An Invariant Information Geometric Method for High-Dimensional Online
  Optimization
Zhengfei Zhang Yunyue Wei Yanan Sui
Sample efficiency is crucial in optimization, particularly in black-box
scenarios characterized by expensive evaluations and zeroth-order feedback.
When computing resources are plentiful, Bayesian optimization is often favored
over evolution strategies. In this paper, we introduce a full invariance
oriented evolution strategies algorithm, derived from its corresponding
framework, that effectively rivals the leading Bayesian optimization method in
tasks with dimensions at the upper limit of Bayesian capability. Specifically,
we first build the framework InvIGO that fully incorporates historical
information while retaining the full invariant and computational complexity. We
then exemplify InvIGO on multi-dimensional Gaussian, which gives an invariant
and scalable optimizer SynCMA . The theoretical behavior and advantages of our
algorithm over other Gaussian-based evolution strategies are further analyzed.
Finally, We benchmark SynCMA against leading algorithms in Bayesian
optimization and evolution strategies on various high dimension tasks, in
cluding Mujoco locomotion tasks, rover planning task and synthetic functions.
In all scenarios, SynCMA demonstrates great competence, if not dominance, over
other algorithms in sample efficiency, showing the underdeveloped potential of
property oriented evolution strategies.