Stochastic gradient based concurrent criterion learning and parameter-estimation

Abstract

For parameter-estimation over non-Gaussian noise, several learning criteria have emerged, which are known for their hyperparameter dependence. This work proposes a random Fourier feature based online hyperparameter free criterion learning algorithm that comprehensively alleviates dependence on hyperparameter choices and learns the criterion by self-adapting to underlying noise. First, for this joint parameter and criterion estimation, dynamical equations for the proposed hyperparameter-free algorithm are derived. Next, regarding the convergence characteristics of the proposed joint hyperparameter free parameter and criterion learning, rigorous analytical results are presented. Finally, case-studies aligned with classical signal processing applications like channel-estimation and channel-equalization are provided for performance validation of the proposed algorithm, and to verify the derived convergence analysis through computer simulations. © 2026 The Authors.