Risk-Sensitive Non-Parametric and Kernel Bandits

TL;DR

The paper introduces Non-Parametric CPT Bandits (NPCB), an algorithm for continuous-action bandits that uses Cumulative Prospect Theory to model risk-sensitive decision-making. It achieves regret bounds matching classical non-parametric bandits in order, showing no additional cost from risk sensitivity. Extensions to unknown noise distributions and kernel-based methods maintain strong theoretical guarantees.

Why It Matters

This work enables more realistic modeling of human-like risk preferences in sequential decision-making under uncertainty, without sacrificing performance. It extends non-parametric bandit theory to behavioral economics frameworks, supporting applications in personalized recommendation, clinical trials, and adaptive systems where risk attitudes matter.

Key Findings

• NPCB achieves order-optimal regret under CPT by decoupling mean estimation from risk-sensitive evaluation.
• The regret bound depends on Eluder dimension and covering number, matching known rates for risk-neutral non-parametric bandits.
• Extensions to unknown noise distributions introduce a distributional Eluder dimension, and kernel-based variants achieve information-gain-based bounds matching risk-neutral rates up to log factors.