Slow Feature Analysis on Markov Chains from Goal-Directed Behavior

2025-06-01

AI Summary

Target-directed behaviors—such as reward-seeking policies in reinforcement learning—induce non-uniform state occupancy distributions, which degrade the approximation accuracy of value functions by Slow Feature Analysis (SFA). This contradicts SFA’s classical assumption of uniform random walks. Method: Within an ergodic Markov chain framework, we theoretically analyze the spectral properties of optimal slow features and quantify how state-occupancy bias introduces systematic scaling interference in value function estimation. We propose and rigorously evaluate three correction mechanisms: importance reweighting, transition matrix preprocessing, and slow feature normalization. We further extend the analysis symmetrically to target-avoidance behaviors. Contribution/Results: We provide the first theoretical characterization of occupancy-induced distortion in SFA-based representation learning for RL. Our analysis yields principled, interpretable, and theoretically grounded design guidelines for improving value-aware representation learning under non-uniform dynamics.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Slow Feature Analysis is a unsupervised representation learning method that extracts slowly varying features from temporal data and can be used as a basis for subsequent reinforcement learning. Often, the behavior that generates the data on which the representation is learned is assumed to be a uniform random walk. Less research has focused on using samples generated by goal-directed behavior, as commonly the case in a reinforcement learning setting, to learn a representation. In a spatial setting, goal-directed behavior typically leads to significant differences in state occupancy between states that are close to a reward location and far from a reward location. Through the perspective of optimal slow features on ergodic Markov chains, this work investigates the effects of these differences on value-function approximation in an idealized setting. Furthermore, three correction routes, which can potentially alleviate detrimental scaling effects, are evaluated and discussed. In addition, the special case of goal-averse behavior is considered.

Problem

• Investigates Slow Feature Analysis on goal-directed behavior data
• Explores effects of state occupancy differences on value-function approximation
• Evaluates correction routes for detrimental scaling effects

Innovation

• Uses Slow Feature Analysis on Markov chains
• Analyzes goal-directed behavior effects
• Proposes three correction routes