arXiv Machine Learning
Follow the Perturbed Leader for Linear Bandits: $\sqrt{T}$ Regret over General Action Sets
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Follow the Perturbed Leader for Linear Bandits: $\sqrt{T}$ Regret over General Convex Sets
The paper presents the first adversarial linear bandit algorithm based on Follow-the-Perturbed-Leader (FTPL) that achieves √T regret over general convex action sets. It achieves a regret of ≥O(d^{5/4}√T) using only linear optimization oracles, and a near‑optimal ≥O(d√T) regret when an optimal‑design exploration distribution is available. The work improves on previous FTPL algorithms and generalizes earlier results for special action sets, offering a simpler and more computationally efficient approach that relies on adaptive perturbation distributions and a new analysis framework based on Fisher information.
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