Let \(X=(X,+)\) be an arbitrary topological group. The aim of the paper is to prove a regularity theorem for K-subquadratic set-valued functions, that is, solutions of the inclusion $$ 2F(s)+2F(t)\subset F(s+t)+F(s-t)+K, \quad s,t\in X, $$ with values in a topological vector space and where \(K\) is a cone in this space.