Task　scheduling　is　one　of　the　key　technologies　in　edge　computing.　End　devices　can　significantly　improve　the　quality　of　service　by　offloading　some　latency-sensitive　tasks　to　edge　servers,　but　a　large　amount　of　power　and　compute　units　are　wasted.　Therefore,　this　paper　proposes　a　two-stage　task　offloading　approach　to　ensure　low　latency　while　reducing　the　energy　consumption　of　edge　computing　units　and　cloud　computing　centers.　The　mobile　edge　computing　environment　contains　edge　computing　nodes　as　well　as　cloud　computing　centers.　A　two-stage　processing　mechanism　based　on　deep　Q-learning　is　used　to　automatically　generate　optimal　long-term　scheduling　decisions　that　reduce　power　consumption　while　ensuring　quality　of　service.　Imitation　learning　is　also　used　in　the　reinforcement　learning　process　to　reduce　the　training　time　of　the　optimal　policy.　To　evaluate　the　effectiveness　of　the　model,　we　use　the　Shortest　job　first　(SJF)　algorithm　and　the　Heterogeneous　Earliest　Finish　Time　(HEFT)　into　as　comparison　algorithms,　comparing　the　running　time　and　energy　consumption　as　a　measure.　Our　proposed　algorithm　has　13%　more　running　time　but　34%　lower　average　energy　consumption　compared　to　other　algorithms.　©　2022,　Springer　Nature　Singapore　Pte　Ltd.