Starting with the general feasibility condition forτ ℓ and applying our two observations, X ak∈Aℓ I n≤ 8 log(1/δ) ∆2 k (∆k,ℓ −3β) + 2 ≥ X ak∈A† I n≤ 8 log(1/δ) ∆2 k (∆k,† −3β) + 2

Since(∆ k,ℓ −3β) + = max{∆k,ℓ −3β,0}, and∆ k,ℓ = (1−α)µ k −µ ℓ, we have∆ k,† ≤∆ k,ℓ ∀ℓ < a ∗

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Cost-Ordered Feasibility for Multi-Armed Bandits with Cost Subsidy

cs.LG · 2026-05-08 · unverdicted · novelty 6.0

Develops COF algorithm for MAB-CS that intelligently checks cheap arm feasibility by pooling samples, with generalized instance-dependent lower bounds and matching upper bounds on cumulative cost and quality regret.

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Cost-Ordered Feasibility for Multi-Armed Bandits with Cost Subsidy cs.LG · 2026-05-08 · unverdicted · none · ref 46
Develops COF algorithm for MAB-CS that intelligently checks cheap arm feasibility by pooling samples, with generalized instance-dependent lower bounds and matching upper bounds on cumulative cost and quality regret.

Starting with the general feasibility condition forτ ℓ and applying our two observations, X ak∈Aℓ I n≤ 8 log(1/δ) ∆2 k (∆k,ℓ −3β) + 2 ≥ X ak∈A† I n≤ 8 log(1/δ) ∆2 k (∆k,† −3β) + 2

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