Soft-Radial Projection for Constrained End-to-End Learning

Battle Count: 59

Highly relevant to quantitative trading. The paper directly addresses portfolio optimization with hard constraints (simplex, capped simplex) and transaction costs, which are central to practical portfolio management. The method enables end-to-end learning of trading policies that strictly satisfy budget and capacity constraints without penalty tuning or post-hoc repair. The Sharpe ratio maximization formulation with L1 turnover costs is directly applicable to real trading systems. The demonstrated improvement over orthogonal projection (0.90 vs 0.25 SR on Liquid dataset) and optimization-based baselines (DC3, HardNet) shows practical significance. However, the paper focuses on the constraint enforcement mechanism rather than alpha generation or market microstructure.

Moderate complexity. For polyhedral constraints (simplex, capped simplex), the radial intersection α*(u) has a closed-form solution (Equation 6) that is O(m) per sample and fully parallelizable. For Euclidean balls, a simple quadratic formula suffices. For general convex sets, a 1D monotonic root-finding (Newton-Raphson or bisection) is needed. The radial contraction functions r(ρ) are simple parameterized forms (rational, exponential, hyperbolic). The main implementation effort lies in correctly computing the Jacobian for backpropagation and handling the non-differentiable boundary points. The method is a drop-in layer requiring no iterative solvers, making it simpler than DC3 or HardNet implementations.

Code is available at an anonymous repository (https://anonymous.4open.science/r/soft-radial-projection-e2e-icml/). Hyperparameters are fully specified in Table 4. The method uses standard architectures (LSTM, MLP) and publicly available data (Yahoo Finance, NYC TLC). Five random seeds are used for all experiments. However, the anonymous link may expire, and some implementation details for competitor methods (DC3, HardNet adaptations) require careful reading of Appendix C.2.