锟斤拷锟斤拷位锟矫ｏ拷锟斤拷页 > 锟斤拷锟斤拷锟教筹拷 > 锟教筹拷 > 锟狡硷拷系统锟斤拷锟斤拷锟脚讹拷目锟斤拷锟节猴拷锟诫超锟斤拷锟斤拷学习锟斤拷锟斤拷

锟狡硷拷系统锟斤拷锟斤拷锟脚讹拷目锟斤拷锟节猴拷锟诫超锟斤拷锟斤拷学习锟斤拷锟斤拷

锟斤拷源锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷|锟斤拷时锟戒：2024-05-18 18:47:31 |锟斤拷锟侥讹拷锟斤拷66锟斤拷|锟斤拷锟斤拷签锟斤拷系锟斤拷锟斤拷学锟斤拷 |锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷/锟斤拷锟脚的革拷锟皆伙拷锟斤拷锟斤拷锟斤拷学习模锟酵ｏ拷锟斤拷预锟斤拷20锟斤拷锟斤拷锟酵拷锟皆わ拷锟街碉拷锟斤拷锟斤拷锟斤拷省锟斤拷锟叫э拷锟斤拷锟斤拷省锟斤拷锟斤拷锟绞憋拷锟斤拷锟斤拷锟斤拷锟斤拷省锟斤拷锟阶拷实龋锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟截ｏ拷锟接讹拷锟斤拷锟斤拷学习锟斤拷锟斤拷目锟斤拷锟斤拷锟斤拷锟叫硷拷锟斤拷一锟斤拷锟斤拷锟缴ｏ拷锟斤拷锟斤拷伟锟斤拷锟叫┰わ拷锟街碉拷诤铣锟揭伙拷锟斤拷锟揭伙拷锟斤拷锟斤拷锟街ｏ拷锟斤拷锟绞碉拷侄锟侥匡拷昃拷拧锟斤拷锟揭诧拷锟斤拷锟斤拷锟斤拷吮锟斤拷锟揭拷锟斤拷艿锟斤拷锟斤拷猓猴拷锟侥匡拷锟斤拷诤希锟絤ulti-task

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷指锟斤拷锟斤拷锟斤拷锟斤拷一锟斤拷锟斤拷锟阶刺拷锟斤拷锟斤拷医锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷说锟叫э拷镁锟斤拷薹锟斤拷锟斤拷锟斤拷魏锟揭伙拷锟斤拷说锟叫э拷锟绞憋拷锟斤拷锟斤拷锟斤拷锟斤拷状态锟酵筹拷之为锟斤拷锟斤拷锟斤拷锟斤拷锟脚★拷

1 锟斤拷锟斤拷

1.1 锟狡硷拷系统锟斤拷锟斤拷锟杰癸拷

锟节斤拷锟杰讹拷目锟斤拷锟节猴拷模锟斤拷之前锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟截癸拷一锟斤拷锟狡硷拷系统锟侥伙拷锟斤拷锟杰癸拷锟斤拷锟皆硷拷锟斤拷目锟斤拷锟节猴拷模锟斤拷锟斤拷锟狡硷拷系统锟斤拷锟斤拷锟斤拷锟侥伙拷锟斤拷位锟矫★拷一锟斤拷锟节革拷锟襟厂ｏ拷锟斤拷锟斤拷锟� ^[1] 锟斤拷锟斤拷锟斤拷 ^[2] 锟斤拷锟斤拷锟斤拷锟斤拷锟� ^[3] 锟饺ｏ拷锟叫筹拷锟斤拷锟侥★拷锟斤拷锟铰╋拷锟斤拷汀锟斤拷萍锟较低筹拷芄锟斤拷锟斤拷拢锟�

推荐系统：精排多目标融合与超参数学习方法

锟斤拷锟斤拷锟斤拷锟斤拷锟叫ｏ拷锟劫回★拷锟斤拷锟脚★拷锟斤拷锟斤拷+锟斤拷目锟斤拷锟节合★拷锟斤拷锟斤拷/锟斤拷锟斤拷锟斤拷锟斤拷锟脚★拷锟届构锟斤拷锟斤拷锟斤拷锟节凤拷锟斤拷私锟斤拷校锟斤拷锟斤拷锟斤拷旃癸拷锟斤拷锟斤拷锟斤拷蟹锟斤拷锟斤拷贫锟斤拷说锟� ^[4] 锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷 ^[4] 锟斤拷锟斤拷锟狡讹拷锟剿斤拷锟叫★拷锟斤拷锟斤拷锟斤拷陆锟斤拷锟揭伙拷锟斤拷锟叫╋拷锟斤拷锟斤拷锟斤拷锟矫ｏ拷

