ConceptApproximation Ratio

Approximation Ratio

A common metric for measuring the gap between an algorithm's performance and that of a theoretically optimal algorithm. In best-arm identification it is defined as the ratio of the algorithm's normalized error exponent to the optimal value; the closer to 1, the closer to fully adaptive.

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Nov 4

For a fixed m, the algorithm achieves an approximation ratio of (1-c_m)/(2-c_m) (ignoring estimation error), and this factor approaches 1/2 as c_m decreases.

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Unverified

For a fixed m, the algorithm achieves an approximation ratio of (1-c_m)/(2-c_m) (ignoring estimation error), and this factor approaches 1/2 as c_m decreases.

50%

Source Articles

Rethinking the Successive Rejects Algorithm: Optimized Stage Scheduling Improves Best-Arm Identification EfficiencyOct 16