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Local learning rules in biological neural networks (BNNs) are commonlyreferred to as Hebbian learning. [26] links a biologically motivated Hebbianlearning rule to a specific zeroth-order optimization method. In this work, westudy a variation of this Hebbian learning rule to recover the regressionvector in the linear regression model. Zeroth-order optimization methods areknown to converge with suboptimal rate for large parameter dimension comparedto first-order methods like gradient descent, and are therefore thought to bein general inferior. By establishing upper and lower bounds, we show, however,that such methods achieve near-optimal rates if only queries of the linearregression loss are available. Moreover, we prove that this Hebbian learningrule can achieve considerably faster rates than any non-adaptive method thatselects the queries independently of the data.

Hebbian learning inspired estimation of the linear regression parameters from queries