AI 中文总结
该研究针对约束动态投资组合，提出同网格对偶框架，利用原始对偶 bracket 实现价值损失证明与最优策略定位，通过多类实验验证了方法在不同资产规模下的有效性及高维瓶颈问题。
AI 中文摘要
神经和数值策略求解器即使在最优规则及其绑定约束不可用时，也能生成可行控制。原始对偶 bracket（区间）可证明价值损失，但无法定位最优策略或解释哪些约束真正绑定。本文证明，在同一声明的模拟网格上，一个 bracket 可同时支持这两个结论。对于多面体控制，精确的条件预算恒等式将残差重写为路径非负终端 Fenchel 缺陷，加上逐约束互补松弛项。标准 Doob 补偿消除了掩盖小残差的预算鞅。随后，Bellman 原语曲率条件产生具有尖锐 O(√G) 半径的占用加权策略区域，而配对约束松弛则对最优乘子进行下界估计并证明绑定面的存在。有限样本分辨率定理量化了证明目标策略容差或面所需的路径预算。锁定单资产和双资产审计覆盖所有外部策略误差且无错误面声明。精确包装器压力测试在 50 个资产下仍保持紧密性，而单独的状态依赖试点则将学习对偶的紧密性识别为高维瓶颈。参考解仅在校准后输入。
英文摘要
Neural and numerical policy solvers can produce feasible controls even when the optimal rule and its binding constraints are unavailable. A primal-dual bracket certifies value loss, but it does not locate the optimal policy or explain which constraints genuinely bind. We show that, on the same declared simulation grid, one bracket can support both conclusions. For polyhedral controls, an exact conditional budget identity rewrites the residual as a pathwise nonnegative terminal Fenchel defect plus date-by-constraint complementary-slackness terms. A canonical Doob compensation removes the budget martingale that obscures small residuals. Bellman-primitive curvature conditions then yield an occupancy-weighted policy region with the sharp O(sqrt(G)) radius, while a paired constraint relaxation lower-bounds the optimal multiplier and certifies a binding face. A finite-sample resolution theorem quantifies the path budget needed to certify a target policy tolerance or face. Locked one-asset and two-asset audits cover every external policy error and make no false face declaration. An exact-wrapper stress test remains tight through 50 assets, while a separate state-dependent pilot identifies learned-dual tightness as the high-dimensional bottleneck. Reference solutions enter only after certification.
