutions, but I think both the insurance and centralized multi signature based solution could work. I think we all subscribed to the core concept of decentralization, but there are use cases when a centralized multi signature centralized wallet is perfectly acceptable. I think majority of bitcoin transactions aren't darknet related, most of the users wouldn't mind to compromise on decentralization and having a centralized multi signature wallet in order to be able perform quick transactions.