Learning Metrics that Maximise Power for Accelerated A/B-Tests

Online controlled experiments are a crucial tool to allow for confident decision-making in technology companies. A North Star metric is defined (such as long-term revenue or user retention), and system variants that statistically significantly improve on this metric in an A/B-test can be considered superior. North Star metrics are typically delayed and insensitive. As a result, the cost of experimentation is high: experiments need to run for a long time, and even then, type-II errors (i.e. false negatives) are prevalent. We propose to tackle this by learning metrics from short-term signals that directly maximise the statistical power they harness with respect to the North Star. We show that existing approaches are prone to overfitting, in that higher average metric sensitivity does not imply improved type-II errors, and propose to instead minimise the $p$-values a metric would have produced on a log of past experiments. We collect such datasets from two social media applications with over 160 million Monthly Active Users each, totalling over 153 A/B-pairs. Empirical results show that we are able to increase statistical power by up to 78% when using our learnt metrics stand-alone, and by up to 210% when used in tandem with the North Star. Alternatively, we can obtain constant statistical power at a sample size that is down to 12% of what the North Star requires, significantly reducing the cost of experimentation.

Variance Reduction in Ratio Metrics for Efficient Online Experiments

Online controlled experiments, such as A/B-tests, are commonly used by modern tech companies to enable continuous system improvements. Despite their paramount importance, A/B-tests are expensive: by their very definition, a percentage of traffic is assigned an inferior system variant. To ensure statistical significance on top-level metrics, online experiments typically run for several weeks. Even then, a considerable amount of experiments will lead to inconclusive results (i.e. false negatives, or type-II error). The main culprit for this inefficiency is the variance of the online metrics. Variance reduction techniques have been proposed in the literature, but their direct applicability to commonly used ratio metrics (e.g. click-through rate or user retention) is limited. In this work, we successfully apply variance reduction techniques to ratio metrics on a large-scale short-video platform: ShareChat. Our empirical results show that we can either improve A/B-test confidence in 77% of cases, or can retain the same level of confidence with 30% fewer data points. Importantly, we show that the common approach of including as many covariates as possible in regression is counter-productive, highlighting that control variates based on Gradient-Boosted Decision Tree predictors are most effective. We discuss the practicalities of implementing these methods at scale and showcase the cost reduction they beget.

Learning-to-Rank with Nested Feedback

Many platforms on the web present ranked lists of content to users, typically optimized for engagement-, satisfaction- or retention- driven metrics. Advances in the Learning-to-Rank (LTR) research literature have enabled rapid growth in this application area. Several popular interfaces now include nested lists, where users can enter a 2nd-level feed via any given 1st-level item. Naturally, this has implications for evaluation metrics, objective functions, and the ranking policies we wish to learn. We propose a theoretically grounded method to incorporate 2nd-level feedback into any 1st-level ranking model. Online experiments on a large-scale recommendation system confirm our theoretical findings.

On Gradient Boosted Decision Trees and Neural Rankers: A Case-Study on Short-Video Recommendations at ShareChat

Practitioners who wish to build real-world applications that rely on ranking models, need to decide which modelling paradigm to follow. This is not an easy choice to make, as the research literature on this topic has been shifting in recent years. In particular, whilst Gradient Boosted Decision Trees (GBDTs) have reigned supreme for more than a decade, the flexibility of neural networks has allowed them to catch up, and recent works report accuracy metrics that are on par. Nevertheless, practical systems require considerations beyond mere accuracy metrics to decide on a modelling approach. This work describes our experiences in balancing some of the trade-offs that arise, presenting a case study on a short-video recommendation application. We highlight (1) neural networks' ability to handle large training data size, user- and item-embeddings allows for more accurate models than GBDTs in this setting, and (2) because GBDTs are less reliant on specialised hardware, they can provide an equally accurate model at a lower cost. We believe these findings are of relevance to researchers in both academia and industry, and hope they can inspire practitioners who need to make similar modelling choices in the future.

Ito Diffusion Approximation of Universal Ito Chains for Sampling, Optimization and Boosting

This work considers a rather general and broad class of Markov chains, Ito chains that look like Euler-Maryama discretization of some Stochastic Differential Equation. The chain we study is a unified framework for theoretical analysis. It comes with almost arbitrary isotropic and state-dependent noise instead of normal and state-independent one, as in most related papers. Moreover, our chain's drift and diffusion coefficient can be inexact to cover a wide range of applications such as Stochastic Gradient Langevin Dynamics, sampling, Stochastic Gradient Descent, or Stochastic Gradient Boosting. We prove an upper bound for $W_{2}$-distance between laws of the Ito chain and the corresponding Stochastic Differential Equation. These results improve or cover most of the known estimates. Moreover, for some particular cases, our analysis is the first.

