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Conservative Contextual Linear Bandits

NeurIPS 2017 · Bandits and online learning › Contextual bandits and Thompson sampling · approach: Oracle-efficient contextual bandits · 38 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Add a safety check that permits optimistic actions only when the worst-case confidence-set estimate satisfies the performance constraintLUCB, yielding CLUCB · Linear contextual bandits (simulation)safety constraint violationsHelped
Add conservative fallback to the baseline policyLUCB, yielding CLUCB · Linear contextual bandits (theory)regret: O\left(d\log\big(\frac{DT}{\lambda\delta}\big)\sqrt{T} + \frac{K\Delta_h}{\alpha r_l(\alpha r_l + \Delta_l)}\right)Mixed
Use CLUCB2 to account for unknown baseline rewards with confidence bounds and observations from both action typesCLUCB · Linear contextual bandits (unknown baseline)regret rate: O\left(d\log\left(\frac{DT}{\lambda\delta}\right)\sqrt{T}\right)No clear effect
Use a tighter safety threshold, i.e. smaller αCLUCB · Linear contextual banditsregretHurt
Increase α, relaxing the safety constraintCLUCB · Linear contextual bandits (simulation)length of conservative phaseHelped
Use the baseline policy as the fallback during early explorationCLUCB · Linear contextual bandits (simulation)early per-step regretHelped
Replace known baseline rewards with unknown rewards handled by confidence bounds (ablation)CLUCB2 · Linear contextual bandits (theory)number of conservative rounds: 256 \frac{d^2(B\sqrt{\lambda}+\sigma)^2}{\alpha^2 r_l^2}\left[\log\left(\frac{10d(B\sqrt{\lambda}+\sigma)\sqrt{D}}{\alphMixed
Update confidence sets using only optimistic-action observations (ablation)CLUCB · Linear contextual bandits (known baseline)confidence-set informationNo clear effect
Use nested confidence sets (ablation)CLUCB2 · Linear contextual bandits (unknown baseline)computational complexityHurt

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