Maximize lift with multi-armed bandit optimizations

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Traditional A/B tests and multi-armed bandits (MABs) differ as:

  • Multi-armed bandits do not generate statistical significance.

  • Multi-armed bandits do not use a control or a baseline experience.

Instead of statistical significance, the MAB results page focuses on improvement over equal allocation as its primary summary of your optimization's performance. This article breaks down the key differences between MABs and traditional A/B tests, demonstrates how each approach would perform in an identical situation, and answers some frequently asked questions.

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 Experimentation'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 important.

Since MABs essentially ignore statistical significance, Optimizely Experimentation 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. Instead, MABs continuously make these decisions throughout the experimentโ€™s lifetime. They explicitly evaluate the tradeoffs between all variations at once instead of continuously comparing performance to baseline experience as a reference. MABs are excellent for validating your optimized variations and confirming whether to deploy a winning variation or stay with the control.

Improvement over original

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

To calculate it, Optimizely Experimentation 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.

There are no statistical significance measures associated with this calculation. It does not predict or guarantee any reproducibility in future tests or campaigns. Also, the original variation in this context is the first variation in the list and may not be named "original" if you changed it.

Algorithms powering Optimizely Experimentation's MAB

Optimizely uses a different algorithm based on what type of metric you are taking:

  • Binary metrics โ€“ Optimizely Experimentation uses a Bayesian MAB procedure called Thompson Sampling [Russo, Van Roy 2013]. For each variation, Optimizely uses the test's current observed number of unique conversions and number of visitors to characterize a beta distribution. Optimizely samples these distributions several times and allocate traffic according to their win ratio.

    For example, suppose you have the following results on comparing unique conversions when Optimizely is updating the traffic allocation:

    results when comparing unique conversions

    Figure 1. The observed results of the experiment under a Bernoulli metric.

    Optimizely characterizes beta distributions, denoted as Beta(๐›ผ, ๐›ฝ), based on these values, where ๐›ผ is the number of unique conversions, and ๐›ฝ is the number of visitors for each variation. For example, the Original variation would be characterized by Beta.

    beta distributions

    Figure 2. The resulting Beta distributions are characterized by the results in Figure 1.

    Optimizely samples these distributions N times โ€” say 10,000 โ€” recording the distribution that yields the highest value in each round. This simulates what might happen if Optimizely had 10,000 visitors allocated to the Original, 10,000 to Variation #1 and 10,000 to Variation #2. The ratio of times each variation wins determines the percentage of new visitors allocated to it:

    results_of_thompson_sampling.png

    Figure 3. Result of Thompson Sampling where N=10000.

    Optimizely Experimentation runs Thompson Sampling again on the next iteration with the updated observations.

  • Numeric metrics โ€“ Optimizely Experimentation uses the Epsilon Greedy procedure, 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.

Set up an MAB optimization in Optimizely Experimentation

Create an MAB optimization in Optimizely Web Experimentation

  1. From the Experiments window, click Create New....

  2. Select Multi-Armed Bandit.

  3. Give your MAB a name, description, and URL to target, just as you would with any Optimizely experiment. Then click Create Bandit.

  4. Create at least two variations in the Visual Editor.

  5. Click Metrics from the left-side menu to choose your primary metric. Your MAB uses the primary metric to determine how traffic is distributed across variations.

    After you start your MAB, you cannot change the primary metric.
  6. Test your MAB.

  7. Click Start Multi-Armed Bandit to launch your optimization.

Create an MAB optimization in Optimizely Feature Experimentation

See Run a multi-armed bandit optimization to create an MAB flag rule in the Optimizely application and implement it in your code using the Feature Experimentation SDKs.

select Multi armed bandit rule

MAB optimization over 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 โ€“ 50%

  • Variation 1 โ€“ 50%

  • Variation 2 โ€“ 45%

  • Variation 3 โ€“ 55%

mab_gif.gif

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 to exploit the perceived advantage and gain more conversions.

The traffic distribution remains fixed for the ordinary A/B experiment to 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.

Traffic distribution is updated frequently, so Optimizely Feature Experimentation customers should implement a user profile service to ensure sticky bucketing to avoid exposing the same visitor to multiple variations. 

FAQs

Does the multi-armed bandit algorithm work with Multivariate tests and Web Personalization?

Yes. To use an MAB in a Multivariate test (MVT), select Partial Factorial. In the Traffic Mode dropdown, select Multi-armed Bandit.

mab in mvt.png

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

create-experience-personalization.png

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, you can contact Optimizely

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

In MVT and Web 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 in the Results page when using a MAB with an Optimizely Web Experimentation or Optimizely Feature Experimentation experiment.

What happens if I change my primary metric?

If you change the primary metric mid-experiment in a Web Experimentation MVT or Web 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 Experimentation or Optimizely Feature Experimentation once your experiment has begun. See Why you should not change a running experiment for more information.

What happens when I stop or pause a variation?

If you pause or stop a variation, the MAB ignores data from those variations when it adjusts traffic distribution among the remaining live variations. But there are side effects you should be aware of. If you change variations mid-experiment, the MAB needs to re-optimize its strategy and adapt the traffic accordingly. Additionally, doing so will add weeks for an experiment to complete. Also, when the swapping occurs, the original bandit model gets destroyed. The MAB has to start from scratch to optimize for the reduction in variations. Because of this, Optimizely recommends not changing variations mid-experiment. See Why you should not change a running experiment for more information.

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

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

Will the traffic allocation always be updated?

The bandit algorithm used by MABs eventually converges. This means that, eventually, the bandit algorithm determines the optimal traffic split among the variations in the experiment. It will no longer update the traffic split between variations. All bandit algorithms are working towards that goal.