Soldiers vs Scouts in the search for the global maximum
"Always seek higher ground"
Fast, decisive, follows orders (the gradient). But if started on the wrong hill, will climb to a local peak and declare victory.
"Survey the territory first"
Slower, willing to explore, may temporarily go downhill. More likely to find the true global maximum.
When you're certain about the landscape (like most GLMs with convex likelihood), soldier algorithms are efficient. When uncertain (complex models, neural networks), scout algorithms are worth the extra cost.
Most GLM likelihoods are concave (bowl-shaped when maximising), meaning there's only one peak. Soldier algorithms like Newton-Raphson are perfect here — they'll always find the global maximum.
But some models have multiple local optima:
The more uncertain you are about your landscape's shape, the more valuable exploration becomes. A soldier who always seeks higher ground will summit a peak quickly — but it may not be the highest one. A scout who surveys the territory first moves slower but is more likely to find the true summit.