A Probabilistic Framework for Learnable Optimization Algorithms

Understand

We propose a statistical-learning framework for optimization algorithms.

• The framework is based on probability distributions over optimization trajectories induced by a distribution of optimization problems and a learnable optimization algorithm.
• Within this setting, optimization performance is represented through measurable performance functionals, including stopping times, contraction factors, and trajectory-level properties.
• The resulting framework provides a statistical perspective on optimization algorithms, allows their performance to be studied at the population level, and naturally accommodates the learning of optimization algorithms from data.