To speed up online testing, adaptive traffic experimentation through multi-armed bandit algorithms is rising as an essential complementary alternative to the fixed horizon A/B testing. Based on recent research on best arm identification and statistical inference with adaptively collected data, this paper derives and evaluates four Bayesian batch bandit algorithms (NB-TS, WB-TS, NB-TTTS, WB-TTTS), which are combinations of two ways of weighting batches (Naive Batch and Weighted Batch) and two Bayesian sampling strategies (Thompson Sampling and Top-Two Thompson Sampling) to adaptively determine traffic allocation. These derived Bayesian sampling algorithms are practically based on summary batch statistics of a reward metric for pilot experiments, where one of the combination WB-TTTS in this paper seems to be newly discussed. The comprehensive evaluation on the four Bayesian sampling algorithms covers trustworthiness, sensitivity and regret of a testing methodology. Moreover, the evaluation includes 4 real-world eBay experiments and 40 reproducible synthetic experiments to reveal the learnings, which covers both stationary and non-stationary situations. Our evaluation reveals that, (a) There exist false positives inflation with equivalent best arms, while seldom discussed in literatures; (b) To control false positives, connections between convergence of posterior optimal probabilities and neutral posterior reshaping are discovered; (c) WB-TTTS shows competitive recall, higher precision, and robustness against non-stationary trend; (d) NB-TS outperforms on minimizing regret trials except on precision and robustness; (e) WB-TTTS is a promising alternative if regret of A/B Testing is affordable, otherwise NB-TS is still a powerful choice with regret consideration for pilot experiments.

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