Towards Co-Designed Event-Triggered Extremum Seeking

What the math gives to ML

The paper's transferable contribution is a co-design principle: choose the feedback or preconditioning matrix and the event-trigger threshold jointly under a robust Lyapunov certificate, rather than selecting an optimizer first and adding communication sparsification afterward. Its quadratic-map model exposes an important opportunity for neural optimization: off-diagonal Hessian couplings can make a full matrix gain substantially better than a diagonal learning-rate vector when stale gradients or parameters are used. A practical adaptation is a robust event-triggered preconditioner for distributed, federated, or blockwise training, with the trigger threshold maximized subject to stability margins over a set of estimated Hessian matrices. The main benefit to test is fewer gradient or model communications at equal convergence speed, while retaining a certificate against curvature variation.