Related papers: MathZero, The Classification Problem, and Set-Theo…

AlphaZero and its extension MuZero are computer programs that use machine-learning techniques to play at a superhuman level in chess, go, and a few other games. They achieved this level of play solely with reinforcement learning from…

The AlphaZero algorithm for the learning of strategy games via self-play, which has produced superhuman ability in the games of Go, chess, and shogi, uses a quantitative reward function for game outcomes, requiring the users of the…

Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a…

The AlphaZero algorithm has achieved superhuman performance in two-player, deterministic, zero-sum games where perfect information of the game state is available. This success has been demonstrated in Chess, Shogi, and Go where learning…

In the last years, the DeepMind algorithm AlphaZero has become the state of the art to efficiently tackle perfect information two-player zero-sum games with a win/lose outcome. However, when the win/lose outcome is decided by a final score…

The game of Go has long served as a benchmark for artificial intelligence, demanding sophisticated strategic reasoning and long-term planning. Previous approaches such as AlphaGo and its successors, have predominantly relied on model-based…

Planning with options -- a sequence of primitive actions -- has been shown effective in reinforcement learning within complex environments. Previous studies have focused on planning with predefined options or learned options through expert…

It is non-trivial to design engaging and balanced sets of game rules. Modern chess has evolved over centuries, but without a similar recourse to history, the consequences of rule changes to game dynamics are difficult to predict. AlphaZero…

Despite the recent successes of deep neural networks in various fields such as image and speech recognition, natural language processing, and reinforcement learning, we still face big challenges in bringing the power of numeric optimization…

The rules governing the essentially algebraic notion of a category with families have been observed (independently) by Steve Awodey and Marcelo Fiore to precisely match those of a representable natural transformation between presheaves.…

AlphaZero-type algorithms may stop improving on single-player tasks in case the value network guiding the tree search is unable to approximate the outcome of an episode sufficiently well. One technique to address this problem is…

Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…

The game of chess is the most widely-studied domain in the history of artificial intelligence. The strongest programs are based on a combination of sophisticated search techniques, domain-specific adaptations, and handcrafted evaluation…

The recently released AlphaZero algorithm achieves superhuman performance in the games of chess, shogi and Go, which raises two open questions. Firstly, as there is a finite number of possibilities in the game, is there a quantifiable…

This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…

In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…

Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single Set Theory formula with parameters unrelated to other formulas. Exotic expressions involving…

AlphaZero-style reinforcement learning (RL) algorithms have achieved superhuman performance in many complex board games such as Chess, Shogi, and Go. However, we showcase that these algorithms encounter significant and fundamental…

Since AlphaGo and AlphaGo Zero have achieved breakground successes in the game of Go, the programs have been generalized to solve other tasks. Subsequently, AlphaZero was developed to play Go, Chess and Shogi. In the literature, the…

Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This…