Rapid and Scalable Bayesian AB Testing

AB testing aids business operators with their decision making, and is considered the gold standard method for learning from data to improve digital user experiences. However, there is usually a gap between the requirements of practitioners, and the constraints imposed by the statistical hypothesis testing methodologies commonly used for analysis of AB tests. These include the lack of statistical power in multivariate designs with many factors, correlations between these factors, the need of sequential testing for early stopping, and the inability to pool knowledge from past tests. Here, we propose a solution that applies hierarchical Bayesian estimation to address the above limitations. In comparison to current sequential AB testing methodology, we increase statistical power by exploiting correlations between factors, enabling sequential testing and progressive early stopping, without incurring excessive false positive risk. We also demonstrate how this methodology can be extended to enable the extraction of composite global learnings from past AB tests, to accelerate future tests. We underpin our work with a solid theoretical framework that articulates the value of hierarchical estimation. We demonstrate its utility using both numerical simulations and a large set of real-world AB tests. Together, these results highlight the practical value of our approach for statistical inference in the technology industry.

Dynamic Memory for Interpretable Sequential Optimisation

Real-world applications of reinforcement learning for recommendation and experimentation faces a practical challenge: the relative reward of different bandit arms can evolve over the lifetime of the learning agent. To deal with these non-stationary cases, the agent must forget some historical knowledge, as it may no longer be relevant to minimise regret. We present a solution to handling non-stationarity that is suitable for deployment at scale, to provide business operators with automated adaptive optimisation. Our solution aims to provide interpretable learning that can be trusted by humans, whilst responding to non-stationarity to minimise regret. To this end, we develop an adaptive Bayesian learning agent that employs a novel form of dynamic memory. It enables interpretability through statistical hypothesis testing, by targeting a set point of statistical power when comparing rewards and adjusting its memory dynamically to achieve this power. By design, the agent is agnostic to different kinds of non-stationarity. Using numerical simulations, we compare its performance against an existing proposal and show that, under multiple non-stationary scenarios, our agent correctly adapts to real changes in the true rewards. In all bandit solutions, there is an explicit trade-off between learning and achieving maximal performance. Our solution sits on a different point on this trade-off when compared to another similarly robust approach: we prioritise interpretability, which relies on more learning, at the cost of some regret. We describe the architecture of a large-scale deployment of automatic optimisation-as-a-service where our agent achieves interpretability whilst adapting to changing circumstances.

Smooth Sequential Optimisation with Delayed Feedback

Stochastic delays in feedback lead to unstable sequential learning using multi-armed bandits. Recently, empirical Bayesian shrinkage has been shown to improve reward estimation in bandit learning. Here, we propose a novel adaptation to shrinkage that estimates smoothed reward estimates from windowed cumulative inputs, to deal with incomplete knowledge from delayed feedback and non-stationary rewards. Using numerical simulations, we show that this adaptation retains the benefits of shrinkage, and improves the stability of reward estimation by more than 50%. Our proposal reduces variability in treatment allocations to the best arm by up to 3.8x, and improves statistical accuracy - with up to 8% improvement in true positive rates and 37% reduction in false positive rates. Together, these advantages enable control of the trade-off between speed and stability of adaptation, and facilitate human-in-the-loop sequential optimisation.