A Perturbation Approach to Unconstrained Linear Bandits

A Perturbation Approach to Unconstrained Linear Bandits | Signal Canvas | ScienceToStartup

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Proof freshness: stale
Proof status: unverified
Display score: 2/10
Last proof check: 2026-03-31
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 54
Source count: 3
Coverage: 50%

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Evidence Receipt

Route status: building

Claims: 8

References: 54

Proof: Verification pending

Freshness state: computing

Source paper: A Perturbation Approach to Unconstrained Linear Bandits

PDF: https://arxiv.org/pdf/2603.28201v1

Source count: 3

Coverage: 50%

Last proof check: 2026-03-31T20:24:27.970Z

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Subject: A Perturbation Approach to Unconstrained Linear Bandits

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Claim map

Strong 8Mixed 0Weak 0

Evidencepartial
We show the surprising result that in the unconstrained setting, this approach effectively reduces Bandit Linear Optimization (BLO) to a standard Online Linear Optimization (OLO) problem.
Implicationpartial
Directly stated in the abstract as the main surprising result of the paper.
Verificationpartial
partial
Evidencepartial
We also extend our analysis to dynamic regret, obtaining the optimal √P_T path-length dependencies without prior knowledge of P_T.
Implicationpartial
Explicitly stated in abstract and supported by theoretical analysis in the paper.
Verificationpartial
partial
Evidencepartial
We then develop the first high-probability guarantees for both static and dynamic regret in uBLO.
Implicationpartial
Directly claimed in abstract as a novel contribution.
Verificationpartial
partial
Evidencepartial
Then, the following hold E[ℓ̃_t | F_{t-1}] = ℓ_t, E[∥ℓ̃_t∥_2^2 | F_{t-1}] = d∥ℓ_t∥_2^2 + d⟨ℓ_t, w_t⟩^2 Tr(H_t)
Implicationpartial
Mathematically proven in Proposition 2.1 with explicit formulas.
Verificationpartial
partial
Evidencepartial
The key feature of Equation (1) is that the bound is adaptive to an arbitrary comparator norm, rather than the worst-case D = sup_{x,y∈W} ∥x-y∥
Implicationpartial
Explicitly stated in the analysis section with mathematical formulation.
Verificationpartial
partial
Evidencepartial
Finally, we discuss lower bounds on the static regret, and prove the folklore Ω(√{dT}) rate for adversarial linear bandits on the unit Euclidean ball, which is of independent interest.
Implicationpartial
Directly stated in abstract as a contribution of independent interest.
Verificationpartial
partial
Evidencepartial
Our framework improves on prior work in several ways. First, we derive expected-regret guarantees when our perturbation scheme is combined with comparator-adaptive OLO algorithms
Implicationpartial
Implied by Proposition 2.3 and the overall framework description.
Verificationpartial
partial
Evidencepartial
Besides this work, all existing works on dynamic regret under bandit feedback fail to obtain the optimal √S_T dependencies without leveraging prior knowledge of the comparator sequence
Implicationpartial
Directly stated as a limitation of prior work with citations.
Verificationpartial
partial

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A Perturbation Approach to Unconstrained Linear Bandits

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