论文标题
部分可观测时空混沌系统的无模型预测
Anderson Acceleration for Partially Observable Markov Decision Processes: A Maximum Entropy Approach
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。
Partially observable Markov decision processes (POMDPs) is a rich mathematical framework that embraces a large class of complex sequential decision-making problems under uncertainty with limited observations. However, the complexity of POMDPs poses various computational challenges, motivating the need for an efficient algorithm that rapidly finds a good enough suboptimal solution. In this paper, we propose a novel accelerated offline POMDP algorithm exploiting Anderson acceleration (AA) that is capable of efficiently solving fixed-point problems using previous solution estimates. Our algorithm is based on the Q-function approximation (QMDP) method to alleviate the scalability issue inherent in POMDPs. Inspired by the quasi-Newton interpretation of AA, we propose a maximum entropy variant of QMDP, which we call soft QMDP, to fully benefit from AA. We prove that the overall algorithm converges to the suboptimal solution obtained by soft QMDP. Our algorithm can also be implemented in a model-free manner using simulation data. Provable error bounds on the residual and the solution are provided to examine how the simulation errors are propagated through the proposed algorithm. Finally, the performance of our algorithm is tested on several benchmark problems. According to the results of our experiments, the proposed algorithm converges significantly faster without degrading the solution quality compared to its standard counterparts.
