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A Lyapunov-Based Methodology for Constrained Optimization with Bandit Feedback

AAAI 2022 · Bandits and online learning › Online convex optimization and games · approach: Best-of-both-worlds bandit algorithms · 9 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use empirical drift-plus-penalty estimates with confidence-bound exploration under bandit feedbackConstrained bandit problem · Constrained bandit problem (theoretical)regret: O(\sqrt{K B \log B})Helped
Use empirical drift-plus-penalty estimates with confidence-bound exploration under bandit feedbackConstrained bandit problem · Constrained bandit problem (theoretical)constraint-violation: O(\frac{-1}{\sqrt{B}})Helped
Use known first-order statistics instead of learning them onlineLyOff · Constrained bandit problem (theoretical)regret: O(\sqrt{B})Helped
Use known first-order statistics instead of learning them onlineLyOff · Constrained bandit problem (theoretical)constraint-violation: O( \frac{-1}{\sqrt{B}} )Helped
Use the optimal stationary randomized policy as a static benchmarkConstrained bandit problem · Constrained bandit problem (theoretical)regret: O(1)Helped
Use the optimal stationary randomized policy as a static benchmarkConstrained bandit problem · Constrained bandit problem (theoretical)constraint-violation: O(\frac{1}{B})Helped
Use LyOn rather than the optimal stationary randomized policyK=2 Bernoulli-arm simulation · K=2 Bernoulli-arm simulationreward rateNo clear effect
Use LyOn rather than the optimal stationary randomized policyK=2 Bernoulli-arm simulation · K=2 Bernoulli-arm simulationconstraint-violation: \Tilde{O}(1/B)Helped
Increase V and tune δ as specified for sufficiently large budgets (ablation)LyOn · Constrained bandit problem (theoretical)constraint-violation: O(\frac{-1}{\sqrt{B}})Helped
Increase V and tune δ as specified for sufficiently large budgets (ablation)LyOn · Constrained bandit problem (theoretical)regret: O(\sqrt{K B\log B})Mixed

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