Horizon-free pure-DP algorithm achieves optimal gap-dependent regret bound 1000*(log K/Δ_min + log K/ε) for stochastic online learning with K actions.
Mehta, and Nidhi Hegde
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Optimal Gap-Dependent Regret for Private Stochastic Decision-Theoretic Online Learning
Horizon-free pure-DP algorithm achieves optimal gap-dependent regret bound 1000*(log K/Δ_min + log K/ε) for stochastic online learning with K actions.