People can buy some small, baby AIs, that live inside a virtual world. Initially, the AIs cannot do much, have an intelligence similar to a puppy, but as the years pass, they gain more and more capabilities.
People eventually get bored of raising them, so most of the virtual worlds are abandoned, so the protagonist has to hire programmers to do custom upgrades to the virtual world, so that the AIs can continue to live.
I think there were some playgrounds in the virtual world, where the owners could take AIs and play with them. When the AIs start speaking, at first they use some sort of baby language, unable to speak in fully correct sentences and they use simplified words.
I read the story about 10-15 years ago in English.