The insights from the reduction to TBSGs can be leveraged to design efficient algorithms for solving discounted-sum reward polytopic RMDPs by utilizing the principles of policy iteration and Blackwell optimality. Policy iteration has been shown to be sound and efficient for solving TBSGs, and the reduction to TBSGs allows for the application of policy iteration techniques to RMDPs.
One approach could be to adapt the policy iteration algorithm used for long-run average TBSGs to handle discounted-sum objectives. By incorporating the principles of discounted-sum reward optimization and leveraging the reduction to TBSGs, it is possible to design an algorithm that iteratively refines policies to converge to optimal solutions for discounted-sum reward polytopic RMDPs.
Additionally, the reduction to TBSGs provides a framework for analyzing the relationship between discounted-sum reward RMDPs and TBSGs, allowing for the transfer of algorithmic techniques and insights between the two domains. By leveraging the connection established through the reduction, researchers can develop efficient algorithms that exploit the similarities and differences between the two problem domains to improve computational efficiency and solution quality.