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.