  Hebbian meta-learning has recently shown promise to solve hard reinforcement
learning problems, allowing agents to adapt to some degree to changes in the
environment. However, because each synapse in these approaches can learn a very
specific learning rule, the ability to generalize to very different situations
is likely reduced. We hypothesize that limiting the number of Hebbian learning
rules through a "genomic bottleneck" can act as a regularizer leading to better
generalization across changes to the environment. We test this hypothesis by
decoupling the number of Hebbian learning rules from the number of synapses and
systematically varying the number of Hebbian learning rules. The results in
this paper suggest that simultaneously learning the Hebbian learning rules and
their assignment to synapses is a difficult optimization problem, leading to
poor performance in the environments tested. However, parallel research to ours
finds that it is indeed possible to reduce the number of learning rules by
clustering similar rules together. How to best implement a "genomic bottleneck"
algorithm is thus an important research direction that warrants further
investigation.
