IEEE Open Journal of Control Systems’ Post

Now published in OJ-CSYS: "Novel Bounds for Incremental Hessian Estimation With Application to Zeroth-Order Federated Learning," by Alessio Maritan, Luca Schenato and Subhrakanti Dey. Link: https://lnkd.in/gN27SuPH The Hessian matrix conveys important information about the curvature, spectrum and partial derivatives of a function, and is required in a variety of tasks. However, computing the exact Hessian is prohibitively expensive for high-dimensional input spaces, and is just impossible in zeroth-order optimization, where the objective function is a black-box of which only input-output pairs are known. In this work we address this relevant problem by providing a rigorous analysis of an Hessian estimator available in the literature, allowing it to be used as a provably accurate replacement of the true Hessian matrix. The Hessian estimator is randomized and incremental, and its computation requires only point function evaluations. We provide non-asymptotic convergence bounds on the estimation error and derive the minimum number of function queries needed to achieve a desired accuracy with arbitrarily high probability. In the second part of the paper we show a practical application of our results, introducing a novel optimization algorithm suitable for non-convex and black-box federated learning. #optimization #dataprivacy #federatedlearning

  • No alternative text description for this image

To view or add a comment, sign in

Explore topics