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A query-optimal algorithm for finding counterfactuals
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:2075-2090, 2022.
Abstract
We design an algorithm for finding counterfactuals with strong theoretical guarantees on its performance. For any monotone model f:Xd→{0,1} and instance x⋆, our algorithm makes S(f)O(Δf(x⋆))⋅logd{queries} to f and returns an {\sl optimal} counterfactual for x⋆: a nearest instance x′ to x⋆ for which f(x′)≠f(x⋆). Here S(f) is the sensitivity of f, a discrete analogue of the Lipschitz constant, and Δf(x⋆) is the distance from x⋆ to its nearest counterfactuals. The previous best known query complexity was dO(Δf(x⋆)), achievable by brute-force local search. We further prove a lower bound of S(f)Ω(Δf(x⋆))+Ω(logd) on the query complexity of any algorithm, thereby showing that the guarantees of our algorithm are essentially optimal.