Adversarial meta-learning of Gamma-minimax estimators that leverage prior knowledge

Bayes estimators are well known to provide a means incorporate prior knowledge that can be expressed in terms of single distribution. However, when this is too vague express with prior, an alternative approach needed. Gamma-minimax such approach. These minimize the worst-case risk over set Γ distributions compatible available knowledge. Traditionally, Gamma-minimaxity defined for parametric models. In work, we define general models and propose adversarial meta-learning algorithms compute them constrained by generalized moments. Accompanying convergence guarantees also provided. We introduce neural network class provides rich, but finite-dimensional, from which estimator selected. illustrate our method two settings, namely entropy estimation prediction problem arises biodiversity studies.