Guided Evolutionary Strategies: Escaping the curse of dimensionality in random search
Authors: Niru Maheswaranathan, Luke Metz, George Tucker, Dami Choi, Jascha Sohl-Dickstein
Keywords: evolutionary strategies, optimization, gradient estimators, biased gradients
TL;DR: We propose an optimization method for when only biased gradients are available--we define a new gradient estimator for this scenario, derive the bias and variance of this estimator, and apply it to example problems.
Abstract: Many applications in machine learning require optimizing a function whose true gradient is unknown, but where surrogate gradient information (directions that may be correlated with, but not necessarily identical to, the true gradient) is available instead. This arises when an approximate gradient is easier to compute than the full gradient (e.g. in meta-learning or unrolled optimization), or when a true gradient is intractable and is replaced with a surrogate (e.g. in certain reinforcement learning applications or training networks with discrete variables). We propose Guided Evolutionary Strategies, a method for optimally using surrogate gradient directions along with random search. We define a search distribution for evolutionary strategies that is elongated along a subspace spanned by the surrogate gradients. This allows us to estimate a descent direction which can then be passed to a first-order optimizer. We analytically and numerically characterize the tradeoffs that result from tuning how strongly the search distribution is stretched along the guiding subspace, and use this to derive a setting of the hyperparameters that works well across problems. Finally, we apply our method to example problems including truncated unrolled optimization and training neural networks with discrete variables, demonstrating improvement over both standard evolutionary strategies and first-order methods (that directly follow the surrogate gradient). We provide a demo of Guided ES at: redacted URL