Stochastic Mirror-Prox Optimisation of Group Distributionally Robust Multimodal Logistic Regression for Multilingual Fact-Checking Verdict Prediction

This paper asks whether group distributionally robust optimisation raises the worst-group macro-F1 of a block-masked multimodal logistic regression with availability indicators for multilingual fact-checking. Stochastic Mirror-Prox solves the resulting convex–concave saddle-point problem. The corpus pools 49,584 X-Fact and MediaEval records with 90 language labels. On the in-domain split, the robust solution lifts worst-group macro-F1 from 0.313 under pooled empirical risk minimisation to 0.401 (95% interval of the gain [0.025,0.134]). Overall macro-F1 drops by 0.040, and dispersion of balanced accuracy across languages falls from 0.166 to 0.131. The gain lies in X-Fact claim groups and the cost in MediaEval posts (macro-F1 0.887 to 0.809). Removing the availability indicators moves no worst-group or overall macro-F1 by more than 0.007. The worst-group difference is negative on unseen languages and not resolved on unseen sites or events. A Friedman test detects no difference between solvers in typical group performance. At equal numbers of sampled records, stochastic mirror descent reaches a smaller mean duality gap than Mirror-Prox at each measured mini-batch size from 2 to 128. On this instance, extrapolation does not repay its second call.