Non-Parametric Rehearsal Learning via Conditional Mean Embeddings

TL;DR

This paper introduces a novel non-parametric rehearsal learning method using kernel embeddings to address the avoiding undesired future problem in machine learning, overcoming limitations of parametric assumptions.

Contribution

It presents the first non-parametric approach for AUF that employs kernel methods and conditional mean embeddings, enabling modeling of nonlinear systems without restrictive assumptions.

Findings

Effective on synthetic and real-data benchmarks.

Handles nonlinear systems and non-additive noise.

Provides theoretical consistency guarantees.

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.