锟劫伙拷 锟劫伙拷锟斤拷锟狡硷拷系统锟侥碉拷一锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷俅哟锟斤拷锟斤拷锟斤拷锟狡凤拷锟缴秆★拷锟揭伙拷锟斤拷趾锟窖★拷锟狡凤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟角э拷锟�/锟斤拷锟津级斤拷锟斤拷1锟斤拷锟斤拷锟揭★拷锟劫回诧拷锟斤拷锟斤拷要十锟斤拷准确锟斤拷锟斤拷锟斤拷要锟斤拷漏锟斤拷锟矫伙拷锟斤拷锟斤拷喜锟斤拷锟斤拷锟斤拷品锟斤拷锟劫伙拷模锟斤拷通锟斤拷锟斤拷锟矫讹拷路锟劫回ｏ拷锟斤拷锟斤拷锟斤拷锟斤拷锟接达拷锟斤拷锟斤拷锟斤拷锟斤拷锟揭伙拷锟斤拷使锟斤拷一些锟津化碉拷锟斤拷锟斤拷锟斤拷模锟酵★拷锟斤拷锟斤拷锟劫伙拷模锟酵帮拷锟斤拷协同锟斤拷锟剿★拷FM锟斤拷DSSM双锟斤拷模锟酵等ｏ拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷莺锟酵硷拷锟斤拷荩锟斤拷锟斤拷锟斤拷锟斤拷锟侥ｏ拷锟絊ASRec锟斤拷图模锟斤拷GraphSAGE锟饺★拷锟劫伙拷锟斤拷源头锟斤拷锟斤拷某锟斤拷锟斤拷锟斤拷锟较撅拷锟斤拷锟斤拷锟斤拷锟斤拷锟狡硷拷系统锟斤拷锟街碉拷锟届花锟藉。
锟斤拷锟斤拷 锟斤拷锟脚匡拷锟斤拷锟斤拷锟斤拷为锟斤拷锟斤拷前锟斤拷一锟街癸拷锟剿伙拷锟狡ｏ拷锟斤拷锟结精锟脚碉拷压锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟接达拷1锟斤拷锟斤拷锟揭斤拷锟斤拷1千/锟斤拷锟劫★拷锟斤拷锟矫达拷锟斤拷模锟斤拷锟皆拷锟斤拷锟斤拷锟绞憋拷锟斤拷倩亟锟斤拷锟斤拷锟斤拷太锟洁，锟斤拷锟脚诧拷锟斤拷俣雀锟斤拷锟斤拷稀锟斤拷锟斤拷锟揭憋拷锟剿撅拷准锟皆和碉拷锟接迟ｏ拷锟斤拷模锟斤拷一锟斤拷也锟斤拷锟斤拷太锟斤拷锟接★拷锟斤拷锟斤拷锟斤拷诖锟斤拷糯锟斤拷锟斤拷倩睾途锟斤拷锟街拷洌拷锟剿达拷锟斤拷锟斤拷要锟斤拷取锟斤拷锟斤拷锟矫革拷锟斤拷锟斤拷锟斤拷锟铰凤拷锟斤拷锟较拷锟斤拷锟斤拷锟叫э拷锟斤拷锟斤拷锟斤拷藕途锟斤拷诺锟斤拷锟斤拷锟揭诧拷锟轿碉拷使锟斤拷锟斤拷锟斤拷锟斤拷锟揭拷锟斤拷俚锟斤拷锟秸斤拷锟�
锟斤拷锟脚ｏ拷 + 锟斤拷目锟斤拷锟节合ｏ拷 锟斤拷锟脚革拷锟斤拷锟饺★拷锟斤拷诺慕锟斤拷锟斤拷锟斤拷锟皆猴拷选锟斤拷锟斤拷锟叫达拷趾锟斤拷锟斤拷颉＞锟斤拷锟斤拷锟揭拷锟斤拷锟斤拷时锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷拢锟斤拷锟街わ拷锟街的撅拷确锟皆ｏ拷锟斤拷锟斤拷锟斤拷系统锟斤拷锟斤拷锟斤拷锟斤拷要锟斤拷一锟斤拷模锟介，也锟斤拷锟筋复锟接★拷锟叫撅拷锟斤拷锟斤拷一锟斤拷模锟介。锟斤拷同锟节达拷锟脚筹拷锟斤拷使锟矫简单碉拷双锟斤拷模锟酵ｏ拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷模锟斤拷锟较讹拷锟斤拷锟斤拷锟侥比较革拷锟接★拷目前锟斤拷锟斤拷锟斤拷模锟斤拷锟窖憋拷锟斤拷锟窖澳ｏ拷汀锟揭煌筹拷锟斤拷隆锟斤拷锟斤拷锟斤拷锟絎ide&Deep锟斤拷DeepFM锟斤拷DIN锟饺ｏ拷锟斤拷锟绞癸拷锟紸ttention锟斤拷锟斤拷DIN锟斤拷锟斤拷锟皆憋拷学习锟斤拷迁锟斤拷学习锟饺伙拷锟斤拷锟斤拷锟斤拷锟侥ｏ拷途锟斤拷取锟斤拷锟斤拷锟斤拷诠锟揭碉拷锟斤拷实锟斤拷锟叫筹拷锟斤拷锟叫讹拷锟斤拷锟斤拷锟街革拷辏拷锟斤拷殖锟绞癸拷锟斤拷锟饺讹拷锟斤拷锟斤拷学习锟斤拷MTL锟斤拷模锟酵★拷锟斤拷锟斤拷锟斤拷诰锟斤拷殴锟阶拷锟斤拷锟斤拷锟狡凤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絣oss锟洁不同锟节筹拷锟斤拷锟斤拷loss锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷学习锟斤拷Learning to Rank锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷啤锟斤拷锟絃TR锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷失锟斤拷锟斤拷loss锟侥诧拷同锟斤拷锟街凤拷为pointwise锟斤拷式锟斤拷pairwise锟斤拷式锟斤拷锟斤拷锟洁。
锟斤拷锟斤拷 锟斤拷锟斤拷模锟斤拷锟斤拷锟斤拷锟斤拷嵌锟街帮拷锟斤拷锟侥ｏ拷锟侥斤拷锟斤拷锟斤拷卸锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷越锟揭伙拷锟斤拷锟斤拷锟狡硷拷锟斤拷准确锟饺和革拷锟皆伙拷锟教度★拷锟斤拷锟斤拷锟斤拷要锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷屑锟街碉拷锟襟化ｏ拷也锟斤拷锟斤拷谓listwise锟斤拷锟斤拷同锟节碉拷item效锟斤拷锟斤拷锟桔计ｏ拷锟斤拷锟斤拷锟斤拷锟狡硷拷锟叫憋拷锟侥讹拷锟斤拷锟皆等等★拷锟斤拷锟斤拷一锟斤拷锟斤拷锟斤拷锟斤拷散锟斤拷锟斤拷锟斤拷业锟斤拷锟斤拷营锟斤拷锟截讹拷强锟斤拷锟斤拷锟斤拷同锟斤拷锟斤拷锟斤拷使锟矫革拷锟接碉拷模锟酵★拷锟斤拷锟解，锟斤拷锟脚伙拷锟斤拷锟斤拷锟斤拷锟狡讹拷锟斤拷锟较ｏ拷锟斤拷锟斤拷谓锟斤拷锟斤拷锟斤拷锟脚★拷
锟斤拷锟斤拷 锟斤拷锟脚碉拷锟斤拷锟斤拷锟斤拷锟节斤拷锟斤拷源锟届构锟斤拷锟捷ｏ拷锟斤拷锟斤拷锟斤拷频锟酵癸拷妫╋拷姆锟斤拷亟锟斤拷锟斤拷锟斤拷恰锟斤拷锟斤拷希锟斤拷玫锟揭伙拷锟斤拷酆霞锟街碉拷锟斤拷姆锟斤拷锟斤拷锟斤拷小锟�

1.2 锟斤拷目锟斤拷锟节合ｏ拷MTF锟斤拷锟斤拷锟�

锟斤拷同锟斤拷学锟斤拷锟斤拷只锟斤拷锟角碉拷锟絩atings预锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟狡硷拷系统锟斤拷模为锟津单的讹拷锟斤拷锟斤拷锟斤拷锟解，然锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟姐单锟斤拷AUC锟斤拷锟斤拷HR/MRR啥锟侥ｏ拷锟斤拷锟狡硷拷系统锟斤拷锟脚伙拷目锟斤拷锟节癸拷业锟斤拷锟绞碉拷锟斤拷谐锟斤拷锟斤拷锟斤拷卸锟斤拷锟侥ｏ拷锟揭达拷锟轿拷锟斤拷锟街革拷辏╋拷锟斤拷锟斤拷锟斤拷嵌锟斤拷锟狡碉拷萍锟斤拷锟斤拷锟斤拷锟斤拷远锟斤拷锟狡碉拷萍锟斤拷锟斤拷锟轿拷锟斤拷锟斤拷锟斤拷萍锟较低筹拷锟斤拷锟斤拷锟侥ｏ拷锟斤拷锟斤拷校锟斤拷锟斤拷锟斤拷锟揭拷锟斤拷锟斤拷没锟斤拷锟绞癸拷锟绞憋拷锟�/锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟劫革拷锟斤拷锟斤拷锟斤拷锟接讹拷锟斤拷锟斤拷没锟斤拷锟斤拷锟斤拷妗ｏ拷锟斤拷锟狡碉拷萍锟斤拷锟斤拷锟斤拷械锟斤拷没锟斤拷锟斤拷锟斤拷煞锟轿拷锟斤拷啵�

