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

Abstract:Matching one distribution to many targets can require repeated evaluations of every target. CAL-$\alpha$-MODM aggregates a nonlinear predictor into one barycenter, calibrates its residual derivatives, and checks steps against the original $f$-divergence objective. Under smoothness assumptions, calibration controls parameter-step model error without requiring targets to be close to the model. Exact-oracle stationarity and local convergence guarantees are established. At common matching, canonical geometry cancels the leading quadratic iteration error, giving cubic convergence with second-order calibration and sufficiently accurate inner solves. High-precision experiments support this prediction. Sensitivity-based initialization also 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. The savings arise when cheaper predictor queries offset calibration overhead.

51 pages, 38 figures, 8 tables, comments are welcome!

Optimization and Control (math.OC); Information Theory (cs.IT); Machine Learning (cs.LG)

arXiv:2610.16819 [math.OC]

(or arXiv:2610.16819v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2610.16819 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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