Enabling Optimal Decisions in Rehearsal Learning under CARE Condition

Abstract

In the field of machine learning (ML), an essential type of decision-related problem is known as AUF (Avoiding Undesired Future): if an ML model predicts an undesired outcome, how can decisions be made to prevent it? Recently, a novel framework called *rehearsal learning* has been proposed to address the AUF problem. Despite its utility in modeling uncertainty for decision-making, it remains unclear *under what conditions* and *how* optimal actions that maximize the *AUF probability* can be identified. In this paper, we propose *CARE* (CAnonical REctangle), a condition under which the maximum AUF probability can be achieved. Under the CARE condition, we present a projection-Newton algorithm to select actions and prove that the algorithm achieves superlinear convergence to the optimal one. Besides, we provide a generalization method for adopting the algorithm to AUF scenarios beyond the CARE condition. Finally, we demonstrate that a closed-form solution exists when the outcome is a singleton variable, substantially reducing the time complexity of decision-making. Experiments validate the effectiveness and efficiency of our method.