Ryan Hayward

Owen Randall, Martin Müller, Ting Han Wei et al.

We propose Expected Work Search (EWS), a new game solving algorithm. EWS combines win rate estimation, as used in Monte Carlo Tree Search, with proof size estimation, as used in Proof Number Search. The search efficiency of EWS stems from minimizing a novel notion of Expected Work, which predicts the expected computation required to solve a position. EWS outperforms traditional solving algorithms on the games of Go and Hex. For Go, we present the first solution to the empty 5x5 board with the commonly used positional superko ruleset. For Hex, our algorithm solves the empty 8x8 board in under 4 minutes. Experiments show that EWS succeeds both with and without extensive domain-specific knowledge.

David Spies, Jia-Huai You, Ryan Hayward

We present an approach to representing large sets of mutual exclusions, also known as mutexes or mutex constraints. These are the types of constraints that specify the exclusion of some properties, events, processes, and so on. They are ubiquitous in many areas of applications. The size of these constraints for a given problem can be overwhelming enough to present a bottleneck for the solving efficiency of the underlying solver. In this paper, we propose a novel graph-theoretic technique based on multicliques for a compact representation of mutex constraints and apply it to domain-independent planning in ASP. As computing a minimum multiclique covering from a mutex graph is NP-hard, we propose an efficient approximation algorithm for multiclique covering and show experimentally that it generates substantially smaller grounding size for mutex constraints in ASP than the previously known work in SAT.

Kenny Young, Ryan B. Hayward

We present Solrex,an automated solver for the game of Reverse Hex.Reverse Hex, also known as Rex, or Misere Hex, is the variant of the game of Hex in which the player who joins her two sides loses the game. Solrex performs a mini-max search of the state space using Scalable Parallel Depth First Proof Number Search, enhanced by the pruning of inferior moves and the early detection of certain winning strategies. Solrex is implemented on the same code base as the Hex program Solver, and can solve arbitrary positions on board sizes up to 6x6, with the hardest position taking less than four hours on four threads.

Kenny Young, Ryan Hayward, Gautham Vasan

DeepMind's recent spectacular success in using deep convolutional neural nets and machine learning to build superhuman level agents --- e.g. for Atari games via deep Q-learning and for the game of Go via Reinforcement Learning --- raises many questions, including to what extent these methods will succeed in other domains. In this paper we consider DQL for the game of Hex: after supervised initialization, we use selfplay to train NeuroHex, an 11-layer CNN that plays Hex on the 13x13 board. Hex is the classic two-player alternate-turn stone placement game played on a rhombus of hexagonal cells in which the winner is whomever connects their two opposing sides. Despite the large action and state space, our system trains a Q-network capable of strong play with no search. After two weeks of Q-learning, NeuroHex achieves win-rates of 20.4% as first player and 2.1% as second player against a 1-second/move version of MoHex, the current ICGA Olympiad Hex champion. Our data suggests further improvement might be possible with more training time.