Thanks　to　the　outstanding　adaptability　and　relatively　simple　design　process,　machine　learning-based　energy　management　strategies　(EMSs)　show　their　superiority　in　reducing　the　energy　consumption　for　multi-power　powertrains.　Given　the　popularity　of　distributed-drive　in　battery　electric　vehicles　(BEVs),　this　study　selects　a　dual-motor　four-speed　electric　bus　to　investigate　the　proposed　soft　actor-critic　(SAC)-based　EMS.　Two　improvements　are　made　to　the　traditional　SAC　algorithm　to　meet　the　special　requirements　of　EMS　in　a　distributed-drive　electric　bus　in　this　study.　Firstly,　the　introduced　combination　of　Gumbel-SoftMax　and　actor-network　allows　the　SAC　agents　to　explore　the　hybrid　action　space　(discrete　operating　modes　and　continuous　torque　distribution　coefficients).　Secondly,　a　heuristic　rule-interposing　action　controller　(HRIAC)　is　involved　to　reduce　illogical　exploration　of　SAC　agents　in　searching　for　optimal　power　distributing　ratio.　Simulation　results　demonstrate　that　Gumbel-SoftMax　facilitates　agents＇　exploration　and　narrows　the　energy　consumption　gap　between　the　proposed　EMS　and　the　global　optimal　EMS,　meanwhile,　HRIAC　accelerates　the　convergence　of　agent　training.　The　comparative　results　of　proposed　EMS　performance　in　unknown　driving　cycles　show　that　the　proposed　EMS　outperforms　other　deep　reinforcement　learning　(DRL)-based　EMSs　in　adaptability,　which　is　taken　as　a　solid　foundation　for　energy　efficiency　improvement　of　dual-motor　electric　bus　in　practice.　©　2023　Elsevier　Ltd