Gradient-based optimisation often refers to differentiable problems.
GAs need not have a differentiable problem, just like nature where
genetic recombination is seen as rather random, GAs use similar
recombination operators. Its more a random swarm walk, when the
GA is multi membered. Sometimes utterly useless walk that
circles around and even doesn’t come close to local optima.
Producing species that do not survive the next summer. On the
other hand does Louise find a global optimum? I was reading the
TOIL paper. It seems that your Hypothesis Space refinement
is a kind of enumerating the Hypothesis Space:
https://arxiv.org/pdf/2106.07464
It just says “Select M e MM”. And returns an M instance if SLD
derives the empty clause from the negation. So you use resolution
with refutation as the formalization, i.e. the reductio ad absurdum:
G, ~A |- f
Classical logic double negation elimination gives you:
G |- A
So if you run it and show the first found M instance, then the order
in the form of doing your “Select M e MM” and the order in which you
determine instances, is your ranking. If the enumeration defines
your ranking from highest to lowest, then your algorithm finds
a global maximum, by a kind of vacous argument. But what if the
end user wants a more complex preference structure? Like supervised
learning (SL), but with a cost function. So you would not only learn
to imitate a ground truth, and since you use rules have a big amount
of generalization. But instead you would have reinforcement
learning (RL) that minimizes some cost? RL is probably more
common for robotics than only SL. But what do you do with the
generalization that rules have? Do you use a small set for initial
learning, and then validate against a larger set?