Smart classify and optimize for portfolio construction - a differentiable quadratic programming approach

Portfolio construction requires not only allocating capital but also selecting which assets to include. In practice, these two steps are typically separated: a clas-sifier such as a support vector machine (SVM) screens assets, after which a mean–variance optimizer (MVO) allocates capital on the retained set. This two-stage design enforces a fixed screening boundary, ignoring the fact that investors with different return targets may prefer different sets of assets. We propose an end-to-end framework that integrates screening and allocation into a single dif-ferentiable optimization pipeline. Both the SVM and the MVO are represented as quadratic programming (QP) layers, connected through a differentiable gat-ing mechanism that enables gradient-based training. This formulation adapts the screening hyperplane to the investor’s return goal, effectively coupling asset selection with allocation. Empirical results on sector-diversified U.S. equities demonstrate that the integrated model delivers improved risk–return trade-offs over the two-stage baseline, with pronounced gains in volatile market regimes, representing the first differentiable integration of SVM and MVO.