RecSys 2019 論文読み会 発表資料

https://connpass.com/event/148001/
A Pareto-Efficient Algorithm for Multiple Objective Optimization in E-Commerce Recommendation

Transcript

1. A Pareto-Efficient Algorithm for Multiple Objective Optimization in E-Commerce Recommendation Xiao Lin, Hongjie Chen, Changhua Pei, Fei Sun, Xuanji Xiao, Hanxiao Sun, Yongfeng Zhang, Wenwu Ou, Peng Jiang RecSys ‘19 Proceedings of the 13th ACM Conference on Recommender Systems Pages 20-28 鈴木 翔吾（ヤフー株式会社）@sz_dr RecSys 2019論文読み会@Wantedly, Inc. 2019/10/5 Alibaba Group, Rutgers University, Kwai Inc.
2. 自己紹介 鈴木 翔吾 (Shogo Suzuki) ヤフー株式会社 p ヤフーショッピング p ヤフー知恵袋 の検索改善を担当しています 名前 所属 興味 p 検索エンジン p ランキング学習 p A/Bテスト @sz_dr
3. どんな論文？ 複数の目的関数が存在するレコメンド問題 →目的関数同士が衝突してしまうことがある！ • Accuracy & Diversity • Accuracy & Fairness • GMV (売上) & CTR (クリック率) ← 本論文で扱う • … Pareto-Efficientな解を得る手法を提案 他の目的関数を悪化させることなく ある目的関数を改善できない状態 →A/Bテストにて, GMVもCTRも向上したことを確認
4. ECのレコメンド GMVとCTR 【例】alibaba.comのレコメンド ECなのでGMV (売上) を追いたい！ …が, CTR (クリック率) が低いと 長期的にはユーザーが離れてしまう GMV (売上) とCTR (クリック率) は逆相関 GMV (売上) とCTR (クリック率) 両方とも良いレコメンドを作りたい GMV CTR
5. Pareto-Efficient K個の目的関数（最小化） f1, . . . , fK <latexit sha1_base64="5eVArRfQS2fWp20z7SDlVqiflws=">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</latexit> dominate 2つの解 si = (fi 1 , . . . , fi K ) <latexit sha1_base64="281F+wsy8E7VH+Jw45b4wTiR43U=">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</latexit> sj = (fj 1 , . . . , fj K ) <latexit sha1_base64="XGvjAUGPzWiSzVZHx7Zzmre+Bt0=">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</latexit> fi 1  fj 1 , fi 2  fj 2 , . . . , fi K  fj K <latexit sha1_base64="AQo9zCutaX4WC6bbUIAf0WXuGwE=">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</latexit> 成り立つかつその時に限り, si <latexit sha1_base64="o1LUOfTzMGsep7LbKJ9oKIvDoiQ=">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</latexit> は sj <latexit sha1_base64="6czXAwQfnwO5c9RLnE1IaIBRy1o=">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</latexit> をdominateするという Pareto-Efficient をdominateする 存在しないときかつその時に限り, si <latexit sha1_base64="o1LUOfTzMGsep7LbKJ9oKIvDoiQ=">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</latexit> sj <latexit sha1_base64="6czXAwQfnwO5c9RLnE1IaIBRy1o=">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</latexit> が が si <latexit