Programs involving discontinuities introduced by control flow constructs such
as conditional branches pose challenges to mathematical optimization methods
that assume a degree of smoothness in the objective function's response
surface. Smooth interpretation (SI) is a form of abstract interpretation that
approximates the convolution of a program's output with a Gaussian kernel, thus
smoothing its output in a principled manner. Here, we combine SI with automatic
differentiation (AD) to efficiently compute gradients of smoothed programs. In
contrast to AD across a regular program execution, these gradients also capture
the effects of alternative control flow paths. The combination of SI with AD
enables the direct gradient-based parameter synthesis for branching programs,
allowing for instance the calibration of simulation models or their combination
with neural network models in machine learning pipelines. We detail the effects
of the approximations made for tractability in SI and propose a novel Monte
Carlo estimator that avoids the underlying assumptions by estimating the
smoothed programs' gradients through a combination of AD and sampling. Using
DiscoGrad, our tool for automatically translating simple C++ programs to a
smooth differentiable form, we perform an extensive evaluation. We compare the
combination of SI with AD and our Monte Carlo estimator to existing
gradient-free and stochastic methods on four non-trivial and originally
discontinuous problems ranging from classical simulation-based optimization to
neural network-driven control. While the optimization progress with the
SI-based estimator depends on the complexity of the programs' control flow, our
Monte Carlo estimator is competitive in all problems, exhibiting the fastest
convergence by a substantial margin in our highest-dimensional problem.

控制流结构中引入的不连续性对于假设目标函数响应曲面具有一定平滑性的数学优化方法构成挑战。在此论文中，我们将平滑解释（SI）与自动微分（AD）相结合，以高效计算平滑程序的梯度。SI 与 AD 的结合使得参数综合可以直接基于梯度进行分支程序，例如校准模拟模型或将其与神经网络模型结合在机器学习流程中。我们详细说明了 SI 中为确保可行性所做的近似效果，并提出了一种新的蒙特卡罗估计器，通过 AD 和抽样的组合来估计平滑程序的梯度，从而避免了潜在的假设。通过使用我们的工具 DiscoGrad 将简单的 C++ 程序自动转换为平滑可微形式，我们进行了广泛的评估。我们将 SI 与 AD 的组合以及我们的蒙特卡罗估计器与现有的无梯度和随机方法在四个非平凡的问题上进行比较，这些问题从经典的基于模拟的优化到神经网络驱动的控制。虽然 SI 估计器的优化进展取决于程序控制流的复杂性，但我们的蒙特卡罗估计器在所有问题中都具有竞争力，在最高维问题中具有明显最快的收敛速度。