Molecular dynamics simulations of solid polymer electrolytes require force fields that are fast enough to converge ion transport over hundreds of nanoseconds, yet accurately describe the ion-polymer interactions that govern it. Fixed-charge force fields meet the first requirement but neglect electronic polarization, an effect often approximated by scaling ionic charges using empirically chosen factors. Here we present AutoDrude, a differentiable framework that parametrizes polarizable Drude force fields directly from DFT energies, forces, and dipoles, with no empirical tuning and at only 1.20 times the cost of a fixed-charge simulation. For PEO-LiTFSI, the dipole-constrained (hard-constraint) AutoDrude model reproduces the experimental ionic conductivity as accurately as the best charge-scaled model (17% versus 16% mean absolute percentage error). We compare the polarizable forcefield to fixed charge ones models by fitting a fixed charge model. Unlike the charge-scaled models tested here, however, AutoDrude also reproduces the dilute-limit cation transference number, its increase with salt concentration, and the absence of Li-TFSI contact ion pairs at low concentration. A penalty-based (soft-constraint) variant yields a closer fit to the DFT reference yet underestimates the conductivity by up to an order of magnitude, demonstrating that closer agreement with DFT training data alone does not guarantee accurate ion transport. These results indicate that although charge scaling can reproduce ionic conductivity the explicit inclusion of polarization is necessary to capture the concentration dependence of cation transport in PEO-LiTFSI.