| Abstract: |
| This paper aims to extend the BML method proposed in [Probabilistic Framework of Howard`s Policy Iteration: BML Evaluation and Robust Convergence Analysis, IEEE TAC, 2024, vo.69, no.8, pp.5200-5215] to make it applicable to more general coupled nonlinear FBSDEs. We interpret BML from the fixed-point iteration perspective and show that optimizing BML is equivalent to minimizing the distance between two consecutive trial solutions in a fixed-point iteration. Thus, this paper provides a theoretical foundation for an optimization-based approach to solving FBSDEs. We also empirically evaluate the method through four numerical experiments. |
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