I was going through ID3 algorithm, and what I believe is it incorporates Greedy Search rule to get come up with the decision tree. If it gives the best split possible at every stage, how does it not give the best decision tree possible?
$\begingroup$ It's a local optimum, not a global one. All tree building algorithms are merely heuristics. $\endgroup$– user2974951Oct 5, 2018 at 10:24
$\begingroup$ Greedy algorithms only rarely guarantee a globally optimal solution. $\endgroup$– Ben Reiniger - on strike ♦Nov 9, 2020 at 15:32
If you want the best decision tree, you need the "optimal decision tree", which you can get nowadays. Just have a look into the vast literature.