Mirror Descent Algorithms for Minimizing Interacting Free Energy
This work addresses a specific optimization problem in probability theory, likely incremental as it builds on mirror descent methods.
The paper tackles the problem of minimizing interacting free energy by proposing a mirror-descent-type algorithm with a novel metric that incorporates the reference measure and interacting term, and numerical results demonstrate its efficiency.
This note considers the problem of minimizing interacting free energy. Motivated by the mirror descent algorithm, for a given interacting free energy, we propose a descent dynamics with a novel metric that takes into consideration the reference measure and the interacting term. This metric naturally suggests a monotone reparameterization of the probability measure. By discretizing the reparameterized descent dynamics with the explicit Euler method, we arrive at a new mirror-descent-type algorithm for minimizing interacting free energy. Numerical results are included to demonstrate the efficiency of the proposed algorithms.