Swarm robots offer fascinating opportunities to perform complex tasks beyond the capabilities of individual machines. Just as a swarm of ants collectively moves a large object, similar functions can emerge within a group of robots through individual strategies based on local sensing. However, realizing collective functions with individually controlled microrobots is particularly challenging due to their micrometer size, large number of degrees of freedom, strong thermal noise relative to the propulsion speed, complex physical coupling between neighboring microrobots, and surface collisions. Here, we implement Multi-Agent Reinforcement Learning (MARL) to generate a control strategy for up to 200 microrobots whose motions are individually controlled by laser spots. During the learning process, we employ so-called counterfactual rewards that automatically assign credit to the individual microrobots, which allows for fast and unbiased training. With the help of this efficient reward scheme, swarm microrobots learn to collectively transport a large cargo object to an arbitrary position and orientation, similar to ant swarms. We demonstrate that this flexible and versatile swarm robotic system is robust to variations in group size, the presence of malfunctioning units, and environmental noise. Such control strategies can potentially enable complex and automated assembly of mobile micromachines, programmable drug delivery capsules, and other advanced lab-on-a-chip applications.