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.