  We consider the problem of estimating an upper bound on the capacity of a
memoryless channel with unknown channel law and continuous output alphabet. A
novel data-driven algorithm is proposed that exploits the dual representation
of capacity where the maximization over the input distribution is replaced with
a minimization over a reference distribution on the channel output. To
efficiently compute the required divergence maximization between the
conditional channel and the reference distribution, we use a modified mutual
information neural estimator that takes the channel input as an additional
parameter. We numerically evaluate our approach on different memoryless
channels and show empirically that the estimated upper bounds closely converge
either to the channel capacity or to best-known lower bounds.
