AA-infinity structures related to bi-Koszul algebras

Let AA be a bi-Koszul algebra. We describe all possible A∞A∞-algebra structures on the Ext-algebra E(A)E(A) and prove that E(A)E(A) must be [m2,m3][m2,m3]-finitely generated. We give an equivalent description of the condition for a connected graded algebra to be a bi-Koszul algebra in the language of A∞A∞-algebras. We discuss decomposition in the case that E(A)E(A) is endowed with minimal number of multiplications.