neonforestmist/improved-dimension-bco-gradient-variation-repro-artifacts / source /challenge_target_snapshot.json
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| "Theorem 1 establishes an Õ(d^{3/2}√V_T) regret bound for one-point bandit convex optimization with gradient variation V_T, improving the dimension dependence over Chiang et al. (2013)'s O(d^3√V_T) bound (Theorem 1, Section 3.1).", | |
| "Theorem 2 gives an O((d/λ) log V_T) regret bound for λ-strongly convex functions, improving the prior O((d^2/λ) log V_T) bound by a factor of d (Theorem 2, Section 3.2).", | |
| "Theorem 3 provides O(√(dW_T) + d) regret for linear functions and O(d√W_T + d) regret for convex functions in terms of the gradient variance W_T (Theorem 3, Section 3.3).", | |
| "Theorem 4 delivers O(√(dF_T) + d) regret bounds for linear and convex functions using the small-loss quantity F_T (Theorem 4, Section 3.3).", | |
| "Section 4 presents the first gradient-variation regret bound for one-point bandit linear optimization over hyper-rectangular domains (Section 4).", | |
| "Table 1 summarizes the dimension-dependence improvements across gradient-variation, gradient-variance, and small-loss metrics for linear, convex, and strongly convex function classes relative to prior best-known results (Table 1)." | |
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| "Improves dimension dependence for both convex and strongly convex functions in Bandit Convex Optimization compared to best known results.", | |
| "First gradient-variation bounds for one-point bandit linear optimization over hyper-rectangular domains.", | |
| "First gradient-variation dynamic and universal regret bounds for two-point Bandit Convex Optimization." | |
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| "Hang Yu", | |
| "Yu-Hu Yan", | |
| "Peng Zhao" | |
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| "title": "Improved Dimension Dependence for Bandit Convex Optimization with Gradient Variation", | |
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