  We show that the Wang-Landau algorithm can be formulated as a stochastic
gradient descent algorithm minimizing a smooth and convex objective function,
of which the gradient is estimated using Markov chain Monte Carlo iterations.
The optimization formulation provides us a new way to establish the convergence
rate of the Wang-Landau algorithm, by exploiting the fact that almost surely,
the density estimates (on the logarithmic scale) remain in a compact set, upon
which the objective function is strongly convex. The optimization viewpoint
motivates us to improve the efficiency of the Wang-Landau algorithm using
popular tools including the momentum method and the adaptive learning rate
method. We demonstrate the accelerated Wang-Landau algorithm on a
two-dimensional Ising model and a two-dimensional ten-state Potts model.
