Optimal node perturbation in linear perceptrons with uncertain eligibility trace

Node perturbation learning has been receiving much attention as a method for achieving stochastic gradient descent. As it does not require direct gradient calculations, it can be applied to a reinforcement learning framework. However, in conventional node perturbation learning, the residual error due to perturbation is not eliminated even after convergence. Using infinitesimal perturbations suppresses the residual error, but such perturbations are less robust against uncertainty and noise in an eligibility trace, which is a memory of perturbation and input. We derive an optimal parameter schedule for node perturbation learning used with linear perceptrons with uncertainty in the eligibility trace. Our adaptive learning rule resolves the trade-off between robustness against the uncertainty and residual error reduction. The results obtained will be useful in designing learning rules and interpreting related biological knowledge.