Joint optimization of bid and budget allocation in sponsored search
1. Joint optimization of bid and budgetJoint optimization of bid and budgetJoint optimization of bid and budgetJoint optimization of bid and budget
allocation in sponsored searchallocation in sponsored searchallocation in sponsored searchallocation in sponsored search
Weinan ZhangƗ, Ying ZhangƗƗ, Bin GaoƗƗƗ, Yong YuƗ, Xiaojie YuanƗƗ, Tie-Yan LiuƗƗƗ
Ɨ Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
ƗƗ Nankai University, Tianjin, 300071, P. R. China
ƗƗƗ Microsoft Research Asia, Beijing, China
(KDD 2012)
@shima_x
4. DATA ANALYSIS
ON SPONSORED SEARCH
- campaign budget -
◆ キャンペーン中に予算が枯渇したaccountの統計
キャンペーン数が2,000を超えるようなaccountもあり、手動での最適化は難しい
5. DATA ANALYSIS
ON SPONSORED SEARCH
- 入札額 -
◆ 入札額の増加割合とランキング(position)上昇との関係
10%10%10%10%上昇させれば、57.36%57.36%57.36%57.36%
の広告が上昇した
10%10%10%10%上昇させれば、57.36%57.36%57.36%57.36%
の広告が上昇した
6. DATA ANALYSIS
ON SPONSORED SEARCH
- Bid Price -
◆ 各広告スロットの相対CTR
- rankingが高ければCTRも高い
- Figure 1の内容と合わせると、入札額の増加がCTRの増加につながる
ことを意味している
-有用なkeywordのみ入札額を増加させる
7. DATA ANALYSIS
ON SPONSORED SEARCH
- Joint Optimization -
◆ 本稿の最適化の考え方
- 予算がすぐに枯渇しそうなキャンペーンもあれば全く消費されていないモノ
もある
- 消費額が少ないキャンペーンの予算を消費の早いキャンペーンに移せば
よいが、それだと前者に機会損失が生じる
- これをうまく解決するようなアルゴリズムを提案する
8. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Probabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad Ranking -
◆ 分布のフィッティング(bid priceとrankingの関係)
- ranking position ρφでの勝利金額の間隔の算出に使用する
- 正規分布である必要はない
9. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Probabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad Ranking -
◆ 入札金額とranking positionに関する定義
入札額
ranking positionranking positionranking positionranking position
入札金額の
確率分布 ρΦ+1+1+1+1で勝つ確率
((((ρΦよりも低いランクだと負ける確率))))
positionpositionpositionposition ρΦに表示される確率
(ヒストリカルデータからの経験分布)
入札条件ω, auction, auction, auction, auction θ, position, position, position, position
ρΦ で勝利する入札金額
10. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Probabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad Ranking -
◆ 正規分布による入札金額の上下限の設定
winning price
勝利入札金額の下限値
勝利入札金額の上限値
11. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Probabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad Ranking -
◆ position ρΦにおけるwinning priceの再定義
標準正規分布に従う
=
quality score:quality score:quality score:quality score:
ユーザが広告に気付いた後にクリックされる確率
(query-ad similarity, semantic similaryty, taxonomy,(query-ad similarity, semantic similaryty, taxonomy,(query-ad similarity, semantic similaryty, taxonomy,(query-ad similarity, semantic similaryty, taxonomy,
user query time, user query locationuser query time, user query locationuser query time, user query locationuser query time, user query location などから決まる))))
winnig scorewinnig scorewinnig scorewinnig score
12. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Probabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad RankingProbabilistic Model for Ad Ranking -
◆ 入札額の確率分布
入札額の確率は下側確率分布の累積値(ピンク色部分)+上側確率分布の累積値(水色部分)
13. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Optimization ProblemOptimization ProblemOptimization ProblemOptimization Problem -
positionpositionpositionpositionρΦにおけるクリックされる確率
positionpositionpositionpositionρΦにおけるposition biasposition biasposition biasposition bias
入札額bbbbωの時の条件ωにおけるclickclickclickclick確率
トータル見積クリック数
◆ クリック数の推定
nnnniiii個ある内のtttt番目の入札キーワード
kkkki,ti,ti,ti,tの元の入札額 kkkki,ti,ti,ti,tのVPCVPCVPCVPC
キャンペーン内のssss番目の広告
キャンペーン数
14. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Optimization ProblemOptimization ProblemOptimization ProblemOptimization Problem -
コスト
※ω’’’’はωの1111ランク下のスロットにおける入札条件アイテム群
◆ 広告主の収益推定
広告主の見積収益
15. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Optimization ProblemOptimization ProblemOptimization ProblemOptimization Problem -
◆ 最適化問題の定義
キャンペーン予算
最小キャンペーン予算
16. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Efficient SolutionEfficient SolutionEfficient SolutionEfficient Solution -
◆ 最適化問題の再定義
広告主のaccountaccountaccountaccount内の入札金額ベクトル:
キャンペーン予算ベクトル:
※詳細は次シートに記載
17. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Efficient SolutionEfficient SolutionEfficient SolutionEfficient Solution -
◆ 最適化問題の再定義
18. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Optimization ProblemOptimization ProblemOptimization ProblemOptimization Problem -
◆ QP下位問題(ニュートン法の直線探索(?))
Lagrangian functionLagrangian functionLagrangian functionLagrangian function
Lagrangian multipliersLagrangian multipliersLagrangian multipliersLagrangian multipliers
Hessian of the Lagrangian functionHessian of the Lagrangian functionHessian of the Lagrangian functionHessian of the Lagrangian function
gradient calculusgradient calculusgradient calculusgradient calculus
19. JOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID ANDJOINT OPTIMIZATION OF BID AND
BUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATIONBUDGET ALLOCATION
- Optimization ProblemOptimization ProblemOptimization ProblemOptimization Problem -
◆ 変数のupdate
QPQPQPQPの下位問題に付随する乗数(????)
QPQPQPQP下位問題の解
参考) 共役勾配法の直線探索