Improving Gradient Methods via Coordinate Transformations: Applications to Quantum Machine Learning
This addresses optimization bottlenecks in machine learning, particularly for quantum applications, but appears incremental as it builds on existing gradient methods with a novel twist.
The paper tackles the problem of local minima and barren plateaus in gradient-based optimization methods, which slow down calculations and increase computational costs, by introducing a generic strategy using coordinate transformations to accelerate performance, resulting in significant improvements in quantum machine learning algorithms.
Machine learning algorithms, both in their classical and quantum versions, heavily rely on optimization algorithms based on gradients, such as gradient descent and alike. The overall performance is dependent on the appearance of local minima and barren plateaus, which slow-down calculations and lead to non-optimal solutions. In practice, this results in dramatic computational and energy costs for AI applications. In this paper we introduce a generic strategy to accelerate and improve the overall performance of such methods, allowing to alleviate the effect of barren plateaus and local minima. Our method is based on coordinate transformations, somehow similar to variational rotations, adding extra directions in parameter space that depend on the cost function itself, and which allow to explore the configuration landscape more efficiently. The validity of our method is benchmarked by boosting a number of quantum machine learning algorithms, getting a very significant improvement in their performance.