Why MABs do not show statistical significance

With a traditional A/B test, the goal is exploration: collecting data to discover if a variation performs better or worse than the control. This is expressed through the concept of statistical significance.

Statistical significance tells you whether a change had the effect you expected. You can use those lessons to make your variations better each time. Fixed traffic allocation strategies are usually the best ways to reduce the time it takes to reach a statistically significant result.

On the other hand, Optimizely’s MAB algorithms are designed for exploitation: MABs aggressively push traffic to whichever variations are performing best, because the MAB does not consider the reason for that superior performance to be very important.

Since MABs essentially ignore statistical significance, Optimizely does too. This is why statistical significance does not appear on the results page for MABs: It avoids confusion about the purpose and meaning of MAB optimizations.

Why MABs do not use a baseline

In a traditional A/B test, statistical significance is calculated relative to the performance of one baseline experience. But MABs do not do this. They are intended to explicitly evaluate the tradeoffs between all variations at once, which means there is no control or baseline experience to compare to.

What is more, MABs are "set-and-forget" optimizations. In an A/B test, you follow up an experiment with a decision: do you deploy a winning variation, or stick with the control? But since MABs continuously make these decisions throughout the experiment’s lifetime, there’s never any need for a baseline reference point for that decision, because you never need to make it yourself.

Improvement over original

Improvement over original is an estimate of the gain in total conversions compared to simply delivering all traffic to the original variation.

To calculate it, Optimizely examines the cumulative average conversions per visitor for each variation. Then it multiplies the original's conversion rate by the total number of visitors in the test. Finally, this number is compared to the observed conversion counts in the test.

MAB optimization vs. A/B testing: a demonstration

In the following head-to-head comparison, simulated data is sent to both an A/B test with fixed traffic distribution and a MAB optimization. Traffic distribution over time and the cumulative count of conversions for each mode are both observed. The true conversion rates driving the simulated data are:

• Original: 50%

• Variation 1: 50%

• Variation 2: 45%

• Variation 3: 55%

The MAB algorithm indicates that Variation 3 is higher-performing from the start. Even without any statistical significance information for this signal (remember, the multi-armed bandit does not show statistical significance), it still begins to push traffic to Variation 3 in order to exploit the perceived advantage and gain more conversions.

For the ordinary A/B experiment, the traffic distribution remains fixed in order to more quickly arrive at a statistically significant result. Because fixed traffic allocations are optimal for reaching statistical significance, MAB-driven experiments generally take longer to find winners and losers than A/B tests.

By the end of the simulation, the MAB optimized the experiment to achieve roughly 700 more conversions than if traffic was held constant.

FAQs

• What algorithms or frameworks does the multi-armed bandit support?

  For binary metrics, Optimizely uses a procedure inspired by Thompson Sampling (Russo, Van Roy 2013). Optimizely characterizes each variation as a Beta distribution, where its parameters are the variation’s observed number of conversions and visitors. These distributions are sampled several times, and Optimizely allocates traffic to the variations according to their win ratio.

  For numeric metrics, Optimizely uses a form of Epsilon Greedy, where a small fraction of traffic is uniformly allocated to all variations and a large amount is allocated to the variation with the highest observable mean.

• Does the multi-armed bandit algorithm work with MVT and Personalization

  Yes. To use MAB in MVT, select Partial Factorial. In the Traffic Mode dropdown, select Multi-Armed Bandit.

  In Personalization, you can apply MAB on the experience level. This works best if when you have two variations aside from the holdback.

• How often does the multi-armed bandit make a decision?

  The MAB model is updated hourly. If you need a different frequency for model updates,  contact Optimizely. 

• Why is a baseline variation listed on the Results page for my multi-armed bandit campaign?

  In MVT and Personalization, your Results page still designates one variation as a baseline. However, this designation does not actually mean anything because MABs do not measure success relative to a baseline variation. It is just a label that has no effect on your experiment or campaign.

  You should not see a baseline variation when using MAB with a Web or Full Stack experiment.

• What happens if I change my primary metric?

  If you change the primary metric mid-experiment in MVT or Personalization, the MAB begins optimizing for the new primary metric, instead of the one you originally selected. For this reason,  do not change the primary metric once you begin the experiment or campaign.

  You cannot change your primary metric in Optimizely Web or Full Stack once your experiment has begun.

• What happens when I stop or pause a variation?

  If you pause or stop a variation, Optimizely’s MAB ignores data from those variations data when it adjusts traffic distribution among the remaining live variations.

• How do multi-armed bandits handle conversion rates that change over time, and Simpson's Paradox?

  Optimizely uses an exponential decay function that weighs recent visitor behavior more strongly, to better adapt to the effect of time variation more quickly. This approach gives less weight to earlier observations and more weight to recent ones.

  Also, Optimizely reserves a portion of traffic for pure exploration, so that time variation is easier to detect.