  In timing-based neural codes, neurons have to emit action potentials at
precise moments in time. We use a supervised learning paradigm to derive a
synaptic update rule that optimizes via gradient ascent the likelihood of
postsynaptic firing at one or several desired firing times. We find that the
optimal strategy of up- and downregulating synaptic efficacies can be described
by a two-phase learning window similar to that of Spike-Timing Dependent
Plasticity (STDP). If the presynaptic spike arrives before the desired
postsynaptic spike timing, our optimal learning rule predicts that the synapse
should become potentiated. The dependence of the potentiation on spike timing
directly reflects the time course of an excitatory postsynaptic potential. The
presence and amplitude of depression of synaptic efficacies for reversed spike
timing depends on how constraints are implemented in the optimization problem.
Two different constraints, i.e., control of postsynaptic rates or control of
temporal locality,are discussed.
