Rethinking Successive Rejects Algorithms
Read the original on arXiv Machine Learning →The paper revisits the Successive Rejects (SR) algorithm for best‑arm identification, showing that although SR appears non‑adaptive due to fixed phase lengths, it achieves an optimal worst‑instance error exponent for Gaussian arms with common variance. The authors formulate an optimization problem to design a phase schedule that maximizes the normalized error exponent, leading to a new variant called H1‑balanced Successive Rejects (H1‑SR). H1‑SR attains at least 11/12 of the optimal normalized rate for all K ≥ 2, approaching the optimum as K grows, and experiments demonstrate significant performance gains over the original SR while highlighting trade‑offs in early elimination strategies.
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