Zahra Khatti | Searcharxiv

arXiv2026

Low-Order Explicit Hessian Imitation Method for Large-Scale Supervised Machine Learning

An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model training. The purpose of the auxiliary loss is to provide a mechanism for creating a low-order Hessian-type approximation for the original loss. The proposed algorithm employs the resulting low-order second-derivative approximation terms in place of the second-order momentum terms (i.e., squared elements of the gradient of the loss function) in an overall scheme that has computational cost on par with an Adam-type approach. Whereas the squared elements of a gradient vector do not necessarily approximate second-order derivatives well, by careful construction of the auxiliary loss, second-order derivative-type approximations for the original loss can be computed and employed by the algorithm in an efficient manner. A convergence guarantee is provided for the proposed algorithm that is on par with guarantees available for similar stochastic diagonal-scaling methods. The results of numerical experiments show situations when the proposed algorithm outperforms Adam and other popular modern optimizers.

math.OC↗

arXiv2025

Fair Supervised Learning Through Constraints on Smooth Nonconvex Unfairness-Measure Surrogates

A new strategy for fair supervised machine learning is proposed. The main advantages of the proposed strategy as compared to others in the literature are as follows. (a) We introduce a new smooth nonconvex surrogate to approximate the Heaviside functions involved in discontinuous unfairness measures. The surrogate is based on smoothing methods from the optimization literature, and is new for the fair supervised learning literature. The surrogate is a tight approximation which ensures the trained prediction models are fair, as opposed to other (e.g., convex) surrogates that can fail to lead to a fair prediction model in practice. (b) Rather than rely on regularizers (that lead to optimization problems that are difficult to solve) and corresponding regularization parameters (that can be expensive to tune), we propose a strategy that employs hard constraints so that specific tolerances for unfairness can be enforced without the complications associated with the use of regularization. (c) Our proposed strategy readily allows for constraints on multiple (potentially conflicting) unfairness measures at the same time. Multiple measures can be considered with a regularization approach, but at the cost of having even more difficult optimization problems to solve and further expense for tuning. By contrast, through hard constraints, our strategy leads to optimization models that can be solved tractably with minimal tuning.

cs.LG↗