论文标题
具有动态时间尺度的持久伴随方法，并应用于质量动力动力学
A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics
论文作者
论文摘要
在本文中，我们考虑了一个优化问题，其中在该控制变量上以控制变量进行参数的收缩映射的固定点进行评估，并在此控制变量上进行了优化。由于通常无法准确评估定点相对于参数的衍生物，因此一种方法是引入一个伴随的动态系统来估计梯度。使用此估计过程，优化算法在衍生估计和近似梯度下降步骤之间交替。我们分析了涉及动态时间缩放的方法的一种变体，在每个参数之后更新伴随系统，直到传递收敛阈值为止。我们证明，在某些条件下，算法可以找到目标函数的近似固定点。我们在化学动力学和吸引力网络中学习的环境中演示了这种方法。
In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, one approach is to introduce an adjoint dynamical system to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. We prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.
