There is basically only one cheat the AI has at Warlord. It is actually on all levels. They know what is on all tiles at all times. This was not done to help them, but rather was done to make the programming easier. The AI plays with a handicap at Chief and Warlord that give the human an advantage.
That is removed at Regent. Above Regent the AI get a bonus that is increased at each level up to deity. At all levels combat is the same for AI as for humans. Combat is just a roll of the die using the defense and attack values with any bonus added (terran/fortification and such).