No algorithm can be optimal in both stochastic and adversarial best-arm identification; a new parameter-free algorithm matches the derived lower bound up to log factors in stochastic cases while handling adversarial rewards.
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Minimax squared l2 error for robust mean estimation under star-shaped sets with heavy-tailed noise and contamination level ε is max(δ*², ε σ²) ∧ d², where δ* is the largest scale satisfying N δ²/σ² ≤ log M^loc(δ, c).
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Best of both worlds: Stochastic & adversarial best-arm identification
No algorithm can be optimal in both stochastic and adversarial best-arm identification; a new parameter-free algorithm matches the derived lower bound up to log factors in stochastic cases while handling adversarial rewards.
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Robust mean estimation under star-shaped constraints with heavy-tailed noise
Minimax squared l2 error for robust mean estimation under star-shaped sets with heavy-tailed noise and contamination level ε is max(δ*², ε σ²) ∧ d², where δ* is the largest scale satisfying N δ²/σ² ≤ log M^loc(δ, c).