锟斤拷式锟斤拷锟斤拷锟斤拷 锟矫伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷为锟斤拷锟界播锟斤拷时锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷省锟斤拷瓴ワ拷锟斤拷锟斤拷锟斤拷鹊取锟�
锟斤拷式锟斤拷锟斤拷锟斤拷 锟矫伙拷锟斤拷锟斤拷识锟斤拷锟斤拷锟斤拷锟侥凤拷锟斤拷锟斤拷锟斤拷锟秸藏★拷锟斤拷锟截★拷锟斤拷注锟斤拷锟斤拷锟睫★拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟桔等等★拷
锟斤拷式锟斤拷锟斤拷锟斤拷 锟矫伙拷锟斤拷式锟斤拷锟斤拷母锟斤拷锟斤拷锟斤拷锟斤拷锟教诧拷锟脚★拷锟矫伙拷锟斤拷止一锟斤拷session锟饺★拷
锟斤拷式锟斤拷锟斤拷锟斤拷 锟矫伙拷锟斤拷式锟斤拷锟斤拷母锟斤拷锟斤拷锟斤拷锟斤拷绮伙拷锟斤拷锟饺わ拷锟斤拷锟斤拷锟斤拷锟斤拷邸锟斤拷俦锟斤拷取锟�

锟斤拷锟角碉拷目锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷俑锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟矫伙拷锟斤拷锟介。然锟斤拷锟斤拷锟斤拷锟斤拷之前说锟斤拷锟斤拷锟斤拷锟斤拷/锟斤拷锟脚的革拷锟皆伙拷锟斤拷锟斤拷锟斤拷学习模锟酵ｏ拷锟斤拷预锟斤拷20锟斤拷锟斤拷锟酵拷锟皆わ拷锟街碉拷锟斤拷锟斤拷锟斤拷省锟斤拷锟叫э拷锟斤拷锟斤拷省锟斤拷锟斤拷锟绞憋拷锟斤拷锟斤拷锟斤拷锟斤拷省锟斤拷锟阶拷实龋锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟截ｏ拷锟接讹拷锟斤拷锟斤拷学习锟斤拷锟斤拷目锟斤拷锟斤拷锟斤拷锟叫硷拷锟斤拷一锟斤拷锟斤拷锟缴ｏ拷锟斤拷锟斤拷伟锟斤拷锟叫┰わ拷锟街碉拷诤铣锟揭伙拷锟斤拷锟揭伙拷锟斤拷锟斤拷锟街ｏ拷锟斤拷锟绞碉拷侄锟侥匡拷昃拷拧锟斤拷锟揭诧拷锟斤拷锟斤拷锟斤拷吮锟斤拷锟揭拷锟斤拷艿锟斤拷锟斤拷猓� 锟斤拷目锟斤拷锟节合ｏ拷multi-task fusion, MTF锟斤拷 锟斤拷

推荐系统：精排多目标融合与超参数学习方法

锟斤拷锟斤拷图锟斤拷示锟斤拷锟斤拷目锟斤拷锟节猴拷模锟斤拷锟节撅拷锟斤拷MTL模锟斤拷锟斤拷锟斤拷锟斤拷预锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷应锟斤拷锟斤拷锟斤拷锟斤拷锟矫伙拷锟侥凤拷锟斤拷锟斤拷之锟襟，对讹拷锟皆わ拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷诤希锟斤拷锟斤拷锟斤拷锟斤拷诤系拇锟街斤拷锟叫撅拷锟脚ｏ拷锟斤拷锟斤拷锟诫到锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷模锟介。

2 锟斤拷目锟斤拷锟节合凤拷锟斤拷锟斤拷锟斤拷

2.1 锟街癸拷锟节猴拷

锟斤拷虻サ亩锟侥匡拷锟斤拷诤戏锟绞斤拷锟斤拷锟斤拷止锟斤拷诤希锟揭伙拷锟斤拷锟斤拷 锟斤拷锟皆加凤拷 锟斤拷 指锟斤拷锟剿凤拷 锟斤拷锟街ｏ拷

锟斤拷锟皆加凤拷
锟斤拷锟皆加凤拷锟斤拷锟节合癸拷式锟斤拷锟铰ｏ拷

锟斤拷锟斤拷 \(\text{score}_i\) 为锟斤拷锟脚的讹拷锟斤拷锟斤拷模锟酵对碉拷 \(i\) 锟斤拷目锟斤拷锟皆わ拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷劭锟斤拷锟斤拷锟斤拷锟较诧拷锟斤拷锟斤拷劭锟绞憋拷锟斤拷目锟斤拷锟皆わ拷锟斤拷锟斤拷锟斤拷锟�

锟斤拷锟皆加凤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷郑锟斤拷锟斤拷锟斤拷锟矫硷拷权Logloss锟斤拷

锟斤拷锟皆加凤拷锟斤拷锟脚碉拷锟斤拷锟斤拷锟斤拷目锟斤拷权锟截撅拷指示锟斤拷目锟斤拷锟斤拷锟节合癸拷式锟叫碉拷锟斤拷要锟饺ｏ拷直锟斤拷锟斤拷锟侥革拷目锟斤拷锟斤拷锟揭拷锟斤拷蔷徒锟斤拷母锟侥匡拷锟斤拷权锟截碉拷锟襟。碉拷然锟斤拷缺锟斤拷也锟角筹拷锟斤拷锟皆ｏ拷锟斤拷锟饺拷锟较碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷偷锟侥匡拷甓硷拷锟揭伙拷锟酵拷实摹锟斤拷锟绞碉拷隙锟斤拷诘锟斤拷锟斤拷锟斤拷锟较★拷锟侥匡拷辏拷锟斤拷锟斤拷锟接︼拷锟斤拷锟皆わ拷锟斤拷锟斤拷锟斤拷叩锟饺拷馗锟斤拷撸锟斤拷锟皆撅拷锟斤拷没锟饺拷馗锟斤拷撸锟斤拷锟皆わ拷锟斤拷锟斤拷锟斤拷偷锟饺拷馗锟斤拷停锟斤拷锟斤拷锟皆撅拷没锟斤拷锟饺拷馗锟斤拷停锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟绞斤拷锟侥匡拷锟斤拷锟饺伙拷锟斤拷锟斤拷锟斤拷锟�
指锟斤拷锟剿凤拷

