arXiv subjects

Henri Doerks

Publications and source records attributed to Henri Doerks.

2 recordsLinked to original sources

arXiv2026

The relative efficiency of sequential tests

While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required to achieve a given power of the test -- but by how much? To address this question, we focus on the scenario of testing the unknown drift of a Brownian motion, comparing the Wald sequential probability ratio test with tests that use a pre-determined fixed sample size. We provide precise bounds on the average reduction in sample size needed to achieve a desired precision. Specifically, we demonstrate that for symmetric error bounds, the sequential test reduces the average sample size by at least 36\% and by at most 75\%. Moreover, the reduction in sample size increases monotonically with the power of the test, meaning that the relative advantage of using a sequential test over a fixed sample size test grows as higher power is required. We also study the relative efficiency in the case with asymmetric error bounds, and we provide a lower bound in terms of the symmetric case.

math.ST↗

arXiv2025

Learning to accelerate distributed ADMM using graph neural networks

Distributed optimization is fundamental to large-scale machine learning and control applications. Among existing methods, the alternating direction method of multipliers (ADMM) has gained popularity due to its strong convergence guarantees and suitability for decentralized computation. However, ADMM can suffer from slow convergence and high sensitivity to hyperparameter choices. In this work, we show that distributed ADMM iterations can be naturally expressed within the message-passing framework of graph neural networks (GNNs). Building on this connection, we propose learning adaptive step sizes and communication weights through a GNN that predicts these yperparameters based on the current iterates. By unrolling ADMM for a fixed number of iterations, we train the network end-to-end to minimize the solution distance after these iterations for a given problem class, while preserving the algorithm's convergence properties. Numerical experiments demonstrate that our learned variant consistently improves convergence speed and solution quality compared to standard ADMM, both within the trained computational budget and beyond. The code is available at https://github.com/paulhausner/learning-distributed-admm.

cs.LG↗