# An Invariant Information Geometric Method for High-Dimensional Online Optimization

arXiv: https://arxiv.org/abs/2401.01579 · HTML: https://mlsanity.com/paper/2401.01579/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 3 Jan 2024.

## Builds on (most cited first, 13 of 13)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Scalable trust-region method for deep reinforcement learning using Kronecker-factored approximation](https://mlsanity.com/paper/1708.05144/) (2017)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [On the Influence of Momentum Acceleration on Online Learning](https://mlsanity.com/paper/1603.04136/) (2016)
- [Accelerating Natural Gradient with Higher-Order Invariance](https://mlsanity.com/paper/1803.01273/) (2018)
- [PyPop7: A Pure-Python Library for Population-Based Black-Box Optimization](https://mlsanity.com/paper/2212.05652/) (2022)
- [Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies](https://mlsanity.com/paper/1905.05885/) (2019)
- [Black-box optimization using geodesics in statistical manifolds](https://mlsanity.com/paper/1309.7168/) (2013)
- [Convergence rate of a simulated annealing algorithm with noisy observations](https://mlsanity.com/paper/1703.00329/) (2017)
- [Sample Reuse via Importance Sampling in Information Geometric Optimization](https://mlsanity.com/paper/1805.12388/) (2018)

## Abstract (arXiv)

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.