Understanding the variational landscape and convergence in variational path sampling

Characterize the structure of the variational landscape of control forces in variational path sampling and determine how this structure relates to system relaxation timescales and to the convergence behavior of the variational optimization algorithm.

Background

Variational path sampling (VPS) estimates rare-event statistics by optimizing control forces that reweight trajectory ensembles via variational bounds. The optimization landscape over these control forces governs how efficiently and reliably the algorithm converges.

The paper notes that this landscape, and its coupling to intrinsic relaxation timescales of the underlying dynamics, can affect convergence but lacks a formal understanding. Establishing this relationship would clarify when and why VPS converges and guide algorithmic improvements.