锟斤拷锟斤拷锟皆加凤拷锟斤拷锟斤拷一锟斤拷锟斤拷唯一锟斤拷锟斤拷锟斤拷锟角帮拷锟桔加伙拷锟斤拷锟斤拷锟桔乘★拷锟斤拷锟脚碉拷锟饺憋拷锟斤拷锟斤拷煤锟斤拷锟斤拷约臃锟斤拷喾达拷锟斤拷锟斤拷诺锟斤拷强锟斤拷锟斤拷锟斤拷锟斤拷锟角匡拷叩锟皆わ拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷频偷锟皆わ拷锟斤拷锟斤拷锟斤拷锟斤拷锟饺憋拷锟斤拷遣锟斤拷艿锟斤拷锟揭荒匡拷锟斤拷指锟斤拷权锟截ｏ拷锟斤拷为锟斤拷锟斤拷虻サ馗锟斤拷锟揭荒匡拷锟斤拷锟斤拷锟街革拷锟斤拷蔷锟斤拷嗟憋拷诙锟斤拷锟斤拷锟侥匡拷甓硷拷锟叫э拷耍锟斤拷燃锟斤拷锟斤拷诤瞎锟绞斤拷锟斤拷锟斤拷一锟斤拷系锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷锟节讹拷目锟斤拷锟节合的筹拷锟斤拷实锟斤拷锟叫诧拷锟矫的撅拷锟角加凤拷锟节合的凤拷式锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷梅侄愿锟斤拷锟侥匡拷锟侥得凤拷值锟斤拷锟斤拷锟斤拷校锟揭诧拷锟斤拷锟斤拷妆锟侥承╋拷锟斤拷锟狡拷锟斤拷目锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟侥匡拷锟酵匡拷锟杰达拷锟斤拷一些锟斤拷锟斤拷偏锟斤拷锟斤拷斐Ｖ碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷 \(\alpha\) 锟斤拷 \(\beta\) 锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟较碉拷锟节革拷锟斤拷目锟斤拷梅值锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟揭诧拷偷玫锟斤拷锟斤拷锟斤拷锟斤拷锟绞撅拷锟� 锟斤拷权指锟斤拷锟接凤拷 ^[5][6] 锟侥癸拷式锟斤拷式锟斤拷

锟斤拷权指锟斤拷锟接凤拷

锟斤拷锟斤拷 \(\text{factor}\) 为锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷示锟斤拷锟饺拷兀锟� \(\beta\) 为锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷源锟斤拷锟斤拷锟� \(\alpha_i\) 锟斤拷为锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷示锟斤拷锟斤拷锟饺★拷

锟斤拷锟斤拷锟斤拷锟节癸拷锟斤拷实锟斤拷锟叫凤拷锟街ｏ拷锟斤拷业锟斤拷目锟斤拷锟斤拷锟绞憋拷锟酵拷锟斤拷臃锟斤拷诤瞎锟绞斤拷锟斤拷锟侥匡拷锟斤拷锟皆讹拷锟斤拷锟节匡拷锟劫伙拷锟斤拷锟斤拷妗ｏ拷锟斤拷锟斤拷锟侥匡拷锟斤拷锟斤拷锟斤拷锟绞憋拷锟斤拷臃锟斤拷诤瞎锟绞斤拷锟斤拷诤锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷蕖锟斤拷锟斤拷锟斤拷锟轿拷约臃锟斤拷诤瞎锟绞斤拷锟斤拷裕锟斤拷锟斤拷锟侥匡拷锟襟，革拷锟斤拷目锟斤拷锟斤拷锟揭拷锟接帮拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷猓拷锟斤拷锟斤拷锟斤拷丫锟斤拷锟斤拷锟斤拷顺锟斤拷锟斤拷锟� \(\alpha\) 锟斤拷 \(\beta\) 锟斤拷锟斤拷锟斤拷拢锟斤拷臃锟斤拷诤瞎锟绞斤拷锟饺伙拷锟斤拷妆锟斤拷锟斤拷锟侥匡拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷朔锟斤拷诤瞎锟绞斤拷筒锟斤拷锟斤拷锟斤拷锟叫╋拷锟斤拷狻ｏ拷锟剿ｏ拷锟节此伙拷锟斤拷锟较ｏ拷锟斤拷锟斤拷锟斤拷锟街把讹拷目锟斤拷锟节合癸拷式锟斤拷锟斤拷为锟剿乘凤拷锟斤拷

锟斤拷权指锟斤拷锟剿凤拷

锟斤拷锟斤公式锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷式一锟铰ｏ拷只锟角帮拷锟桔加伙拷锟斤拷锟斤拷锟桔乘★拷

锟街癸拷锟节合碉拷锟脚碉拷锟斤拷锟斤拷锟斤拷目锟斤拷权锟截撅拷指示锟斤拷目锟斤拷锟斤拷锟节合癸拷式锟叫碉拷锟斤拷要锟饺ｏ拷锟饺斤拷直锟斤拷锟揭可斤拷锟斤拷锟斤拷强锟斤拷锟斤拷然锟斤拷缺锟斤拷也锟角筹拷锟斤拷锟皆ｏ拷锟斤拷锟饺拷锟较碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷没锟斤拷锟斤拷锟揭伙拷锟斤拷模锟饺憋拷俑锟斤拷曰锟斤拷锟斤拷锟斤拷猓拷锟斤拷锟斤拷锟斤拷鄱锟皆わ拷锟斤拷锟斤拷锟绞癸拷眉臃锟斤拷锟斤拷浅朔锟斤拷姆锟绞斤拷锟斤拷诤希锟侥ｏ拷锟絪erving时锟侥筹拷锟斤拷锟斤拷锟斤拷锟斤拷通锟斤拷 锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷grid search锟斤拷 ^[7] 锟斤拷锟矫碉拷锟斤拷锟斤拷锟斤拷锟脚的硷拷锟斤拷狻ｏ拷锟斤拷锟斤拷锟街拷锟斤拷锟斤拷萍锟较低筹拷锟绞碉拷时锟斤拷只锟斤拷锟揭拷锟斤拷锟紸/B实锟斤拷锟斤拷锟饺凤拷锟斤拷模锟斤拷獾硷拷赂梅锟斤拷锟叫э拷式系汀锟斤拷锟斤拷锟斤拷锟斤拷锟侥ｏ拷偷牡锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷植锟斤拷谋浠拷锟斤拷锟斤拷挪锟斤拷锟揭诧拷诒浠拷锟斤拷锟斤拷锟街癸拷锟节合碉拷缺锟姐还锟斤拷锟斤拷锟斤拷维锟斤拷锟缴憋拷锟竭ｏ拷锟斤拷为锟斤拷锟斤拷要锟斤拷锟叫讹拷蔚锟斤拷止锟斤拷锟斤拷锟斤拷锟斤拷锟�

锟斤拷么锟斤拷锟斤拷锟斤拷锟角凤拷锟斤拷锟斤拷锟侥ｏ拷锟斤拷锟窖帮拷锟斤拷锟斤拷锟斤拷兀锟斤拷锟斤拷锟芥及锟斤拷锟斤拷 锟节合筹拷锟斤拷锟斤拷锟斤拷学习锟斤拷锟斤拷 ^[8] 锟剿ｏ拷也锟斤拷锟斤拷一锟斤拷模锟斤拷锟斤拷学习锟斤拷预锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟饺拷亍锟�

