4. 2. 問題設定
• Pairwise Comparison
– ⼊入⼒力力 : ペア < a, b >
– 出⼒力力 : どちらが好まれるか/勝つか
• 実例例
– ⼆二⼈人のチェスプレイヤーのどちらが勝つか?
– どちらの寿司ネタが好まれるか?
– 応⽤用 : XBox Live におけるマッチング
• 強すぎる/弱すぎる相⼿手と当たっても⾯面⽩白く無い
5. 3. 既存⼿手法
• Bradlley-‐‑‒Terry (BT) model
– 古典的なモデル
– 仮定 : 各ユーザの強さは実数値 γ で表現される
– この時, a が b に勝つ確率率率は
matchup
func)on
6. 3. BTモデルの性質
• M(a, b) = 0 で a の勝率率率は50%
– M(a, b) > 0 になるにつれ, a の勝率率率が上がる
• M(a, b) = -‐‑‒M(b, a)
– P(a > b) = 1 – P(b > a)
• 推移性
– P(a > b) > 0 かつ P(b > c) > 0 なら P(a > c) > 0
7. 4-‐‑‒1. 提案⼿手法 – アイデア
• アイデア : ⾮非推移性 (intransitivity)
– 定義 : プレイヤー a, b, c について以下が成⽴立立する
• P(a > b) > 0.5
• P(b > c) > 0.5
• P(c > a) > 0.5
– じゃんけんの3つの⼿手の関係
• これを実現するため,各ユーザを多次元で表現する
9. 4-‐‑‒2. 提案⼿手法 – 定式化
• d 次元ベクトル a_̲blade / a_̲chest を⽤用いて
– blade-‐‑‒chest-‐‑‒dist-‐‑‒model
– blade-‐‑‒chest-‐‑‒inner-‐‑‒model
• d 次元のユーザ表現→戦いのスタイル
10. 4-‐‑‒2. 提案⼿手法 – 推定
• 推定 : SGDによる対数尤度度最⼤大化
– 勝敗データ集合 D におけるプレイヤー a/b について
a が na 回,b が nb 回勝利利していたとすると尤度度は
以下の式
11. 5-‐‑‒1. 実験 – ⼈人⼯工データ
• ⼊入⼒力力 : じゃんけん / 5すくみゲームの勝敗データ
• 出⼒力力 : d = 2 で推定した blade/chest
– ⽮矢印の先 : blade
– ⽮矢印の尾 : chest
Figure 2: The visualization of our model trained on rock-paper-scissors (left panel) and rock-paper-scissors-lizard-Spock (right
panel) datasets without bias terms and d set to 2. Each player is represented by an arrow, with the head being the blade vector and
the tail being the chest vector.
attack range, toughness, etc. The choice of what and when to build
based on scouting information from the enemy is an essential part
of the strategy of Starcraft II.
We collected all the match results of professional Starcraft II
players from the website aligulac.com up until February 20, 2014
(the day we did the crawling). There are two phases of Starcraft
II: the original game StarCraft II: Wings of Liberty (WoL), and the
later released expansion StarCraft II: Heart of the Swarm (HotS),
which adds more options for the players and is often considered as
a different game. We treat them separately. For of WoL, we have
4, 381 players with 61, 657 games, and 2, 287 players with 28, 582
main types of strategies called rush, boom and turtle[13], with rush
(early aggression) beating boom (economy first), boom beating tur-
tle (pure defensive), and turtle beating rush9
. We believe that the
relations between different types of general strategies that are as-
sociated with the nature of the game could also give rise to the
captured intransitivity in the Starcraft II data.
4.3.2 Defense of the Ancients 2
Defense of the Ancients 2 (DotA 2)10
is a multi-player online bat-
tle arena (MOBA) game developed by Valve Corporation. In con-
trast to Starcraft II, where each player commands a whole army, in
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元論文
Figure
2