  A common way of characterizing minimax estimators in point estimation is by
moving the problem into the Bayesian estimation domain and finding a least
favorable prior distribution. The Bayesian estimator induced by a least
favorable prior, under mild conditions, is then known to be minimax. However,
finding least favorable distributions can be challenging due to inherent
optimization over the space of probability distributions, which is
infinite-dimensional. This paper develops a dimensionality reduction method
that allows us to move the optimization to a finite-dimensional setting with an
explicit bound on the dimension. The benefit of this dimensionality reduction
is that it permits the use of popular algorithms such as projected gradient
ascent to find least favorable priors. Throughout the paper, in order to make
progress on the problem, we restrict ourselves to Bayesian risks induced by a
relatively large class of loss functions, namely Bregman divergences.
