Biological neurons meet zeroth order optimisation
Wouter Koolen, CWI Amsterdam / University of Twente
We investigate a simple model for biological neurons from the perspective of optimisation. We start by reviewing some descriptive empirical neuroscience to motivate a particular iterative scheme for updating weights based on reward. We then wonder if, and how well, this scheme actually optimises reward. To study this question, we will analyse the scheme as a two-point zeroth-order optimisation method, and evaluate it for the one-neuron task of linear regression. We derive upper bounds for the scheme, present lower bounds for the problem, and contrast the results with first-order methods. We conclude by reflecting on the consequences for neuroscience.
Based on joint work with Johannes Schmidt-Hieber.
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