Inner Optimization

Inner optimization is a crucial sub-problem within many machine learning algorithms, particularly those involving bilevel optimization, where an outer objective function depends on the solution of an inner optimization problem. Current research focuses on improving the efficiency and accuracy of these inner loops, exploring techniques like preconditioning, reparameterization, and novel candidate selection strategies (e.g., Voronoi or Delaunay triangulation) to reduce computational cost and enhance performance. These advancements are significant because efficient inner optimization is critical for scaling up complex machine learning models and improving the performance of applications ranging from hyperparameter tuning to robotic co-design and robust combinatorial optimization.