---
title: "Does LinUCB Need Valid Confidence Sets?"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.04641v1"
permalink: "https://feed.astralor.com/items/itm_578a01f84a6968bdb2858be0"
published: "2026-11-03T10:30:32.000Z"
score: 56
channel: "ai"
tags: ["Does LinUCB Need","Valid Confidence Sets","LinUCB","Our"]
---

# Does LinUCB Need Valid Confidence Sets?

## 速览

We show that replacing LinUCB's usual confidence width $β$ by any fixed $α>0$ preserves sublinear regret when the action set is $M$-smooth and $m$-strongly convex. Our high-probability regret bound for this generalisati…

## 关键点

- We show that replacing LinUCB's usual confidence width $β$ by any fixed $α>0$ preserves sublinear regret when the action set is $M$-smooth and $m$-strongly convex.
- Our high-probability regret bound for this generalisation, $α$-LinUCB, establishes that valid confidence sets are not necessary for the success of LinUCB.
- We identify the mechanism behind this result: action-set curvature drives $α$-LinUCB to explore every direction, even when optimism is not guaranteed.

## 全文

We show that replacing LinUCB's usual confidence width $β$ by any fixed $α>0$ preserves sublinear regret when the action set is $M$-smooth and $m$-strongly convex. Our high-probability regret bound for this generalisation, $α$-LinUCB, establishes that valid confidence sets are not necessary for the success of LinUCB. We identify the mechanism behind this result: action-set curvature drives $α$-LinUCB to explore every direction, even when optimism is not guaranteed. To analyse this mechanism, we introduce a logarithmically capped spectral potential that, unlike the standard log-determinant potential, caps contributions from well-explored directions. This yields lower bounds on the smallest eigenvalue of the design matrix. At the standard confidence width $α=β\asymp\sqrt{d\log T}$, our $T$-round regret bound in $d$ dimensions is $O\bigl(\frac{M}{m}d\sqrt{T\log T}\bigr)$, up to iterated-logarithmic factors, improving the horizon dependence of the classical LinUCB guarantee by a factor of $\sqrt{\log T}$.

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