锟斤拷锟斤拷锟节合筹拷锟斤拷锟斤拷锟斤拷学习锟斤拷锟斤拷锟斤拷锟斤拷锟皆ｏ拷锟斤拷锟斤拷锟斤拷锟诫到锟斤拷应锟斤拷锟斤拷锟斤拷锟竭凤拷锟斤拷锟斤拷也锟斤拷锟斤拷锟斤拷一锟斤拷锟斤拷锟斤拷模锟斤拷锟斤拷学习锟斤拷预锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟饺拷亍锟斤拷锟斤拷址锟斤拷锟斤拷锟斤拷诺锟斤拷缺锟姐都锟斤拷锟斤拷锟皆ｏ拷锟街憋拷锟斤拷锟斤拷锟斤拷示锟斤拷

锟脚碉拷 锟斤拷锟竭凤拷锟斤拷锟斤拷off-policy锟侥凤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟绞高ｏ拷100%锟斤拷锟斤拷锟斤拷锟斤拷锟皆憋拷使锟矫ｏ拷锟斤拷锟斤拷模锟酵碉拷锟斤拷锟缴度和革拷锟接度较高ｏ拷锟斤拷锟斤拷锟斤拷锟斤拷item embedding锟斤拷使锟斤拷稀锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷训锟斤拷千锟节癸拷模锟侥诧拷锟斤拷锟斤拷
缺锟斤拷 锟脚伙拷锟斤拷锟斤拷锟斤拷AUC锟睫凤拷直锟接凤拷映业锟斤拷指锟疥。锟斤拷为锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷撕芏锟津化ｏ拷锟狡硷拷系统锟斤拷锟角撅拷锟斤拷之锟斤拷锟街憋拷佣越锟斤拷没锟斤拷耍锟斤拷屑浠癸拷锟斤拷锟斤拷牛锟斤拷锟斤拷锟斤拷锟斤拷锟皆ｏ拷锟饺碉拷影锟届，锟斤拷锟斤拷锟斤拷锟斤拷一些锟斤拷业锟斤拷/锟斤拷营锟斤拷锟斤拷锟侥伙拷锟斤拷锟节合ｏ拷锟斤拷锟皆该凤拷锟斤拷锟斤拷锟皆匡拷锟角碉拷锟斤拷锟较革拷锟接讹拷模锟斤拷锟斤拷锟斤拷锟斤拷影锟届。锟斤拷锟解，锟斤拷锟斤拷训锟斤拷锟斤拷锟捷猴拷锟斤拷锟斤拷锟斤拷锟斤拷也锟斤拷锟节分诧拷锟斤拷一锟铰碉拷锟斤拷锟解。

锟斤拷锟角碉拷锟斤拷锟竭筹拷锟斤拷锟斤拷学习锟斤拷锟斤拷锟斤拷锟叫碉拷锟斤拷锟斤拷锟斤拷缺锟姐，锟斤拷实锟绞癸拷业锟斤拷锟接︼拷锟斤拷校锟斤拷锟斤拷浅锟斤拷锟绞癸拷锟斤拷锟斤拷叩某锟斤拷锟斤拷锟窖帮拷锟斤拷锟斤拷锟斤拷锟斤拷叻锟斤拷锟斤拷墓锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟酵硷拷锟绞撅拷锟�

推荐系统：精排多目标融合与超参数学习方法

锟斤拷锟皆匡拷锟斤拷锟斤拷锟斤拷锟竭筹拷锟斤拷锟斤拷学习锟姐法锟斤拷锟斤拷 探锟斤拷锟斤拷锟斤拷锟斤拷 锟斤拷锟狡ｏ拷锟斤拷锟斤拷baseline锟斤拷锟斤拷探锟斤拷锟斤拷锟斤拷 \(N\) 锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷萍锟较低筹拷锟斤拷锟斤拷锟� \(N\) 锟斤拷锟斤拷锟斤拷锟接︼拷锟秸癸拷指锟斤拷没锟斤拷牟锟斤拷旎拷锟斤拷锟斤拷锟斤拷锟斤拷佣锟斤拷锟矫诧拷同锟矫伙拷锟侥凤拷锟斤拷锟斤拷之锟斤拷锟斤拷锟秸硷拷锟斤拷些锟斤拷锟斤拷锟斤拷志锟斤拷锟斤拷锟斤拷锟芥（reward锟斤拷统锟狡ｏ拷锟斤拷锟斤拷锟酵革拷BayesOpt/ES/CEM锟饺碉拷锟斤拷锟姐法锟斤拷锟斤拷锟斤拷一锟斤拷锟斤拷玫牟锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟酵ｏ拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷突锟斤拷锟揭伙拷锟斤拷锟侥匡拷锟叫拷锟斤拷锟斤拷诺姆锟斤拷锟角帮拷锟斤拷锟�

锟斤拷锟竭的筹拷锟斤拷锟斤拷学习锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷缺锟姐：

锟脚碉拷 直锟斤拷锟脚伙拷锟斤拷锟斤拷指锟疥，锟斤拷锟斤拷愿锟斤拷曳锟斤拷锟窖革拷伲锟斤拷锟斤拷铱锟斤拷园锟斤拷萍锟较低筹拷锟斤拷锟揭伙拷锟斤拷诤校锟斤拷锟斤拷锟斤拷锟斤拷锟节诧拷细锟节★拷锟揭匡拷锟斤拷锟斤拷锟洁场锟斤拷锟斤拷锟斤拷锟脚伙拷锟斤拷锟斤拷锟斤拷锟斤拷ranking锟斤拷锟斤拷锟劫回等筹拷锟斤拷也锟斤拷锟斤拷锟矫★拷
缺锟斤拷 锟斤拷要锟斤拷锟斤拷锟较伙拷锟街筹拷一锟斤拷锟斤拷探锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷约5%锟斤拷锟斤拷锟接讹拷影锟斤拷锟劫诧拷锟斤拷锟矫伙拷锟斤拷锟介，锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷稀锟借，锟斤拷锟斤拷锟斤拷影锟斤拷洗锟斤拷锟斤拷锟斤拷锟揭恍┫★拷锟侥讹拷锟斤拷锟斤拷签锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷亍锟斤拷詹氐龋锟斤拷锟斤拷锟斤拷傻牟锟斤拷锟斤拷锟斤拷锟叫★拷锟揭伙拷慵甘拷锟斤拷锟斤拷伲锟斤拷锟斤拷锟斤拷锟斤拷学习锟侥诧拷锟斤拷锟斤拷模小锟杰多。

