ES Is More Than Just a Traditional Finite-Difference Approximator

An evolution strategy (ES) variant based on a simplification of a natural evolution strategy recently attracted attention because it performs surprisingly well in challenging deep reinforcement learning domains. It searches for neural network parameters by generating perturbations to the current set of parameters, checking their performance, and moving in the aggregate direction of higher reward. Because it resembles a traditional finite-difference approximation of the reward gradient, it can naturally be confused with one. However, this ES optimizes for a different gradient than just reward: It optimizes for the average reward of the entire population, thereby seeking parameters that are robust to perturbation. This difference can channel ES into distinct areas of the search space relative to gradient descent, and also consequently to networks with distinct properties. This unique robustness-seeking property, and its consequences for optimization, are demonstrated in several domains. They include humanoid locomotion, where networks from policy gradient-based reinforcement learning are significantly less robust to parameter perturbation than ES-based policies solving the same task. While the implications of such robustness and robustness-seeking remain open to further study, this work's main contribution is to highlight such differences and their potential importance

Safe Mutations for Deep and Recurrent Neural Networks through Output Gradients

While neuroevolution (evolving neural networks) has a successful track record across a variety of domains from reinforcement learning to artificial life, it is rarely applied to large, deep neural networks. A central reason is that while random mutation generally works in low dimensions, a random perturbation of thousands or millions of weights is likely to break existing functionality, providing no learning signal even if some individual weight changes were beneficial. This paper proposes a solution by introducing a family of safe mutation (SM) operators that aim within the mutation operator itself to find a degree of change that does not alter network behavior too much, but still facilitates exploration. Importantly, these SM operators do not require any additional interactions with the environment. The most effective SM variant capitalizes on the intriguing opportunity to scale the degree of mutation of each individual weight according to the sensitivity of the network's outputs to that weight, which requires computing the gradient of outputs with respect to the weights (instead of the gradient of error, as in conventional deep learning). This safe mutation through gradients (SM-G) operator dramatically increases the ability of a simple genetic algorithm-based neuroevolution method to find solutions in high-dimensional domains that require deep and/or recurrent neural networks (which tend to be particularly brittle to mutation), including domains that require processing raw pixels. By improving our ability to evolve deep neural networks, this new safer approach to mutation expands the scope of domains amenable to neuroevolution