In this lecture, we introduce a fundamentally different family of evolution-inspired search algorithms, the Evolution Strategies (ES). Rather than treating a population as a set of hypothetical good solutions that must be retained or discarded, as in the GA, the Evolution Strategies adapt the search process itself by allowing different decision variables to be able to mutate using different step sizes, and the resulting adaptive step sizes reflect the curvature of the underlying fitness landscape. We discuss how this heuristic idea was formalized in Natural Evolution Strategies (NES), which leverage the information-theoretic natural gradient to learn productive directions to climb, and then how that was made more practical and effective via Covariance Matrix Adaptation Evolution Strategy (CMA-ES). We close with a discussion of how CMA-ES facilitates adaptive restarts, making CMA-ES not only a good tool for high-resolution search of a single fitness peak but also a candidate for global optimization – seeking out new peaks in a sort of "depth-first" order (in contrast to the "breadth-first" order of the GA). We then put the GA, ES, and conventional (stochastic) gradient descent together as complementary tools for complex optimization.
Whiteboard notes for this lecture can be found at:
https://www.dropbox.com/scl/fi/tnq6ol9soph5cxjcqnf73/IEE598-Lecture2A-2026-02-10-Introduction_to_Evolution_Strategies_and_CMA-ES-Notes.pdf?rlkey=9brna7e54fkh9ljf00uexxmjk&dl=0
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