锟斤拷锟斤拷锟斤拷锟斤拷锟竭筹拷锟斤拷锟斤拷学习锟斤拷锟斤拷锟斤拷锟斤拷 锟斤拷叶斯锟脚伙拷锟斤拷锟斤拷锟斤拷Bayesian optimization锟斤拷 ^[9] 锟斤拷 锟斤拷锟斤拷锟斤拷锟斤拷锟姐法锟斤拷evolutionary strategy锟斤拷 ^[10] 锟斤拷 CMA-ES锟斤拷锟斤拷应锟斤拷锟斤拷锟姐法 ^[11] 锟饺ｏ拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷要锟斤拷锟杰憋拷叶斯锟脚伙拷锟斤拷锟斤拷锟酵斤拷锟斤拷学习锟姐法锟斤拷

2.2 锟节合筹拷锟斤拷锟斤拷学习锟斤拷锟斤拷

2.2.1 锟斤拷叶斯锟脚伙拷锟姐法

锟斤拷叶斯锟脚伙拷锟姐法锟斤拷挚锟斤拷锟斤拷锟斤拷锟绞碉拷锟斤拷锟斤拷锟斤拷锟斤拷妫拷锟斤拷占锟斤拷锟斤拷锟叫★拷锟斤拷锟斤拷锟斤拷椋拷锟斤拷锟叫★拷锟斤拷锟绞碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷胁锟斤拷锟斤拷呕锟斤拷锟�

锟斤拷叶斯锟脚伙拷锟侥伙拷锟斤拷思锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷实锟脚伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷太锟斤拷锟斤拷歉锟斤拷诤校锟斤拷锟斤拷锟斤拷萍锟斤拷锟斤拷锟斤拷锟斤拷没锟斤拷锟斤拷锟绞碉拷锟斤拷锟斤拷锟斤拷妫╋拷锟斤拷锟斤拷锟斤拷锟揭拷锟揭伙拷锟� 锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷surrogate function锟斤拷 锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟节达拷锟斤拷锟斤拷锟斤拷锟斤拷围锟斤拷锟斤拷锟斤拷锟斤拷小值锟斤拷母锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷诨锟矫伙拷胁锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟铰的碉拷之锟斤拷锟斤拷锟角就匡拷锟皆革拷锟铰达拷锟斤拷锟斤拷锟斤拷锟斤拷使之锟斤拷锟较逼斤拷目锟疥函锟斤拷锟斤拷锟斤拷锟角筹拷锟斤拷锟斤拷 锟斤拷斯锟斤拷锟教ｏ拷Gaussian process, GP锟斤拷 锟斤拷锟斤拷模锟斤拷锟绞达拷锟斤拷锟斤拷锟斤拷锟侥分诧拷锟斤拷然锟斤拷锟斤拷锟斤拷锟揭伙拷锟� 锟缴硷拷锟斤拷锟斤拷锟斤拷acquisition function锟斤拷 锟斤拷锟斤拷锟节革拷斯锟斤拷锟教回癸拷慕锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷一锟斤拷锟斤拷芨锟斤拷诺牟锟斤拷锟斤拷悖ㄊ癸拷杉锟斤拷锟斤拷锟斤拷锟襟化ｏ拷锟斤拷注锟解：锟斤拷锟斤拷之锟斤拷锟斤拷使锟缴硷拷锟斤拷锟斤拷锟斤拷蠡锟斤拷锟斤拷锟斤拷锟街憋拷锟绞癸拷锟斤拷锟斤拷锟斤拷锟斤拷锟襟化ｏ拷锟斤拷为直锟斤拷锟脚伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷目锟斤拷锟角筹拷耍锟斤拷锟轿拷锟斤拷腔锟揭拷锟斤拷遣锟饺凤拷锟斤拷浴锟斤拷锟绞碉拷希锟斤拷锟揭诧拷锟揭伙拷锟教斤拷锟斤拷锟絜xploration锟斤拷锟斤拷锟狡碉拷锟斤拷锟街★拷锟斤拷叶斯锟脚伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟侥诧拷同之锟斤拷锟斤拷锟节ｏ拷锟斤拷锟节筹拷锟斤拷锟铰的筹拷锟斤拷锟斤拷锟斤拷锟绞憋拷峥硷拷锟街帮拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷证锟捷ｏ拷锟斤拷evidence锟斤拷锟斤拷息锟斤拷锟斤拷锟狡达拷锟斤拷锟斤拷锟斤拷锟侥猴拷锟斤拷植锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷诖锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷杉锟斤拷锟斤拷锟斤拷募锟街碉拷锟斤拷佣锟饺凤拷锟斤拷锟揭伙拷锟斤拷锟斤拷锟斤拷恪�

锟斤拷叶斯锟脚伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟截硷拷锟斤拷刹锟斤拷郑锟�

锟斤拷锟绞达拷锟斤拷模锟斤拷 锟斤拷锟节对达拷锟斤拷锟斤拷锟斤拷锟侥分诧拷锟斤拷锟叫斤拷模锟斤拷锟节碉拷锟斤拷锟斤拷始前锟斤拷始锟斤拷为一锟斤拷指锟斤拷锟斤拷锟斤拷锟斤拷植锟斤拷锟斤拷锟斤拷玫母锟斤拷蚀锟斤拷锟侥ｏ拷锟斤拷校锟斤拷锟剿癸拷锟斤拷蹋锟紾P锟斤拷锟斤拷锟斤拷锟斤拷Parzen锟斤拷锟斤拷锟斤拷锟斤拷tree-structured parzen estimator, TPE锟斤拷锟斤拷锟斤拷锟斤拷锟界、锟斤拷锟斤拷锟斤拷锟饺★拷
锟缴硷拷锟斤拷锟斤拷 \(u\) 锟缴硷拷锟斤拷锟斤拷锟斤拷锟节猴拷锟斤拷每一锟斤拷锟斤拷值锟斤拷探锟斤拷锟侥程度★拷每锟街碉拷锟斤拷锟姐法锟斤拷锟斤拷锟斤拷锟斤拷械母锟剿癸拷锟斤拷蹋锟斤拷雍锟窖★拷锟斤拷锟窖★拷锟斤拷锟揭伙拷锟斤拷牡锟斤拷锟斤拷锟斤拷锟绞癸拷貌杉锟斤拷锟斤拷锟斤拷锟襟化★拷锟斤拷叶斯锟脚伙拷效锟斤拷锟杰采硷拷锟斤拷锟斤拷锟斤拷影锟斤拷洗锟窖★拷癫缓锟斤拷实幕锟斤拷锟斤拷锟斤拷锟斤拷锟街诧拷锟斤拷锟脚解。锟缴硷拷锟斤拷锟斤拷锟斤拷选取锟斤拷锟皆匡拷锟斤拷一锟斤拷探锟斤拷-锟斤拷锟斤拷锟斤拷锟解，锟斤拷锟矫采硷拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟较界（Upper Confidence Bound, UCB锟斤拷锟斤拷锟斤拷锟斤拷POI锟斤拷锟斤拷锟斤拷EI锟斤拷锟斤拷锟饺ｏ拷锟斤拷锟斤拷锟斤拷为锟斤拷锟斤拷锟矫碉拷锟斤拷UCB锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟饺ｏ拷锟姐法锟斤拷锟绞硷拷锟揭伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟街诧拷锟斤拷然锟斤拷始锟斤拷锟斤拷锟斤拷锟姐法锟侥碉拷 \(t\) 锟斤拷锟斤拷锟斤拷锟斤拷伪锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟铰ｏ拷

