Using Data-Driven Feasible Region Approximations to Handle Nonlinear Constraints When Applying CMA-ES to the Initial Margin Optimization Problem

Sammanfattning: The introduction of initial margin requirements for non-cleared OTC derivatives has made it possible to optimize initial margin when considering a network of trading participants. Applying CMA-ES, this thesis has explored a new method to handle the nonlinear constraints present in the initial margin optimization problem. The idea behind the method and the research question in this thesis are centered around leveraging data created during optimization. Specifically, by creating a linear approximation of the feasible region using support vector machines and in turn applying a repair strategy based on projection. The hypothesis was that by repairing solutions an increase in convergence speed should follow. In order to answer the research question, a reference method was at first created. Here CMA-ES along with feasibility rules was used, referred to as CMA-FS. The proposed method of optimization data leveraging (ODL) was then appended to CMA-FS, referred to as CMA-ODL. Both algorithms were then applied to a single initial margin optimization problem 100 times each with different random seeds used for sampling in the optimization algorithms. The results showed that CMA-ODL converged significantly faster than CMA-FS, without affecting final objective values significantly negatively. Convergence was measured in terms of iterations and not computational time. On average a 5% increase in convergence speed was achieved with CMA-ODL. No significant difference was found between CMA-FS and CMA-ODL in terms of the percentage of infeasible solutions generated. A reason behind the lack of a reduction in violations can be due to how ODL is implemented with the CMA-ES algorithm. Specifically, ODL will lead to a greater number of feasible solutions being available during recombination in CMA-ES. Although, due to the projection, the solutions after projection are not completely reflective of the actual parameters used for that generation. The projection should also bias the algorithm towards the boundary of the feasible region. Still, the performative difference in terms of convergence speed was significant. In conclusion, the proposed boundary constraint handling method increased performance, but it is not known whether the method has any major practical applicability, due to the restriction to only considering the number of iterations and not the computational time.