  Excitation-inhibition (E-I) balance is ubiquitously observed in the cortex.
Recent studies suggest an intriguing link between balance on fast timescales,
tight balance, and efficient information coding with spikes. We further this
connection by taking a principled approach to optimal balanced networks of
excitatory (E) and inhibitory (I) neurons. By deriving E-I spiking neural
networks from greedy spike-based optimizations of constrained minimax
objectives, we show that tight balance arises from correcting for deviations
from the minimax optima. We predict specific neuron firing rates in the network
by solving the minimax problem, going beyond statistical theories of balanced
networks. Finally, we design minimax objectives for reconstruction of an input
signal, associative memory, and storage of manifold attractors, and derive from
them E-I networks that perform the computation. Overall, we present a novel
normative modeling approach for spiking E-I networks, going beyond the
widely-used energy minimizing networks that violate Dale's law. Our networks
can be used to model cortical circuits and computations.
