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Renewed interest in the relationship between artificial and biological neuralnetworks motivates the study of gradient-free methods. Considering the linearregression model with random design, we theoretically analyze in this work thebiologically motivated (weight-perturbed) forward gradient scheme that is basedon random linear combination of the gradient. If d denotes the number ofparameters and k the number of samples, we prove that the mean squared error ofthis method converges for $k\gtrsim d^2\log(d)$ with rate $d^2\log(d)/k.$Compared to the dimension dependence d for stochastic gradient descent, anadditional factor $d\log(d)$ occurs.

Convergence guarantees for forward gradient descent in the linear regression model