A　novel　Caching-at-STARS　structure,　where　dedicated　smart　controller　and　cache　memory　are　installed　at　the　STARS,　is　proposed　to　satisfy　user　demands　with　fewer　hops　and　desired　channel　condition.　Then,　a　joint　caching　replacement　and　information-centric　hybrid　beamforming　optimization　problem　is　formulated　for　minimizing　the　network　power　consumption.　We　conceive　a　cooperative　twin　delayed　deep　deterministic　policy　gradient　&　deep-Q　network　(TD3-DQN)　algorithm　comprised　by　TD3　and　DQN　agents　to　decide　on　continuous　and　discrete　variables　respectively　by　observing　the　network　external　and　internal　environment.　The　numerical　results　demonstrate　that:　1)　The　Caching-at-STARS-enabled　edge　caching　system　has　advantages　over　traditional　edge　caching,　especially　in　scenarios　where　Zipf　skewness　factors　or　cache　capacity　is　large;　2)　STARS　outperforms　RIS　significantly　in　edge　caching　systems;　3)　The　proposed　cooperative　TD3-DQN　algorithms　is　superior　in　reducing　network　power　consumption　than　conventional　TD3.　©　2023　IEEE.