  Sutton, Szepesv\'{a}ri and Maei introduced the first gradient
temporal-difference (GTD) learning algorithms compatible with both linear
function approximation and off-policy training. The goal of this paper is (a)
to propose some variants of GTDs with extensive comparative analysis and (b) to
establish new theoretical analysis frameworks for the GTDs. These variants are
based on convex-concave saddle-point interpretations of GTDs, which effectively
unify all the GTDs into a single framework, and provide simple stability
analysis based on recent results on primal-dual gradient dynamics. Finally,
numerical comparative analysis is given to evaluate these approaches.
