黑盒优化器与偏好冲击（Taste Shocks）的对比
Black-box Optimizers vs Taste Shocks
AI总结：
针对离散状态空间法不可行的多维动态规划求解问题，对比偏好冲击与四种黑盒优化器在含长期债务的违约投资组合模型中的表现，发现结合B样条的Powell算法最可行。
摘要：
我们评估并拓展了动态规划中含二元及多个连续选择变量模型的求解方法，尤其适用于离散状态空间求解方法不可行的场景。为此，我们采用偏好冲击（taste shocks）或应用数学家用于算法基准测试的黑盒优化器来近似求解。我们将这些方法应用于一个违约框架，其中智能体需要求解含长期债务的投资组合问题。研究表明，求解方法的选择至关重要，因为偏好冲击方法在多维问题中无法实现收敛。我们对比了四种优化算法的相对优势：Nelder-Mead下山单纯形算法、带LINMIN的Powell方向集算法、共轭梯度法BOBYQA，以及拟牛顿Davidon-Fletcher-Powell（DFPMIN）算法。除最后一种外，其余所有方法都适用于导数难以计算的场景。最终我们发现，结合B样条求值的Powell程序虽然速度较慢，但是最可行的选择；BOBYQA位居第二，另外两种方法表现较差。
英文摘要：
We evaluate and extend the solution methods for models with binary and multiple continuous choice variables in dynamic programming, particularly in cases where a discrete state space solution method is not viable. Therefore, we approximate the solution using taste shocks or black-box optimizers that applied mathematicians use to benchmark their algorithms. We apply these methods to a default framework in which agents have to solve a portfolio problem with long-term debt. We show that the choice of solution method matters, as taste shocks fail to attain convergence in multidimensional problems. We compare the relative advantages of using four optimization algorithms: the Nelder-Mead downhill simplex algorithm, Powell's direction-set algorithm with LINMIN, the conjugate gradient method BOBYQA, and the quasi-Newton Davidon-Fletcher-Powell (DFPMIN) algorithm. All of these methods, except for the last one, are preferred when derivatives cannot be easily computed. Ultimately, we find that Powell's routine evaluated with B-splines, while slow, is the most viable option. BOBYQA came in second place, while the other two methods performed poorly.
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