TL;DR#
Many real-world sequential decision-making problems involve uncertainties and long-term costs. Traditional methods often struggle with these, and robust average cost MDPs are designed to handle such complexities. However, finding efficient and reliable algorithms for robust average-cost MDPs is challenging. Existing approaches often lack guarantees of convergence to the globally optimal solution.
This paper introduces a robust policy mirror descent algorithm to solve this problem. The algorithm cleverly handles the non-differentiability inherent in robust average cost MDPs using a sub-gradient approach and guarantees global convergence. The authors prove that it converges linearly with increasing step size and with a complexity of O(1/ε) for constant step sizes. Simulation results demonstrate the method’s effectiveness on various benchmark problems.
Key Takeaways#
Why does it matter?#
This paper is crucial for researchers in reinforcement learning and robust optimization because it presents the first policy-based algorithm with proven global convergence for robust average cost Markov Decision Processes (MDPs). This addresses a significant limitation in existing methods and opens up new avenues for tackling real-world problems with uncertain dynamics and long-term cost considerations. The theoretical analysis provides valuable insights for algorithm design and understanding convergence behavior, and the simulation results demonstrate its practical effectiveness.
Visual Insights#
🔼 The figure displays the results of two algorithms, Robust Policy Mirror Descent and Non-Robust Policy Mirror Descent, applied to the Garnet(3, 2) problem. The x-axis represents the iteration number, and the y-axis represents the average cost. The graph shows the convergence of both algorithms over multiple trials (indicated by shaded regions representing standard deviations), demonstrating the performance of the robust method relative to the non-robust approach.
read the caption
Figure 1: Garnet(3, 2)
Full paper#
