Calibrated α-Barycenters for Multiobjective f-Divergence Optimization
Abstract
Matching one distribution to many targets can require repeated evaluations of every target. CAL-α-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× over L-BFGS and 1.10× 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.
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BibTeX
@misc{tang2026calibrated,
title = {{Calibrated $α$-Barycenters for Multiobjective $f$-Divergence Optimization}},
author = {Dier Tang and Peijie Li and Xiaoyuan Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16819},
eprint = {2610.16819},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16819},
}
RIS
TY - UNPB
TI - Calibrated α-Barycenters for Multiobjective f-Divergence Optimization
AU - Dier Tang
AU - Peijie Li
AU - Xiaoyuan Zhang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16819
UR - https://arxiv.org/abs/2610.16819
AB - Matching one distribution to many targets can require repeated evaluations of every target. CAL-α-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× over L-BFGS and 1.10× 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.
ER -