We propose an AdversariaL training algorithm for commonsense InferenCE (ALICE). We apply small perturbations to word embeddings and minimize the resultant adversarial risk to regularize the model. We exploit a novel combination of two different approaches to estimate these perturbations: 1) using the true label and 2) using the model prediction. Without relying on any human-crafted features, knowledge bases, or additional datasets other than the target datasets, our model boosts the fine-tuning performance of RoBERTa, achieving competitive results on multiple reading comprehension datasets that require commonsense inference.