使用熵正则化的软量化
Soft Quantization using Entropic Regularization
AI总结：
本文研究了熵正则化量化问题的性质与鲁棒性，采用 softmin 函数和熵正则化的 Wasserstein 距离，通过随机梯度方法求解，控制参数可调整难度，并在多种实验中验证了性能。
摘要：
量化问题旨在使用有限离散测度寻找 ${\mathbb{R}}^d$ 上概率测度的最佳近似。Wasserstein 距离是衡量近似质量的典型选择。本文研究了熵正则化量化问题的性质和鲁棒性，该问题放松了标准量化问题。所提出的近似技术自然地采用了 softmin 函数，该函数因在理论和实用性方面的鲁棒性而闻名。此外，我们使用熵正则化的 Wasserstein 距离来评估软量化问题近似的质量，并实现了随机梯度方法以获得最优解。我们提出的控制参数允许调整优化问题的难度级别，在处理极具挑战性的问题时提供了显著优势。同时，本文通过实验展示了该方法在各种情况下的性能。
英文摘要：
The quantization problem aims to find the best possible approximation of probability measures on ${\mathbb{R}}^d$ using finite, discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation. This contribution investigates the properties and robustness of the entropy-regularized quantization problem, which relaxes the standard quantization problem. The proposed approximation technique naturally adopts the softmin function, which is well known for its robustness in terms of theoretical and practicability standpoints. Moreover, we use the entropy-regularized Wasserstein distance to evaluate the quality of the soft quantization problem's approximation, and we implement a stochastic gradient approach to achieve the optimal solutions. The control parameter in our proposed method allows for the adjustment of the optimization problem's difficulty level, providing significant advantages when dealing with exceptionally challenging problems of interest. As well, this contribution empirically illustrates the performance of the method in various expositions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
