Non-Parametric Rehearsal Learning via Conditional Mean Embeddings

In machine learning, a critical class of decision-related problems concerns preventing predicted undesirable outcomes, referred to as the *avoiding undesired future* (AUF) problem. To address this, the *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 retain constraint-margin information beyond binary success labels, we present a smooth Probit surrogate with an approximation error bound. We estimate the smoothed AUF objective by scalar response regression and CME-based adjustment, with pointwise consistency at a fixed query and fixed smoothing parameter under stated spectral conditions. Such a formulation naturally accommodates nonlinear systems and non-additive noise; empirical results on synthetic and real-data-derived semi-synthetic benchmarks demonstrate effectiveness and flexibility of our approach.