A　simultaneously　transmitting　and　reflecting　surface　(STARS)　enabled　edge　caching　system　is　proposed　for　reducing　backhaul　traffic　and　ensuring　the　quality　of　service.　A　novel　Caching-at-STARS　structure,　where　a　dedicated　smart　controller　and　cache　memory　are　installed　at　the　STARS,　is　proposed　to　satisfy　user　demands　with　fewer　hops　and　desired　channel　conditions.　Then,　a　joint　caching　replacement　and　information-centric　hybrid　beamforming　optimization　problem　is　formulated　for　minimizing　the　network　power　consumption.　As　long-term　decision　processes,　the　optimization　problems　based　on　independent　and　coupled　phase-shift　models　of　Caching-at-STARS　contain　both　continuous　and　discrete　decision　variables,　and　are　suitable　for　solving　with　deep　reinforcement　learning　(DRL)　algorithm.　For　the　independent　phase-shift　Caching-at-STARS　model,　we　develop　a　frequency-aware　based　twin　delayed　deep　deterministic　policy　gradient　(FA-TD3)　algorithm　that　leverages　user　historical　request　information　to　serialize　high-dimensional　caching　replacement　decision　variables.　For　the　coupled　phase-shift　Caching-at-STARS　model,　we　conceive　a　cooperative　TD3　&　deep-Q　network　(TD3-DQN)　algorithm　comprised　of　FA-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)　Caching-at-STARS　outperforms　the　RIS-assisted　edge　caching　systems;　3)　The　proposed　FA-TD3　and　cooperative　TD3-DQN　algorithms　are　superior　in　reducing　network　power　consumption　than　conventional　TD3.