Efficient Algorithms for Large-Scale Optimization

Modern machine learning systems require optimization algorithms that scale gracefully with data volume. In this post, we present a new approach that achieves state-of-the-art performance on standard benchmarks.

Background

Previous approaches to large-scale optimization have relied on stochastic gradient descent variants. While effective, these methods struggle when the objective function exhibits high curvature or when the data distribution is non-stationary.

Our Approach

We introduce a novel algorithm that combines second-order information with adaptive step sizing. The key insight is that local curvature estimates can be computed efficiently using a low-rank approximation of the Hessian matrix.