---
title: "Risk-Sensitive Non-Parametric and Kernel Bandits"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.06489v1"
permalink: "https://feed.astralor.com/items/itm_75af5caab0e871cb6253cb0f"
published: "2026-11-04T13:27:07.000Z"
score: 57
channel: "tech"
tags: ["Risk-Sensitive Non-Parametric","Kernel Bandits","Cumulative Prospect Theory","CPT","Non-Parametric","Non-Parametric CPT Bandits"]
---

# Risk-Sensitive Non-Parametric and Kernel Bandits

## At a glance

We study non-parametric bandits in which arms are evaluated using Cumulative Prospect Theory (CPT) rather than expected reward. We consider continuous action spaces with arm-dependent noise and propose Non-Parametric CP…

## Key points

- We study non-parametric bandits in which arms are evaluated using Cumulative Prospect Theory (CPT) rather than expected reward.
- We consider continuous action spaces with arm-dependent noise and propose Non-Parametric CPT Bandits ($\mathtt{NPCB}$), an optimistic algorithm that decouples mean estimation from CPT-based decision-making.
- We prove CPT regret of order $\widetilde{\mathcal O}\bigl(\sqrt{T\,\dim_E(\mathcal F,T^{-2})\,\log N(\mathcal F,T^{-2},\|\cdot\|_\infty)}\bigr)$, where $\dim_E$ is the Eluder dimension of the function class $\mathcal F$…

## Full text

We study non-parametric bandits in which arms are evaluated using Cumulative Prospect Theory (CPT) rather than expected reward. We consider continuous action spaces with arm-dependent noise and propose Non-Parametric CPT Bandits ($\mathtt{NPCB}$), an optimistic algorithm that decouples mean estimation from CPT-based decision-making. We prove CPT regret of order $\widetilde{\mathcal O}\bigl(\sqrt{T\,\dim_E(\mathcal F,T^{-2})\,\log N(\mathcal F,T^{-2},\|\cdot\|_\infty)}\bigr)$, where $\dim_E$ is the Eluder dimension of the function class $\mathcal F$, $T$ is the time horizon, and $N$ is its covering number in the sup norm. This matches the order-wise regret of classical non-parametric bandits, showing that CPT risk sensitivity incurs no additional order-wise regret cost. We extend $\mathtt{NPCB}$ to unknown noise CDFs, retaining the known-CDF mean-learning term and adding a CDF-learning cost governed by a distributional Eluder dimension. We also study Kernel-CPT bandits and obtain information-gain-based regret bounds for a broad range of kernels, matching the corresponding risk-neutral kernel rates up to logarithmic factors.

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