Distributional shift: relax the statistics, or rewrite the contract
Training data and deployment data rarely stay the same distribution for long, and Concrete Problems refuses to settle on one way of handling that mismatch. It offers two answers that barely resemble each other: one keeps the statistics, the other rewrites the terms.
Relaxing what the training data has to guarantee, through importance weighting and partial specification, comes first; abandoning that framing altogether for causal reasoning and checkable contracts on a model's assumptions comes after. The same formal-verification toolkit used elsewhere in the corpus turns up again underneath the contracts idea.
Concrete Problems' robustness-to-distributional-shift problem receives two conceptually distinct answers. Weakening statistical assumptions to survive distribution shift keeps the classical ML framing, reusing training data under covariate-shift-style importance weighting, partially specified models, generalized method of moments, or training deliberately across multiple distributions, requiring less of the statistics connecting train and test. Reframing distributional shift as broken contracts and causal structure abandons that framing for two others: treating shift through counterfactual, causal reasoning, and treating a model's training assumptions as an explicit software contract that can be stated, checked, and, via model repair, restored after the fact when violated. Formal verification and control theory recur as safety building blocks joins this pairing through that last technique, since model repair is one of the recurring formal-methods tools the paper reaches for throughout, tying this problem's remedies to the same technical substrate used for side effects and exploration elsewhere in the corpus.