How do cockroaches learn?Roaches have brains, albeit very simple ones. Actually, they have at least five. A main "brain" that processes information and does the thinking, and four ganglia that coordinate their mouthparts and three pairs of legs respectively.
How do they think? We're still not sure how anything thinks: the way brains work is mysterious. Computers are much simpler. Roaches are simpler than humans, however, and they are indeed capable of learning, so people are studying roach learning to gather insight on how human minds work. So far we know roaches can learn simple conditioned responses, like associating a food with an odor, the same way dogs can learn that certain commands and actions bring treats, or that a bell means dinnertime. Future research will be to identify exactly which neurons in the roach brain are responsible for learning, and how.
See for yourself: Pavlov's Cockroach: Classical Conditioning of Salivation in an Insect
For a summary: Cockroaches can learn -- like dogs and humans