Non-Parametric Rehearsal Learning via Conditional Mean Embeddings

2026-05-09

AI Summary

This study addresses the Avoiding Undesirable Futures (AUF) problem, which involves steering decisions away from predicted undesirable outcomes. The work proposes the first nonparametric rehearsal-based learning approach, reformulating the AUF objective via kernel methods into a unified representation that decouples desirability modeling from action-induced distributional shifts. It employs conditional mean embeddings to capture nonlinear dynamics and non-additive noise, and introduces a smooth Probit surrogate to handle the discontinuity of the desirability indicator function. By eschewing conventional parametric assumptions—such as linearity or additive noise—and avoiding reliance on specific data-generation mechanisms, the method demonstrates effectiveness, flexibility, and consistency on both synthetic and semi-synthetic benchmarks, while providing a controllable bound on approximation error.

Abstract

In machine learning, a critical class of decision-related problems concerns preventing predicted undesirable outcomes, referred to as the \textit{avoiding undesired future} (AUF) problem. To address this, the \textit{rehearsal learning} framework has been proposed to model influence relations for effective decisions. However, existing rehearsal methods rely on restrictive parametric assumptions such as linear systems or additive noise, limiting their practical applicability. In this paper, we propose the first non-parametric rehearsal learning approach for AUF without assuming specific functional forms of data generation processes. Specifically, we use kernel machinery to reformulate the AUF objective into a unified representation that disentangles desirability modeling from action-induced distributional changes. To handle the discontinuity of desirability indicator, we present a smooth Probit surrogate and provide an approximation error bound. Meanwhile, we capture the action-induced changes via conditional mean embeddings, and develop a kernel ridge regression based nested estimator for AUF objective with consistency guarantees. Such a formulation naturally accommodates nonlinear systems and non-additive noise, and empirical results on synthetic and real-data-derived semi-synthetic benchmarks demonstrate the effectiveness and flexibility of our approach.

Problem

• avoiding undesired future
• rehearsal learning
• non-parametric
• conditional mean embeddings
• machine learning

Innovation

• non-parametric rehearsal learning
• conditional mean embeddings
• avoiding undesired future
• kernel methods
• distributional shift