论文标题
自适应能力方法用于估计马尔可夫链中的大偏差
Adaptive power method for estimating large deviations in Markov chains
论文作者
论文摘要
我们基于功率方法研究了随机算法的性能，该方法可以适应地学习了表征Markov过程加性功能的波动的大偏差功能，该功能用于物理中，用于建模非平衡系统。该算法是在对马尔可夫链的风险敏感控制的背景下引入的，最近适应了及时不断发展的扩散。在这里，我们对这种算法的收敛性进行了深入的研究，该算法接近动态相变，探索收敛速度作为学习率的函数以及包括传递学习的效果。我们用作测试示例，在Erdös-rényi随机图上随机步行的平均程度，该图显示了大部分图中随机行走的高度轨迹与悬空边缘演变的低度轨迹之间的过渡。结果表明，自适应能力方法有效接近动态相变，而与用于计算大偏差功能的其他算法相比，性能和复杂性具有许多优势。
We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model nonequilibrium systems. This algorithm was introduced in the context of risk-sensitive control of Markov chains and was recently adapted to diffusions evolving continuously in time. Here we provide an in-depth study of the convergence of this algorithm close to dynamical phase transitions, exploring the speed of convergence as a function of the learning rate and the effect of including transfer learning. We use as a test example the mean degree of a random walk on an Erdös-Rényi random graph, which shows a transition between high-degree trajectories of the random walk evolving in the bulk of the graph and low-degree trajectories evolving in dangling edges of the graph. The results show that the adaptive power method is efficient close to dynamical phase transitions, while having many advantages in terms of performance and complexity compared to other algorithms used to compute large deviation functions.
