Rational design of solid-state electrolytes(SSEs)with high ionic conductivity and low activation energy(Ea)is vital for all solid-state batteries.Machine learning(ML)techniques have recently been successful in predicting Li+conduction property in SSEs with various descriptors and accelerating the development of SSEs.In this work,we extend the previous efforts and introduce a framework of ML prediction for Ea in SSEs with hierarchically encoding crystal structure-based(HECS)descriptors.Taking cubic Li-argyrodites as an example,an Ea prediction model is developed to the coefficient of determination(R2)and root-mean-square error(RMSE)values of 0.887 and 0.02 eV for training dataset,and 0.820 and 0.02 eV for test dataset,respectively by partial least squares(PLS)analysis,proving the prediction power of HECS-descriptors.The variable importance in projection(VIP)scores demonstrate the combined effects of the global and local Li+conduction environments,especially the anion size and the resultant structural changes associated with anion site disorder.The developed Ea prediction model directs us to optimize and design new Li-argyrodites with lower Ea,such as Li6-xPS5-xCl1+x(<0.322 eV),Li6+xPS5+xBr1-x(<0.273 eV),Li6+xPS5+xBr0.25I0.75-*(<0.352 eV),Li6+(5-n)yP1-yNyS5I(<0.420 eV),Li6.(5-n)yAs1-yNyS5I(<0.371 eV),Li6+(5-n)yAs1-yNySe5I(<0.450 eV),by broadening bottleneck size,invoking site disorder and activating concerted Li+conduction.This analysis shows great potential in promoting rational design of advanced SSEs and the same approach can be applied to other types of materials.