Risk-Sensitive Non-Parametric and Kernel Bandits
Abstract
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 (NPCB), an optimistic algorithm that decouples mean estimation from CPT-based decision-making. We prove CPT regret of order 𝒪̃(√(T dimE(ℱ,T−2) log N(ℱ,T−2,|·|∞))), where dimE is the Eluder dimension of the function class 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 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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BibTeX
@misc{dey2026risksensitive,
title = {{Risk-Sensitive Non-Parametric and Kernel Bandits}},
author = {Devdan Dey and Sujoy Bhore and Avishek Ghosh},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06489},
eprint = {2611.06489},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06489},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Risk-Sensitive Non-Parametric and Kernel Bandits
AU - Devdan Dey
AU - Sujoy Bhore
AU - Avishek Ghosh
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06489
UR - https://arxiv.org/abs/2611.06489
AB - 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 (NPCB), an optimistic algorithm that decouples mean estimation from CPT-based decision-making. We prove CPT regret of order 𝒪̃(√(T dim_E(ℱ,T^−2) log N(ℱ,T^−2,|·|_∞))), where dim_E is the Eluder dimension of the function class 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 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.
ER -