Erdős problem 1028

Let $$H(n)=\min_f \max_{X\subseteq \{1,\ldots,n\}} \left\lvert \sum_{x<y\in X} f(x,y)\right\rvert,$$ where $f$ ranges over all functions $f:\{1,\ldots,n\}^2\to \{-1,1\}$. Estimate $H(n)$.