An invariant information geometric method for high-dimensional online optimization

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, including 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.