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arXiv · 2410.14270

FINDER: Stochastic Mirroring of Noisy Quasi-Newton Search and Deep Network Training

Uttam Suman·Mariya Mamajiwala·Mukul Saxena·Ankit Tyagi·Debasish Roy
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Abstract

Our proposal is on a new stochastic optimizer for non-convex and possibly non-smooth objective functions typically defined over large dimensional design spaces. Towards this, we have tried to bridge noise-assisted global search and faster local convergence, the latter being the characteristic feature of a Newton-like search. Our specific scheme -- acronymed FINDER (Filtering Informed Newton-like and Derivative-free Evolutionary Recursion), exploits the nonlinear stochastic filtering equations to arrive at a derivative-free update that has resemblance with the Newton search employing the inverse Hessian of the objective function. Following certain simplifications of the update to enable a linear scaling with dimension and a few other enhancements, we apply FINDER to a range of problems, starting with some IEEE benchmark objective functions to a couple of archetypal data-driven problems in deep networks to certain cases of physics-informed deep networks. The performance of the new method vis-\'a-vis the well-known Adam and a few others bears evidence to its promise and potentialities for large dimensional optimization problems of practical interest.

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Uttam Suman, Mariya Mamajiwala, Mukul Saxena, Ankit Tyagi, Debasish Roy. 2024-10-18. FINDER: Stochastic Mirroring of Noisy Quasi-Newton Search and Deep Network Training. https://arxiv.org/abs/2410.14270

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