Jakub Pawlewicz

Improving depth-first PN-search: 1 + Ɛ trick

A diaper cover type garment has a first panel with lateral edges which curve from a maximum near a rearward edge to an intermediate minimum corresponding to a between leg portion and which curve outward to a front edge. A second panel slightly and uniformly tapers from a rear edge connection to a front edge connection. The second panel is formed of an inward fabric layer and a waterproof sheet layer facing the first panel. The first and second panels are stitched downward along lateral edges of the second panel in a back portion of the garment. Fasteners are arranged in sloping lines on a front portion of the garment, and complementary fasteners are mounted within rearward corners of the front panel. Hook and loop fasteners are mounted on the panels without reinforcement. Reinforcement panels are provided on the inside of the first panel with snap type fasteners.

MoHex 2.0: A Pattern-Based MCTS Hex Player

In recent years the Monte Carlo tree search revolution has spread from computer Go to many areas, including computer Hex. MCTS-based Hex players now outperform traditional knowledge-based alpha-beta search players, and the reigning Computer Olympiad Hex gold medallist is the MCTS player MoHex. In this paper we show how to strengthen MoHex, and observe that—as in computer Go—using learned patterns in priors and replacing a hand-crafted simulation policy by a softmax policy that uses learned patterns significantly increases playing strength. The result is MoHex 2.0, about 250 Elo points stronger than MoHex on the 11\(\times \)11 board, and 300 Elo points stronger on the 13\(\times \)13 board.

Scalable Parallel DFPN Search

We present Scalable Parallel Depth-First Proof Number Search, a new shared-memory parallel version of depth-first proof number search. Based on the serial DFPN \(1+\varepsilon \) method of Pawlewicz and Lew, SPDFPN searches effectively even as the transposition table becomes almost full, and so can solve large problems. To assign jobs to threads, SPDFPN uses proof and disproof numbers and two parameters. SPDFPN uses no domain-specific knowledge or heuristics, so it can be used in any domain. Our experiments show that SPDFPN scales well and performs well on hard problems.

Order Statistics in the Farey Sequences in Sublinear Time and Counting Primitive Lattice Points in Polygons

We present the first sublinear-time algorithms for computing order statistics in the Farey sequence and for the related problem of ranking. Our algorithms achieve a running times of nearly O(n2/3), which is a significant improvement over the previous algorithms taking time O(n).We also initiate the study of a more general problem: counting primitive lattice points inside planar shapes. For rational polygons containing the origin, we obtain a running time proportional to D6/7, where D is the diameter of the polygon.

Feature Strength and Parallelization of Sibling Conspiracy Number Search

Recently we introduced Sibling Conspiracy Number Search — an algorithm based not on evaluation of leaf states of the search tree but, for each node, on relative evaluation scores of all children of that node — and implemented an SCNS Hex bot. Here we show the strength of SCNS features: most critical is to initialize leaves via a multi-step process. Also, we show a simple parallel version of SCNS: it scales well for 2 threads but less efficiently for 4 or 8 threads.

Order statistics in the Farey sequences in sublinear time

The paper presents the first sublinear algorithm for computing order statistics in the Farey sequences. The algorithm runs in time O(n3/4 log n) and in space O(√n ) for Farey sequence of order n. This is a significant improvement to the algorithm from [1] that runs in time O(n log n).

Stronger Virtual Connections in Hex

For connection games such as Hex or Y or Havannah, finding guaranteed cell-to-cell connection strategies can be a computational bottleneck. In automated players and solvers, sets of such virtual connections are often found with Anshelevichs H-search algorithm: initialize trivial connections, and then repeatedly apply an AND-rule (for combining connections in series) and an OR-rule (for combining connections in parallel). We present FastVC Search, a new algorithm for finding such connections. FastVC Search is more effective than H-search when finding a representative set of connections quickly is more important than finding a larger set of connections slowly. We tested FastVC Search in an alpha-beta player Wolve, a Monte Carlo tree search player MoHex, and a proof number search implementation called Solver. It does not strengthen Wolve, but it significantly strengthens MoHex and Solver.

Mohex Wins 2015 Hex 11×11 and Hex 13×13 Tournaments

DeepHex is a new program based on Sibling Conspiracy Number Search (Pawlewicz and Hayward, 2015a,b). DeepHex, like MoHex, is based on the Benzene framework, developed by Broderick Arneson, Philip Henderson, Ryan Hayward, Aja Huang, and Jakub Pawlewicz. DeepHex ran on a 16 core shared-memory machine. As an opening book, DeepHex cached its evaluation scores in a database, running for 24 hours on each possible opening.

Conspiracy number search with relative sibling scores

For some two-player games (e.g. Go), no accurate and inexpensive heuristic is known for evaluating leaves of a search tree. For other games (e.g. chess), a heuristic is known (sum of piece values). For other games (e.g. Hex), only a local heuristic - one that compares children reliably, but non-siblings poorly - is known (cell voltage drop in the Shannon/Anshelevich electric circuit model). In this paper we introduce a search algorithm for a two-player perfect information game with a reasonable local heuristic.Sibling Conspiracy Number Search (SCNS) is an anytime best-first version of Conspiracy Number Search based not on evaluation of leaf states of the search tree, but - for each node - on relative evaluation scores of all children of that node. SCNS refines CNS search value intervals, converging to Proof Number Search. SCNS is a good framework for a game player.We tested SCNS in the domain of Hex, with promising results. We implemented an 11-by-11 SCNS Hex bot, DeepHex. We competed DeepHex against current Hex bot champion MoHex, a Monte Carlo Tree Search player, and previous Hex bot champion Wolve, an Alpha-Beta Search player. DeepHex widely outperforms Wolve at all time levels, and narrowly outperforms MoHex once time reaches 4 min/move.We tested the strength of SCNS features: most critical is to initialize leaves via a multi-step process. Also, we show a simple parallel version of SCNS: it scales well for 2 threads but less efficiently for 4 or 8 threads.

485 – A New Upper Bound for Morpion Solitaire

In previous research an upper bound of 705 was proved on the number of moves in the 5T variant of the Morpion Solitaire game. We show a new upper bound of 485 moves. This is achieved in the following way: we encode Morpion 5T rules as a linear program and solve 126912 instances of this program on special octagonal boards. In order to show correctness of this method we analyze rules of the game and use a concept of a potential of a given position. By solving continuous-valued relaxations of linear programs on these boards, we obtain an upper bound of 586 moves. Further analysis of original, not relaxed, mixed-integer programs leads to an improvement of this bound to 485 moves. However, this is achieved at a significantly higher computational cost.