集成动态策略的结构化随机表示
Structured Stochastic Representations of Integrated Dynamic Strategies
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- Universidad Nacional Autónoma de Honduras (UNAH)（洪都拉斯国立自治大学）
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中文总结 AI 辅助
本文提出一种基于制度索引和图约束列随机算子的结构化表示方法，用于动态分配决策，并通过可辨识性分析和认证测试实现近最优决策，贡献在于表示-辨识-决策工作流程。
中文摘要 AI 辅助
动态分配决策将当前资源使用与不断演变的内部条件、延迟回报和未来成本联系起来。我们通过四个概率定位来表示这种相互作用，这些定位通过基于制度索引的、图约束的列随机算子相互关联。行动前的状态或上下文选择一个局部仿射模型，而依赖于行动的变化更新后续制度，从而产生非线性演化的因果切换表示。我们刻画了算子相对于图、随机约束和采样嵌入的可辨识性，将系数恢复与决策域上的预测等价性区分开来。随后，决策制定通过可实施的回报-成本可接受区域来表述。有限时域误差传播提供了保守的分类边界，同时区间区分了模型相对近最优性与在声明的有限策略类上认证的ε-最优性。当制度索引的随机反馈满足相同的认证测试时，允许其被采纳。用于个人准备、供应商参与和客户保留的可复现合成实验室展示了精确、算子提供和噪声反馈的情况。多项实验表明，随着样本量的增加，反馈函数的恢复得到改善，未解决的决策减少，而无限制的离策略恢复仍然有限。贡献在于一个保持结构的表示-辨识-决策工作流程，而非特定领域的生理或商业校准。
英文摘要
Dynamic allocation decisions couple present resource use to evolving internal conditions, delayed returns, and future costs. We represent this interaction by four probability localizations linked through regime-indexed, graph-constrained column-stochastic operators. Pre-action state or context selects a locally affine model, while action-dependent changes update subsequent regimes, yielding a causal switched representation of nonlinear evolution. We characterize operator identifiability relative to the graph, the stochastic constraints, and the sampled embedding, separating coefficient recovery from predictive equivalence on the decision domain. Decision making is then formulated through implementable return--cost acceptability regions. Finite-horizon error propagation supplies conservative classification margins, and simultaneous intervals distinguish model-relative near-optimality from certified $ε$-optimality over a declared finite policy class. Regime-indexed stochastic feedback is admitted when it satisfies the same certification test. Reproducible synthetic laboratories for personal preparation, supplier participation, and customer retention illustrate exact, operator-supplied, and noisy feedback cases. Multinomial experiments show improving recovery of the feedback function and fewer unresolved decisions with increasing sample size, while unrestricted off-policy recovery remains limited. The contribution is a structure-preserving representation--identification--decision workflow, not a domain-specific physiological or commercial calibration.
