Disclosed is a method for producing a polymer through living polymerization, comprising forming an oligomer having a polymerization active end, which is an oligomer higher than an average 1.0-mer and lower than an average 4.0-mer or an average 4.0-mer, and polymerizing using the oligomer having a polymerization active end as an initiating species, wherein the acrylic acid-based polymer comprising a repeating unit derived from a poly(α-lower alkyl)acrylate, and a repeating unit derived from an (α-lower alkyl)acrylic ester represented by formula (I) wherein R1 represents a hydrogen atom or a lower alkyl group, and R2 represents an organic group having a polar group in an arm portion.