Value functions for depth-limited solving in zero-sum imperfect-information games

We provide a formal definition of depth-limited games together with an accessible and rigorous explanation the underlying concepts, both which were previously missing in imperfect-information games. The works for arbitrary (perfect recall) extensive-form game is not tied to any specific game-solving algorithm. Moreover, this framework unifies significantly extends three approaches solving that existed multiagent reinforcement learning but known be compatible. A key ingredient these value functions. Focusing on two-player zero-sum games, we show how obtain optimal functions prove public information provides necessary sufficient context computing them. domain-independent encoding domains allows approximating even by simple feed-forward neural networks, are then able generalize unseen parts game. use resulting network implement version counterfactual regret minimization. In distinct domains, algorithm's exploitability roughly linearly dependent network's quality it difficult train CFR's performance as good CFR access full