sha1_base64="o1LUOfTzMGsep7LbKJ9oKIvDoiQ=">AAACb3ichVHLSgMxFD0d3/VVFVQQpFgquimpLhRXohuXVq0VbCkzY1qD82ImLejgD/gBunDhA0RE/Apd+AMu3LgXV1LBjQtvpwXRot6Q5OTknpuTRHMM4UnGHkNKU3NLa1t7R7izq7unN9LXv+7ZJVfnad02bHdDUz1uCIunpZAG33BcrpqawTPazmJ1P1Pmridsa03uOjxnqkVLFISuSqKyWVOV21rB9/bzIh+JsQQLItoIknUQmx9MPYmbhbtlO3KJLLZgQ0cJJjgsSMIGVHjUNpEEg0NcDj5xLiER7HPsI0zaEmVxylCJ3aGxSKvNOmvRulrTC9Q6nWJQd0kZRZw9sCtWYffsmj2zj19r+UGNqpddmrWaljv53oPh1fd/VSbNEttfqj89SxQwG3gV5N0JmOot9Jq+vHdUWZ1bifvj7Jy9kP8z9shu6QZW+U2/SPGVY4TpA5I/n7sRrE8lktOJqRT9xAJq0Y4RjGGC3nsG81jCMtJ0roNDnOA09KoMKaNKtJaqhOqaAXwLZfITYY6SkA==</latexit> をPareto-Efficientという f1 <latexit sha1_base64="aROl0w87fAisd5jy8SBo9MJO/7E=">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</latexit> f2 <latexit sha1_base64="h/pDGO7atcb8qZtP848dcpatT6k=">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</latexit> Pareto-Efficient dominate解が存在
6. 提案手法 | Pareto-Efficient LTR Pareto-Efficientな解を得る手法を考える ※Pareto-Efficientでないなら, もっと良いレコメンドが存在する！ モデルパラメータ ✓ <latexit sha1_base64="bltlUSbduvfFzVrr6EoD3Qdq4jE=">AAACdHichVHNLkNBGD29/q+fFhsJC9FUrJqvLIhECBtLWkWi0tx7TfXG/cu90yY0XsALWHTlpxHxGBa8gIhHEEvCxsLX2yaC4JvMzJkz3/nmzIzuWWYgiR4iSktrW3tHZ5fa3dPbF431D6wHbsk3RNZwLdff1LVAWKYjstKUltj0fKHZuiU29L2l+v5GWfiB6Tprct8T27a265gF09AkU/lYNGdrsqgXKjlZFFI7zMfilKQwRn+CVBPE52/UOe/sXl1xYxfIYQcuDJRgQ8CBZGxBQ8BtCykQPOa2UWHOZ2SG+wKHUFlb4izBGRqzezzu8mqryTq8rtcMQrXBp1jcfVaOIkF3dEnPdEtX9Ejvv9aqhDXqXvZ51hta4eWjR0OZt39VNs8SxU/Vn54lCpgJvZrs3QuZ+i2Mhr58cPycmU0nKuN0Sk/s/4Qe6Jpv4JRfjNqqSFeh8gekvj/3T7A+mUxNJSdXKb6wiEZ0YhhjmOD3nsYClrGCbPgnVZyjFnlVRpS4kmikKpGmZhBfQkl+ACj3k7Y=</latexit> K個の微分可能な損失関数 Li(✓), 8i 2 {1, . . . , K} <latexit sha1_base64="BFL1NftJwRs1rnjeva20FkUQPDA=">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</latexit> 重み付きの損失関数を最小化する問題に落とす L(✓) = K X i=1 !i Li(✓) <latexit sha1_base64="OKFYyS1mQupaRKhEBiIEJtPmYE8=">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</latexit> K X i=1 !i = 1 <latexit sha1_base64="Rd9jHzdHxDqZ0EUqGkRWH0e8pMk=">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</latexit> !i 0, 8i 2 {1, . . . , K} <latexit sha1_base64="qJpGOEq9xIY22OmDyB0CPGrOKfQ=">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</latexit> !i ci, 8i 2 {1, . . . , K} <latexit sha1_base64="gl2nFoiQtD171TvU10XcRqd2kOY=">AAACk3ichVFNSxtBGH6yVZumfsSWguBlURShIczaQ0u9BOtBKEI0RgVXlt11kg7O7qy7k0AM/oGeAz14aqGU4j/wqof+gR7yE8RjCl566JtNoFRp+w4z88wz7/POMzNeJEWiGetmjAcjo2MPs49yj8cnJqfy0092EtWIfV71lVTxnucmXIqQV7XQku9FMXcDT/Jd7+hNf3+3yeNEqHBbtyJ+ELj1UNSE72qinHzRVgGvu44w7To/Nn1HFEy7pmJXSpM4EZp22yrYh0onhbf2qZOfZ0WWhnkfWEMwX5qzn3e6pVZZ5b/AxiEUfDQQgCOEJizhIqG2DwsMEXEHaBMXExLpPscpcqRtUBanDJfYIxrrtNofsiGt+zWTVO3TKZJ6TEoTC+w7+8p67Bs7Z9fs519rtdMafS8tmr2BlkfO1PuZyu1/VQHNGu9+q/7pWaOGV6lXQd6jlOnfwh/omycfepXXWwvtRfaJ3ZD/j6zLLukGYfOH/3mTb50hRx9g3X3u+2BnuWi9KC5v0k+sYhBZzGIOS/TeL1HCOsqo0rkdXOASV8YzY8VYNdYGqUZmqHmKP8LY+AXlpZ1y</latexit> 