Randomized Forward Mode of Automatic Differentiation For Optimization Algorithms
This work addresses optimization efficiency for machine learning practitioners, but it appears incremental as it builds on existing forward mode automatic differentiation and focuses on specific algorithms like gradient descent and Polyak's heavy ball.
The authors tackled the problem of gradient computation in optimization by introducing a randomized forward mode gradient (RFG) as an alternative to backpropagation, resulting in a class of RFG-based algorithms with convergence analysis for quadratic functions and experimental verification.
We present a randomized forward mode gradient (RFG) as an alternative to backpropagation. RFG is a random estimator for the gradient that is constructed based on the directional derivative along a random vector. The forward mode automatic differentiation (AD) provides an efficient computation of RFG. The probability distribution of the random vector determines the statistical properties of RFG. Through the second moment analysis, we found that the distribution with the smallest kurtosis yields the smallest expected relative squared error. By replacing gradient with RFG, a class of RFG-based optimization algorithms is obtained. By focusing on gradient descent (GD) and Polyak's heavy ball (PHB) methods, we present a convergence analysis of RFG-based optimization algorithms for quadratic functions. Computational experiments are presented to demonstrate the performance of the proposed algorithms and verify the theoretical findings.