Adaptive portfolio optimization-based metamodel method for the multi-armed bandit problem of learning function in slope reliability analysis

Adaptive metamodels using single learning functions fail to consistently maintain the high accuracy or efficiency in calculating failure probabilities of slopes under all scenarios (e.g., natural vs. reservoir slopes) due to the No Free Lunch theorem. It poses a challenge in the adaptive selection of the optimal function under high-dimensional random field domains. To this end, we consider the selection problem as a multi-armed bandit problem, and thus propose a portfolio optimization-based adaptive polynomial-chaos Kriging (POPCK) method that dynamically balances exploration and exploitation of six distinct learning functions, thereby adaptively selecting better functions based on their historical performance. This adaptive selection could be performed under high-dimensional variables by incorporating Karhunen–Loève expansion and sliced inverse regression techniques into POPCK. The feasibility of the proposed method is demonstrated through four classic examples (involving natural, four soil layers, rainfall infiltration, and water level drawdown conditions). Results show that the proposed method exhibits good robustness for all examples, high accuracy (ranking 1st) and computational efficiency (ranking 2nd), whereas the performance of PCKs using the single learning functions fluctuates greatly. This method effectively mitigates the randomness of learning function selection, which is valuable for engineers who lack prior knowledge of optimal learning functions.