On limitations of learning algorithms in competitive environments

Playing human games such as chess and Go has long been considered to be a major benchmark of human capabilities. Computer programs have become robust chess players and, since the late 1990s, have been able to beat even the best human chess champions; though, for a long time, computers were unable to beat expert Go players -- the game of Go has proven to be especially difficult for computers. However, in 2016, a new program called AlphaGo finally won a victory over a human Go champion, only to be beaten by its subsequent versions (AlphaGo Zero and AlphaZero). AlphaZero proceeded to beat the best computers and humans in chess, shogi and Go, including all its predecessors from the Alpha family [1]. Core to AlphaZero's success is its use of a deep neural network, trained through reinforcement learning, as a powerful heuristic to guide a tree search algorithm (specifically Monte Carlo Tree Search). The recent successes of machine learning are good reason to consider the limitations of learning algorithms and, in a broader sense, the limitations of AI. In the context of a particular competition (or'game'), a natural question to ask is whether an absolute winner AI might exist -- one that, given sufficient resources, will always achieve the best possible outcome.