0  ci  1, 8i 2 {1, . . . , K} <latexit sha1_base64="ORS5zjXS0lvfemG8+mVkgFmPDfo=">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</latexit> K X i=1 ci  1 <latexit sha1_base64="p5A2Y/gpV0ExPoFEM4rbo41johY=">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</latexit> 重みは0以上で, 合計が1 重みにbound制約を与える
7. 提案手法 | Pareto-Efficient LTR 損失関数の重み を得る方法を考える !i <latexit sha1_base64="VXm+w4UacEL14DzaFnSkvdxZG4M=">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</latexit> (1) KKT条件から以下の最適化問題を導出 (2) 重みの非負制約を一旦外して, 二次計画問題を解く ⇔ ˆ !i = !i ci <latexit sha1_base64="JFoqYdZpOgBVjZae5raYivN2C1g=">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</latexit> とした (3) 重みの非負制約を満たすために, 非負最小二乗法を解く ※なぜこのアルゴリズムで良いのかは [Ozan Sener, Wladlen Kotun, NIPS2018]を参照
8. 提案手法 | Pareto-Efficient LTR 手法まとめ 損失関数の重み !i <latexit sha1_base64="VXm+w4UacEL14DzaFnSkvdxZG4M=">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</latexit> は 1 K <latexit sha1_base64="R5vegfjRbezP4HpCYfeWMy37OuA=">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</latexit> で初期化 モデルのパラメータ更新 損失関数の重み更新 バッチで更新を 繰り返す
9. 提案手法 | Pareto-Efficient解の選び方 Pareto-Efficient解は複数存在するが, 選び方どうする？ (A) ビジネスロジック等で重みbound が定義できるなら, アルゴリズム1回実行すればOK ci <latexit sha1_base64="jwxAMI+yQfZnACFBjybuFkN7fwQ=">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</latexit> (B) 重みbound をどうするか分からないときは, 色々重みboundを変えてアルゴリズムを実行し, 複数解を比べてみる ci <latexit sha1_base64="jwxAMI+yQfZnACFBjybuFkN7fwQ=">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</latexit> “Least Misery” !i ci, 8i 2 {1, . . . , K} <latexit sha1_base64="gl2nFoiQtD171TvU10XcRqd2kOY=">AAACk3ichVFNSxtBGH6yVZumfsSWguBlURShIczaQ0u9BOtBKEI0RgVXlt11kg7O7qy7k0AM/oGeAz14aqGU4j/wqof+gR7yE8RjCl566JtNoFRp+w4z88wz7/POMzNeJEWiGetmjAcjo2MPs49yj8cnJqfy0092EtWIfV71lVTxnucmXIqQV7XQku9FMXcDT/Jd7+hNf3+3yeNEqHBbtyJ+ELj1UNSE72qinHzRVgGvu44w7To/Nn1HFEy7pmJXSpM4EZp22yrYh0onhbf2qZOfZ0WWhnkfWEMwX5qzn3e6pVZZ5b/AxiEUfDQQgCOEJizhIqG2DwsMEXEHaBMXExLpPscpcqRtUBanDJfYIxrrtNofsiGt+zWTVO3TKZJ6TEoTC+w7+8p67Bs7Z9fs519rtdMafS8tmr2BlkfO1PuZyu1/VQHNGu9+q/7pWaOGV6lXQd6jlOnfwh/omycfepXXWwvtRfaJ3ZD/j6zLLukGYfOH/3mTb50hRx9g3X3u+2BnuWi9KC5v0k+sYhBZzGIOS/TeL1HCOsqo0rkdXOASV8YzY8VYNdYGqUZmqHmKP8LY+AXlpZ1y</latexit> 