论文标题
线性收敛的道格拉斯 - 拉赫福德分裂求解器，用于马尔可夫信息理论优化问题
A Linearly Convergent Douglas-Rachford Splitting Solver for Markovian Information-Theoretic Optimization Problems
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
In this work, we propose solving the Information bottleneck (IB) and Privacy Funnel (PF) problems with Douglas-Rachford Splitting methods (DRS). We study a general Markovian information-theoretic Lagrangian that includes IB and PF into a unified framework. We prove the linear convergence of the proposed solvers using the Kurdyka-Łojasiewicz inequality. Moreover, our analysis is beyond IB and PF and applies to any convex-weakly convex pair objectives. Based on the results, we develop two types of linearly convergent IB solvers, with one improves the performance of convergence over existing solvers while the other can be independent to the relevance-compression trade-off. Moreover, our results apply to PF, yielding a new class of linearly convergent PF solvers. Empirically, the proposed IB solvers IB obtain solutions that are comparable to the Blahut-Arimoto-based benchmark and is convergent for a wider range of the penalty coefficient than existing solvers. For PF, our non-greedy solvers can characterize the privacy-utility trade-off better than the clustering-based greedy solvers.
