Write an evolutionary ML bot network that trades stocks in 5 minute intervals. Don't try to compete on the nanosecond micro trading end, just try to beat the market by making "good" decisions in a reasonable, human timeframe.
The question your bot is trying to solve is, "should I buy or sell this stock?" And the criteria is, "will this stock be up or down in the next X minutes."
Let the bots play in a fake market until they start to make money. It should be enough to give each bot a pot of money ($10k?) and call it dead when it goes broke or call it "good" when it makes good bets.
This is a good space for ML because the inputs are fairly well understood (stock tickers and a small set of common stock metric values). You can add in some novel inputs, like weather data in all of the trading capitals of the world (NYC, Toyko, etc).
The two tricks are this:
1) You need a community of bots that are all communicating with each other. Meaning, each bot knows what the other bots think, and how much money they have.
2) You need to let each individual bot's neural network evolve. Meaning, let the "best" performing bots "breed" with each other. Also meaning, let the values in the neural network set themselves through evolution/random rather than bothering with backpropagation.
This toy [1], showing an evolutionary neural network "learning" to follow a maze should be inspiring. Or, imagine a version of Agar.io [2] where you had to decide if a pellet (a stock) was a good idea to eat/purchase.
[1] http://ml-games.tomasz-rewak.com/
[2] http://agar.io/