0  ci  1, 8i 2 {1, . . . , K} <latexit sha1_base64="ORS5zjXS0lvfemG8+mVkgFmPDfo=">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</latexit> K X i=1 ci  1 <latexit sha1_base64="p5A2Y/gpV0ExPoFEM4rbo41johY=">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</latexit> min max{L1, L2, . . . , LK } <latexit sha1_base64="wrgRp35gkhi2iTgddvGRREJ3Lw0=">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</latexit> “Marginal Utility” min k@(L1, L2, . . . , LK)/@✓k2 <latexit sha1_base64="cWUFjk2xkoP1oZpU/eQvxQS+wjI=">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</latexit>
10. 提案手法 | GMVとCTR最適化への適用 CTRに関する損失関数 (xj, yj, zj), 8 2 [1, . . . , N] <latexit sha1_base64="iUSYhY6VCwZG0PxN3WIU+5tqrA4=">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</latexit> 学習データ：特徴量, クリック(1/0), 購買(1/0) LCT R(✓, x, y, z) = 1 N N X j=1 log(P(yj |✓, xj)) <latexit sha1_base64="2Jb/bFBXUBsC6PbaKzDUBFbaz98=">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</latexit> GMVに関する損失関数 LGMV (✓, x, y, z) = 1 N N X j=1 h(pricej ) · log(P(zj = 1|✓, xj)) <latexit sha1_base64="+uS1NzpyHdUbvWuDV7Z+eGdtzmQ=">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</latexit> 商品価格のlogを取る 損失関数定義が論文中にはあっさり書かれていて、 お気持ちがイマイチ分からない…
11. 実験 | オフライン評価 Alibabaのレコメンドにおけるユーザー行動ログ ・1週間 ・700万 impression ・各impressionに対しクリック/購買ラベルが付与 ・ユーザー特徴/商品特徴が与えられている 評価指標 NDCG@K:クリックに関する評価指標 G-NDCG@K:購買/価格に関する評価指標 PE-LTR：提案手法 LETORIF：既存GMV最適化手法 CTR/CVRを個別にモデリング MTL-REC：既存GMV最適化手法 CTR/CVRをmulti-task学習 PO-EA：既存Pareto-Efficient探索手法 遺伝的アルゴリズムベース CXR-RL：既存CTR/CVR最適化手法 強化学習ベース Item-CF：アイテムベース協調フィルタリング LambdaMART：GBDT+NDCG最適化 提案手法PE-LTRが精度良いとこ取り！ NDCG@K G-NDCG@K
12. 実験 | オンライン評価 3日間のオンラインテストで評価 CXR-RL:既存CTR/CVR最適化手法 強化学習ベース PO-EA:既存Pareto-Efficient探索手法 遺伝的アルゴリズムベース PE-LTR:提案手法 ・CTR (Click Through Rate)：クリック率 ・IPV (Individual Page View)：ユーザー商品表示数(?) ・PAY (number of payments)：購買商品数 ・GMV (Gross Merchandise Volume)：流通総額 提案手法PE-LTRが全ての評価指標で他手法を上回る
13. まとめ・疑問点 複数の目的関数が存在するレコメンド問題 （CTR・GMV両方とも良くしたい） Pareto-Efficientな解を得る手法を提案 ・各損失関数の重み付き損失関数を最小化 ・重みは二次計画問題を解くことで得られる ・パラメータ・損失関数の重みを交互に更新 オフライン評価 → 精度良いとこ取りできていることを確認 オンライン評価 → 全ての評価指標で既存手法を上回ることを確認 Q. 今回はpointwise損失が使われたが pairwise/listwise損失も使える？ A. 損失関数の勾配が得られれば使えるはず(?) Q. GMV最適化するなら損失関数の価格項は log(price)じゃなくてpriceの方が良い？ A. priceそのままだと外れ値の影響が大きい(?) Q. 損失関数の勾配が取るスケールが大きく 異なっていても、重みは正しく得られる？ A. たぶん…。 boundはうまく指定する必要あるかも(?)
14. EOP