Given the high economic and environmental costs of using large vision or language models, analog in-memory accelerators present a promising solution for energy-efficient AI. While inference on analog accelerators has been studied recently, the training perspective is underexplored. Recent studies have shown that the "workhorse" of digital AI training - stochastic gradient descent (SGD) algorithm converges inexactly when applied to model training on non-ideal devices. This paper puts forth a theoretical foundation for gradient-based training on analog devices. We begin by characterizing the non-convergent issue of SGD, which is caused by the asymmetric updates on the analog devices.