Edge　computing　is　an　emerging　promising　computing　paradigm,　which　can　significantly　reduce　the　service　latency　by　moving　computing　and　storage　demands　to　the　edge　of　the　network.　Resource-constrained　edge　servers　may　fail　to　process　multiple　tasks　simultaneously　when　several　time-delay-sensitive　and　computationally　demanding　tasks　are　offloaded　to　only　one　edge　server,　and　results　in　some　issues　such　as　high　task　processing　costs.　In　this　paper,　we　introduce　a　novel　idea　by　dividing　one　task　into　several　sub-tasks　via　the　dependencies　within　the　task　and　then　offloading　the　sub-tasks　to　other　edge　servers　in　light　of　high　concurrency　for　synchronization　to　minimize　the　total　cost　of　task　processing.　To　address　the　challenge　of　task　dependencies　and　adaptation　to　dynamic　scenes,　we　propose　a　Multi-Task　Dependency　Offloading　Algorithm　(MTDOA)　based　on　deep　reinforcement　learning.　The　task　offloading　decision　is　modeled　as　a　Markov　decision　process,　and　then　a　graph　attention　network　is　applied　to　extract　the　dependency　information　of　different　tasks,　while　LSTM　and　DQN　are　combined　to　deal　with　sequential　problems.　The　simulation　results　show　that　the　proposed　MTDOA　has　better　convergence　ability　compared　with　the　baseline　algorithms.　©　2024　Elsevier　B.V.