A slightly better algorithm can be derived by doing a few more analytic steps before substituting in v t . Continuing from (11.29): w t+1 = w t + ↵E ⇥ ⇢ t (x t x t+1 )x > t ⇤ E ⇥ x t x > t ⇤ 1 E[⇢ t t x t ] = w t + ↵ E ⇥ ⇢ t x t x > t ⇤ E ⇥ ⇢ t x t+1 x > t ⇤ E ⇥ x t x > t ⇤ 1 E[⇢ t t x t ] = w t + ↵ E ⇥ x t x > t ⇤ E ⇥ ⇢ t x t+1 x > t ⇤ E ⇥ x t x > t ⇤ 1 E[⇢ t t x t ] = w t + ↵ ⇣ E[x t ⇢ t t ] E ⇥ ⇢ t x t+1 x > t ⇤ E ⇥ x t x > t ⇤ 1 E[⇢ t t x t ] ⌘ ⇡ w t + ↵ E[x t ⇢ t t ] E ⇥ ⇢ t x t+1 x > t ⇤ v t (based on (11.28)) ⇡ w t + ↵⇢ t t x t x t+1 x > t v t , (sampling) which again is O ( d ) if the final product ( x > t v t ) is done first. This algorithm is known as either TD(0) with gradient correction (TDC) or, alternatively, as GTD(0)