通锟斤拷锟脚伙拷锟缴硷拷锟斤拷锟斤拷 \(u\) 锟皆伙拷锟� \(x^{t+1}\) 锟斤拷 \(x^{t+1}=\text{arg max}_{x} \space u(x\mid \mathcal{D}^{t})\) 锟斤拷
通锟斤拷锟矫伙拷锟斤拷锟斤拷锟竭凤拷锟斤拷锟斤拷锟斤拷 \(r\) 锟斤拷锟斤拷应锟斤拷叶斯锟脚伙拷锟叫碉拷目锟疥函锟斤拷锟斤拷锟矫碉拷 \(y^{t+1}\) 锟斤拷
锟斤拷锟斤拷锟捷斤拷锟斤拷锟斤拷锟姐： \(\mathcal{D}^{t+1} = \{\mathcal{D}^t,\quad (x^{t+1},\quad y^{t+1})\}\) 锟斤拷
锟斤拷锟铰革拷锟绞达拷锟斤拷模锟酵ｏ拷锟斤拷锟剿癸拷锟斤拷袒毓椋╋拷锟斤拷玫锟揭伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷暮锟斤拷锟街诧拷锟斤拷锟斤拷为锟斤拷一锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷植锟斤拷锟斤拷锟�

锟姐法锟斤拷锟斤拷示锟斤拷图锟斤拷锟铰ｏ拷

推荐系统：精排多目标融合与超参数学习方法

注锟解，锟斤拷实锟绞碉拷锟狡硷拷系统锟斤拷锟斤拷锟叫ｏ拷锟斤拷锟斤拷锟斤拷锟节讹拷锟斤拷锟剿癸拷锟斤拷痰拇锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟街帮拷锟斤拷锟斤拷锟斤拷锟节猴拷锟捷乘猴拷锟斤拷锟斤拷锟斤拷 \(\text{score} = \prod_{i=1}^n \space \text{score}_i^{w_i}\) 锟斤拷锟斤拷锟斤拷锟节讹拷锟斤拷频锟狡硷拷锟斤拷锟斤拷锟叫ｏ拷 \(\text{score}_i\) 锟斤拷锟斤拷为锟矫伙拷time锟斤拷like锟斤拷follow锟斤拷锟斤拷为锟斤拷预锟斤拷锟斤拷锟斤拷锟斤拷锟矫伙拷锟斤拷锟斤拷锟竭凤拷锟斤拷锟斤拷锟斤拷 \(r\) 锟斤拷锟斤拷锟借定为锟斤拷锟斤拷锟斤拷幕刷锟斤拷锟叫的碉拷锟斤拷锟绞★拷平锟斤拷锟斤拷频锟斤拷锟斤拷时锟斤拷锟饺ｏ拷锟斤拷锟斤拷锟斤拷锟斤拷 \(\mathcal{D}=\{(x, y)\}\) 锟斤拷锟斤拷锟斤拷 \(x =(w_1, w_2, \cdots, w_n), y=r\) 锟斤拷

2.2.2 锟斤拷锟斤拷锟斤拷锟皆ｏ拷ES锟斤拷锟姐法

前锟芥讲锟斤拷锟侥伙拷锟节憋拷叶斯锟脚伙拷锟侥讹拷目锟斤拷锟节猴拷锟姐法锟斤拷然锟斤拷锟斤拷锟斤拷止锟斤拷诤系锟斤拷锟斤拷锟斤拷锟斤拷猓拷锟侥ｏ拷偷牟锟斤拷锟斤拷锟斤拷锟斤拷锟侥匡拷锟斤拷诤喜锟斤拷锟斤拷锟斤拷锟饺伙拷堑锟揭伙拷模锟斤拷锟斤拷锟斤拷锟斤拷曰锟斤拷锟斤拷嗖伙拷弑锟斤拷锟教拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟接︼拷浴锟�

锟斤拷锟斤拷锟斤拷锟节讹拷目锟斤拷锟节合诧拷锟斤拷锟斤拷锟角筹拷锟斤拷锟叫碉拷锟斤拷锟斤拷锟斤到锟剿百硷拷锟金）ｏ拷锟斤拷锟斤拷锟斤拷要一锟街革拷锟斤拷效锟斤拷锟斤拷锟皆讹拷锟斤拷锟侥凤拷式锟斤拷锟脚伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟接讹拷锟杰癸拷锟斤拷态锟斤拷锟斤拷锟斤拷同锟斤拷群锟侥碉拷目锟斤拷锟脚伙拷锟斤拷锟斤拷锟斤拷锟斤拷耍锟斤拷锟斤拷锟斤拷锟斤拷使锟矫斤拷锟斤拷锟斤拷锟斤拷锟姐法锟斤拷锟斤拷锟斤拷锟斤拷实时锟斤拷锟斤拷实锟斤拷锟斤拷为指锟斤拷锟斤拷锟斤拷模锟酵的诧拷锟斤拷锟斤拷锟斤拷锟脚伙拷锟斤拷

注锟解，锟斤拷锟斤拷学习锟斤拷强锟斤拷学习锟斤拷锟脚伙拷目锟疥都锟斤拷预锟节碉拷reward锟斤拷锟斤拷强锟斤拷学习锟角斤拷锟斤拷锟斤拷锟斤拷锟诫动锟斤拷锟秸间并使锟矫凤拷锟津传诧拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷拢锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟街憋拷锟斤拷锟斤拷锟斤拷锟秸硷拷注锟斤拷锟斤拷锟斤拷锟斤拷

推荐系统：精排多目标融合与超参数学习方法

锟斤拷锟斤拷图锟斤拷示锟斤拷使锟矫斤拷锟斤拷学习锟姐法锟斤拷锟斤拷锟较讹拷模锟酵诧拷锟斤拷锟斤拷锟斤拷锟脚讹拷锟斤拷锟斤拷锟斤拷锟脚讹拷锟斤拷慕锟斤拷锟斤拷锟斤拷锟斤拷reward锟斤拷锟斤拷锟斤拷锟斤拷为锟剿撅拷锟斤拷刷锟斤拷停锟斤拷时锟斤拷/锟斤拷锟斤拷时锟斤拷/锟斤拷锟斤拷锟斤拷训裙丶锟揭碉拷锟街革拷辏╋拷锟斤拷锟斤拷锟斤拷呓锟斤拷锟叫∈憋拷锟侥ｏ拷锟窖碉拷锟斤拷锟斤拷鄄斓斤拷锟斤拷锟侥ｏ拷筒锟斤拷锟斤拷锟较猴拷锟斤拷锟斤拷锟斤拷锟斤拷系锟絙aseline模锟酵诧拷锟斤拷锟斤拷

