Research map / Bandits and online learning / Multi-armed bandits
Refined Lower Bounds for Adversarial Bandits
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Require a high-probability guarantee against adversarial losses | Any randomized bandit algorithm · Adversarial bandits | regret lower bound: 1/27 sqrt((K-1)T log(1/(4δ))) | Hurt |
| Require a single algorithm to provide an expected-regret guarantee of order sqrt((K-1)T) | Any bandit algorithm · Adversarial bandits | high-probability regret lower bound: sqrt((K-1)T) log(1/(4δ))/(203 C) | Hurt |
| Know only that the best arm's cumulative loss is at most αT | Any randomized bandit algorithm · Small-loss ball B_{α,T} | expected regret lower bound: sqrt(α T K) / 27 | Hurt |
| Know only that quadratic variation is at most αTK | Any randomized bandit algorithm · Small-variation ball V_{α,T} | expected regret lower bound: sqrt(α T K) / 25 | Hurt |
| Constrain every round's effective loss range to at most ρ | Any randomized bandit algorithm · Loss vectors with effective range at most ρ | expected regret lower bound: sqrt(T (K-1)) / 504 | Hurt |
| Assume one arm is optimal in every round | Any randomized bandit algorithm · Loss sequences with one arm optimal every round | expected regret lower bound: sqrt(T (K-1)) / 504 | Hurt |
| Use δ-independent rather than δ-dependent tuning | Exp3.P / Exp3-IX · Adversarial bandits, high-probability regret | regret upper bound: c sqrt(KT log(K/δ)) -> c sqrt(KT)(sqrt(log(K)) + log(1/δ)/sqrt(log(K))) | Mixed |
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