While state-of-the-art NLP models have demonstrated excellent performance for aspect based sentiment analysis (ABSA), substantial evidence has been presented on their lack of robustness. This is especially manifested as significant degradation in performance when faced with out-of-distribution data. Recent solutions that rely on counterfactually augmented datasets show promising results, but they are inherently limited because of the lack of access to explicit causal structure. In this paper, we present an alternative approach that relies on non-counterfactual data augmentation. Our proposal instead relies on using noisy, cost-efficient data augmentations that preserve semantics associated with the target aspect. Our approach then relies on modelling invariances between different versions of the data to improve robustness. A comprehensive suite of experiments shows that our proposal significantly improves upon strong pre-trained baselines on both standard and robustness-specific datasets. Our approach further establishes a new state-of-the-art on the ABSA robustness benchmark and transfers well across domains.