锟斤拷锟斤拷锟姐法锟斤拷 \(t\) 锟斤拷模锟酵碉拷锟斤拷伪锟斤拷锟斤拷锟斤拷锟铰ｏ拷

锟斤拷锟斤拷锟斤拷锟斤拷 \(\varepsilon_1, \cdots, \varepsilon_n \sim \mathcal{N}(\boldsymbol{0}, \boldsymbol{I})\) 锟斤拷
锟斤拷锟斤拷reward \(r_i = r (\theta_t + \sigma \varepsilon_i),\space \text{for}\space i = 1, \cdots, n\) 锟斤拷
锟斤拷 \(\theta^{t+1} = \theta^t + \alpha \frac{1}{n\sigma}\sum_{i=1}^nr_i\varepsilon_i\) 锟斤拷

锟节癸拷锟斤拷实锟斤拷锟叫ｏ拷锟矫凤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷 锟斤拷锟饺拷锟絩eward 锟斤拷锟斤拷锟解。锟皆讹拷锟斤拷频锟狡硷拷锟斤拷锟斤拷为锟斤拷锟斤拷锟斤拷锟角筹拷锟斤拷锟斤拷注锟斤拷锟斤拷锟斤拷幕刷锟斤拷锟叫碉拷平锟斤拷锟斤拷锟斤拷时锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷为锟斤拷喜锟斤拷锟斤拷锟斤拷注锟饺ｏ拷锟侥憋拷锟绞ｏ拷锟斤拷么锟斤拷锟角撅拷锟斤拷锟斤拷锟斤拷锟斤拷锟街斤拷戏锟绞斤拷锟�

锟斤拷实锟斤拷锟叫ｏ拷通锟斤拷reward \((2)\) 锟斤拷锟饺讹拷锟皆革拷锟竭★拷

锟斤拷锟角斤拷一锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷一锟斤拷锟斤拷锟斤拷呕锟斤拷锟斤拷猓拷锟斤拷锟斤拷锟斤拷锟缴诧拷同业锟斤拷指锟斤拷之锟斤拷拇锟斤拷锟斤拷顺锟斤拷锟揭诧拷锟斤拷锟斤拷锟轿斤拷摹锟斤拷锟斤拷伟锟叫в︼拷锟斤拷锟斤拷锟斤拷佣锟斤拷锟斤拷锟街诧拷锟斤拷锟脚ｏ拷锟斤拷锟斤拷效锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟解。

锟斤拷锟斤拷锟斤拷锟斤拷锟轿帮拷锟斤拷锟斤拷时锟斤拷锟斤拷锟角匡拷锟皆斤拷锟斤拷锟斤拷reward锟斤拷锟叫斤拷一锟斤拷锟斤拷郑锟斤拷锟斤拷缃玦nteration_rate锟斤拷锟轿猯ike_rate锟斤拷follow_rate锟斤拷锟斤拷锟斤拷同锟斤拷指锟疥：

锟缴硷拷锟斤拷锟斤拷reward锟斤拷锟脚伙拷锟叫ｏ拷锟斤拷锟斤拷一直锟节癸拷懿锟酵拷锟揭革拷锟街拷锟斤拷锟矫伙拷锟斤拷锟襟，硷拷时锟斤拷锟斤拷reward锟斤拷锟斤拷式锟斤拷锟斤拷锟斤拷追锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟揭诧拷锟斤拷锟絇areto锟斤拷锟斤拷状态锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷锟街斤拷锟斤拷锟斤拷锟斤拷锟姐法锟斤拷锟斤拷一锟斤拷锟轿拷锟饺伙拷锟斤拷锟斤拷锟斤拷裕锟絥atual evolutionary strategy, NES锟斤拷锟姐法锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷NES锟姐法之锟解，锟斤拷锟斤拷锟秸伙拷锟斤拷锟斤拷锟斤拷圆锟斤拷锟斤拷锟斤拷锟绞斤拷锟� 锟斤拷锟斤拷群锟脚伙拷锟斤拷particle swarm optimization, PSO锟斤拷 ^[5][6] 锟姐法锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟节合诧拷锟斤拷锟斤拷锟斤拷锟姐法锟斤拷锟斤拷锟斤拷也锟斤拷锟斤拷一锟街斤拷锟斤拷锟斤拷锟斤拷锟姐法锟斤拷锟斤拷锟斤拷锟斤拷同锟斤拷NES锟姐法锟斤拷锟斤拷锟斤拷锟斤拷锟皆ｏ拷PSO锟姐法锟斤拷锟斤拷锟竭的ｏ拷锟斤拷旨锟节从革拷锟藉构锟缴碉拷群锟斤拷锟叫诧拷锟斤拷锟斤拷锟斤拷锟斤拷锟叫成癸拷锟侥革拷锟斤拷锟斤拷锟斤拷锟斤拷未锟斤拷锟斤拷锟斤拷姆植锟斤拷锟�

PSO锟姐法通锟斤拷锟斤拷始锟斤拷一群锟斤拷锟斤拷锟斤拷锟斤拷樱锟斤拷锟斤拷锟绞斤拷亟锟斤拷卸锟轿碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷沤狻Ｃ恳伙拷蔚锟斤拷锟斤拷校锟斤拷锟斤拷锟酵拷锟斤拷锟斤拷寮碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟绞凤拷锟斤拷沤猓╋拷锟饺猴拷寮碉拷锟斤拷锟饺猴拷业锟斤拷锟斤拷锟斤拷沤猓╋拷锟斤拷锟斤拷赂锟斤拷缘锟轿伙拷谩锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷械锟斤拷锟斤拷踊锟斤拷烁锟斤拷锟斤拷锟斤拷史锟斤拷锟脚斤拷锟饺猴拷锟斤拷锟斤拷锟斤拷锟斤拷锟饺拷锟斤拷锟斤拷沤锟街憋拷锟斤拷锟斤拷锟斤拷锟�

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷墙锟斤拷艿亩锟斤拷锟斤拷锟斤拷氐慕锟斤拷锟斤拷惴拷锟饺憋拷锟斤拷锟斤拷锟斤拷锟斤拷榷锟斤拷院锟斤拷远锟斤拷锟斤拷锟窖帮拷实锟斤拷锟斤拷浴锟斤拷锟斤拷裕锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷协锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟接︼拷锟斤拷裕锟絚ovariance matrix adaptation evolutionary strategies, CMA-ES锟斤拷锟斤拷一锟斤拷锟斤拷锟斤拷锟斤拷目锟斤拷锟节猴拷模锟酵碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷趣锟侥讹拷锟竭匡拷锟皆参硷拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷讯锟斤拷锟脚筹拷锟斤拷锟铰的讹拷目锟斤拷锟节猴拷实战锟斤拷锟侥ｏ拷锟斤拷 ^[11] 锟斤拷