A method for producing a copolymer for semiconductor lithography containing less metal impurities, and a method for purifying a polymerization initiator for production of the copolymer, are provided. The method for purifying a polymerization initiator to be used for production of a polymer includes a filtering step wherein a solution of a polymerization initiator dissolved in an organic solvent is allowed to pass through a filter having a nominal pore size of not more than 1.0 μm, to reduce the sodium content of the polymerization initiator solution to not more than 300 ppb with respect to the weight of the polymerization initiator. Further, the method for producing a copolymer for semiconductor lithography includes a polymerization step wherein the polymer for semiconductor lithography is synthesized by a radical polymerization reaction in the presence of a polymerization initiator purified by the above purification method.