They're related in that less complex models will degrade more gracefully when making predictions on novel anomalies, and that in general model complexity drives

They're related in that less complex models will degrade more gracefully when making predictions on novel anomalies, and that in general model complexity drives the bias-variance trade-off. But, erring on the side of efficiency in this discussion is more like over-fitting, which implies an overly complex model. It's making your model too good for one situation, such that it fails to generalize. You'd rather pull back on accuracy and choose a simpler model, in the hopes that it's more resilient to novel observations.