Riemannian Stochastic Gradient Method for Nested Composition Optimization

arXiv:2207.09350v2 Announce Type: replace-cross
Abstract: This work considers optimization of composition of functions in a nested form over Riemannian manifolds where each function contains an expectation. This type of problems is gaining popularity in applications such as policy evaluation in reinforcement learning or model customization in meta-learning. The standard Riemannian stochastic gradient methods for non-compositional optimization cannot be directly applied as stochastic approximation of inner functions create bias in the gradients of the outer functions. For two-level composition optimization, we …

abstract applications arxiv cs.lg customization evaluation form function functions gradient math.oc meta meta-learning model customization optimization policy reinforcement reinforcement learning standard stochastic type work