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Quantum Multi-Armed Bandits and Stochastic Linear Bandits Enjoy Logarithmic Regrets
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use quantum reward oracles and Quantum Monte Carlo estimation in the UCB algorithm | MAB · QMAB, bounded value | expected cumulative regret: \Theta(\sqrt{nT}) -> O(n\log (T)) | Helped |
| Use quantum reward oracles and Quantum Monte Carlo estimation in the linear UCB algorithm | SLB · QSLB, bounded value | expected cumulative regret: \widetilde{\Theta}\left(d\sqrt{T}\right) -> O(d^2\log^{5/2}(T)) | Helped |
| Use quantum reward oracles and Quantum Monte Carlo estimation | MAB · QMAB, bounded variance | expected cumulative regret: O(n\sigma\log^{5/2} (T)\log\log (T)) | Helped |
| Use quantum reward oracles and weighted least squares with accuracy-based weights | SLB · QSLB, bounded variance | expected cumulative regret: O(d^2\log^4 (T)\log\log(T)) | Helped |
| Use QUCB instead of UCB | 2-arm MAB with small reward gaps · QMAB, no quantum noise, T=10^6 | expected regret | Helped |
| Use QLinUCB instead of LinUCB | 2-dimensional QSLB instance · QSLB, no quantum noise, T=10^6 | regret | Helped |
| Add depolarizing noise with two-qubit error rate no greater than 0.00683 | QUCB · 2-arm QMAB, T=10^5 | expected regret | No clear effect |
| Add depolarizing noise with two-qubit error rate 0.01 | QLinUCB · QSLB, T=10^5 | expected regret | Hurt |
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