From Value Bounds to Policy-Distance and Active-Face Certificates: Same-Grid Duality for Constrained Dynamic Portfolios

Battle Count: 68

Highly relevant for quantitative trading practitioners who deploy neural or simulation-based portfolio policies. The paper provides a rigorous framework to answer two critical validation questions: (1) how far the optimal policy can be from the deployed rule, and (2) whether boundary decisions (zero holdings, binding leverage caps) are economically genuine or numerical artifacts. This is directly applicable to portfolio construction, risk budgeting, and strategy validation. The Merton and predictable-return models are standard in quantitative finance. However, the method is primarily a verification/audit tool rather than a trading strategy generator, and the high-dimensional learned-dual bottleneck limits immediate practical scalability.

The verification pipeline involves multiple stages: (1) training and freezing a neural primal policy via BPTT, (2) generating and algebraically restoring a feasible dual (polyhedral projection, canonical multiplier selection), (3) computing Doob-compensated residuals on held-out paths, (4) estimating Bellman-primitive curvature via conditional dual restarts, (5) constructing occupancy-weighted policy radii, and (6) performing paired constraint relaxation tests with simultaneous Bonferroni corrections. The mathematical machinery (Fenchel duality, Doob decomposition, KKT ledger attribution) is sophisticated. The state-dependent experiments require neural dual networks, conditional restarts, and stratified sampling. However, the Merton benchmark with exact dual wrapper is tractable. The paper provides detailed implementation specifications in the Electronic Companion.

The paper provides extensive implementation details in the Electronic Companion, including exact parameterizations, locked protocols with pre-declared hyperparameters, seed-level results, computational budgets, and wall-clock accounting. All proofs are provided. The neural architectures (3-layer width-128 for Merton, specific dual network outputs) are fully specified. However, no code repository is explicitly linked, and the state-dependent experiments require specific neural training infrastructure. The locked replication protocol (development seeds vs. held-out seeds) is well-documented.