Calibrated $\alpha$-Barycenters for Multiobjective $f$-Divergence Optimization

Matching one distribution to many targets can require repeated evaluations. CAL-$\alpha$-MODM aggregates a nonlinear predictor into one barycenter, calibrates its residual derivatives, and checks steps against the original $f$-divergence objective. Residual calibration controls step-local model error under smoothness assumptions without requiring targets to be close to the model. Under stated exact-oracle assumptions, we establish convergence to stationarity. A local expansion shows that canonical geometry cancels the leading quadratic iteration error at common matching, yielding cubic convergence with second-order calibration and sufficiently accurate inner solves. High-precision experiments support this local prediction. Sensitivity prediction accelerates preference continuation along regular stationary branches. On 300-target Jensen–Shannon problems, CAL-p2 achieves median paired speedups of $3.15\times$ over L-BFGS and $1.10\times$ over second-order Direct-TR, across 23/25 and 24/25 objective-comparable stationary pairs, respectively. Gains arise when predictor savings outweigh calibration overhead.