Geometric Ergodicity

Geometric ergodicity, a property signifying the long-term stability and convergence of a system's behavior, is a central theme in diverse fields, from robotics and machine learning to statistical physics. Current research focuses on establishing conditions for geometric ergodicity in various models, including stochastic gradient Langevin dynamics (SGLD) and Adam-type algorithms, and on developing methods to achieve or leverage this property for improved performance, such as ergodic search strategies in robotics and robust reinforcement learning. Understanding and ensuring geometric ergodicity is crucial for guaranteeing the reliability and efficiency of algorithms and systems across numerous applications, leading to more robust and predictable outcomes.