Robust bandits have a sharp computational boundary: a specific case is tractable with efficient algorithms, but small generalizations become NP-hard, suggesting this marks the frontier of what's computationally feasible for unrealizable learning.
This paper studies how to efficiently learn in bandit problems when the true environment doesn't match the learner's model. The authors identify a tractable special case with polynomial-time algorithms and $\tilde{O}(\sqrt{T})$ regret, while showing that natural generalizations become NP-hard—establishing where the problem transitions from solvable to hard.