> In the context of this post, that’s just “which of these N discrete variables, if moved from 0 to 1, will increase the quantity of interest according to the linear model?” “Which will decrease it?”
Yes, you are right in that abstract setting.
If you always have the full hypercube of available, the problem is as easy as you describe. But if there are constraints between the variables, it gets hairier.
But the parent comment is not talking about constrained optimization, just gradient following.
In the context of this post, that’s just “which of these N discrete variables, if moved from 0 to 1, will increase the quantity of interest according to the linear model?” “Which will decrease it?”
The question is not, “if I can only set M of these N variables to 1, which should I choose?”
That’s a good question, and it leads to problems in NP, but that’s not what the comment was referring to.