Heads-up: nowadays, when people talk about neural networks for games, they really mean deep learning combined with reinforcement learning.
Back to your question: When you don’t have a log of games, you typically have some other way of assessing performance, e.g. assigning a “score” to the state of the game, which you can quantify and optimize.
For a specific well-known example, I think this paper on training to play Atari games with deep reinforcement learning goes over a lot of the actual math / implementation details.
Heads-up: nowadays, when people talk about neural networks for games, they really mean deep learning combined with reinforcement learning.
Back to your question: When you don’t have a log of games, you typically have some other way of assessing performance, e.g. assigning a “score” to the state of the game, which you can quantify and optimize.
For a specific well-known example, I think this paper on training to play Atari games with deep reinforcement learning goes over a lot of the actual math / implementation details.