A　simultaneously　transmitting　and　reflecting　surface　(STARS)　assisted　multi-user　downlink　multiple-input　signal-output　(MISO)　multi-cellular　edge　caching　system　is　investigated.　The　deployment　of　STARS　enhances　the　coverage　of　base　stations　(BSs),　particularly　at　cellular　boundaries.　However,　this　advancement　introduces　a　complex　user　association　issue　that　necessitates　the　consideration　of　both　caching　state　and　channel　state　information　(CSI).　In　this　paper,　we　formulate　a　joint　optimization　problem　involving　content　caching,　user　association,　active　beamforming　at　BS,　and　passive　beamforming　at　STARS　for　minimizing　long-term　power　consumption.　We　propose　two　algorithms　for　the　formulated　problem:　1)　A　two　time-scale　cooperative　twin　delayed　deep　deterministic　policy　gradients　(TD3).　Considering　the　distinct　time　scales　of　the　pushing　and　delivering　phases　in　edge　caching,　the　Markov　decision　process　(MDP)　models　of　dual　time　scales　are　constructed　and　two　deep　reinforcement　learning　(DRL)　agents　work　together　to　jointly　address　the　optimization　problem.　2)　A　bio-inspired　DRL　framework,　especially,　a　particle　swarm　optimization　(PSO)-inspired　TD3　algorithm　is　introduced　in　detail.　Inspired　by　the　behavior　of　the　biological　population　in　nature,　this　algorithm　regards　agents　as　individuals　and　enables　the　concurrent　training　of　multiple　agents　while　they　interact　with　global　information　via　a　biological　population　information　interaction　mode,　thereby　enhancing　the　performance　of　power　optimization.　The　numerical　results　demonstrate　that　the　STARS-assisted　multi-cellular　edge　caching　system　has　advantages　over　traditional　cellular　systems,　especially　in　scenarios　where　the　number　of　mobile　users　and　Zipf　skewness　factor　is　large.　Moreover,　the　proposed　two　time-scale　cooperative　TD3　and　PSO-inspired　TD3　algorithms　are　superior　in　reducing　network　power　consumption　than　conventional　TD3.