We introduce AdaSub, a stochastic optimization algorithm that computes a search direction based on second-order information in a low-dimensional subspace that is defined adaptively based on available current and past information. Compared to first-order methods, second-order methods exhibit better convergence characteristics, but the need to compute the Hessian matrix at each iteration results in excessive computational expenses, making them impractical. To address this issue, our approach enables the management of computational expenses and algorithm efficiency by enabling the selection of the subspace dimension for the search. Our code is freely available on GitHub, and our preliminary numerical results demonstrate that AdaSub surpasses popular stochastic optimizers in terms of time and number of iterations required to reach a given accuracy.

This paper summarizes our approach (team Math-Land) to the DSAA 2023 Data Science Competition, which focuses on link prediction. Our proposed model is based on embedding techniques commonly used for natural language processing, and the embedding is constructed as part of the neural network training, eliminating the need for a separate step. We train the model using the binary cross entropy loss and the Adam optimizer. The approach achieves high F1-scores on validation and test sets.