On (Normalised) Discounted Cumulative Gain as an Offline Evaluation Metric for Top-$n$ Recommendation

Approaches to recommendation are typically evaluated in one of two ways: (1) via a (simulated) online experiment, often seen as the gold standard, or (2) via some offline evaluation procedure, where the goal is to approximate the outcome of an online experiment. Several offline evaluation metrics have been adopted in the literature, inspired by ranking metrics prevalent in the field of Information Retrieval. (Normalised) Discounted Cumulative Gain (nDCG) is one such metric that has seen widespread adoption in empirical studies, and higher (n)DCG values have been used to present new methods as the state-of-the-art in top-$n$ recommendation for many years. Our work takes a critical look at this approach, and investigates when we can expect such metrics to approximate the gold standard outcome of an online experiment. We formally present the assumptions that are necessary to consider DCG an unbiased estimator of online reward and provide a derivation for this metric from first principles, highlighting where we deviate from its traditional uses in IR. Importantly, we show that normalising the metric renders it inconsistent, in that even when DCG is unbiased, ranking competing methods by their normalised DCG can invert their relative order. Through a correlation analysis between off- and on-line experiments conducted on a large-scale recommendation platform, we show that our unbiased DCG estimates strongly correlate with online reward, even when some of the metric's inherent assumptions are violated. This statement no longer holds for its normalised variant, suggesting that nDCG's practical utility may be limited.

Deep Stochastic Mechanics

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit computational complexity that scales exponentially in the problem dimension, our method allows us to adapt to the latent low-dimensional structure of the wave function by sampling from the Markovian diffusion. Depending on the latent dimension, our method may have far lower computational complexity in higher dimensions. Moreover, we propose novel equations for stochastic quantum mechanics, resulting in linear computational complexity with respect to the number of dimensions. Numerical simulations verify our theoretical findings and show a significant advantage of our method compared to other deep-learning-based approaches used for quantum mechanics.

Gradient Boosting Performs Low-Rank Gaussian Process Inference

This paper shows that gradient boosting based on symmetric decision trees can be equivalently reformulated as a kernel method that converges to the solution of a certain Kernel Ridgeless Regression problem. Thus, for low-rank kernels, we obtain the convergence to a Gaussian Process' posterior mean, which, in turn, allows us to easily transform gradient boosting into a sampler from the posterior to provide better knowledge uncertainty estimates through Monte-Carlo estimation of the posterior variance. We show that the proposed sampler allows for better knowledge uncertainty estimates leading to improved out-of-domain detection.

Which Tricks are Important for Learning to Rank?

Nowadays, state-of-the-art learning-to-rank (LTR) methods are based on gradient-boosted decision trees (GBDT). The most well-known algorithm is LambdaMART that was proposed more than a decade ago. Recently, several other GBDT-based ranking algorithms were proposed. In this paper, we conduct a thorough analysis of these methods in a unified setup. In particular, we address the following questions. Is direct optimization of a smoothed ranking loss preferable over optimizing a convex surrogate? How to properly construct and smooth surrogate ranking losses? To address these questions, we compare LambdaMART with YetiRank and StochasticRank methods and their modifications. We also improve the YetiRank approach to allow for optimizing specific ranking loss functions. As a result, we gain insights into learning-to-rank approaches and obtain a new state-of-the-art algorithm.

Uncertainty in Gradient Boosting via Ensembles

Gradient boosting is a powerful machine learning technique that is particularly successful for tasks containing heterogeneous features and noisy data. While gradient boosting classification models return a distribution over class labels, regressions models typically yield only point predictions. However, for many practical, high-risk applications, it is also important to be able to quantify uncertainty in the predictions to avoid costly mistakes. In this work, we examine a probabilistic ensemble-based framework for deriving uncertainty estimates in the predictions of gradient boosting classification and regression models. Crucially, the proposed approach allows the total uncertainty to be decomposed into \textit{data uncertainty}, which comes from the complexity and noise in data distribution, and \textit{knowledge uncertainty}, coming from the lack of information about a given region of the feature space. Two approaches for generating ensembles are considered: Stochastic Gradient Boosting (SGB) and Stochastic Gradient Langevin Boosting (SGLB). Notably, SGLB also enables the generation of a \emph{virtual} ensemble via only one gradient boosting model, which significantly reduces complexity. Experiments on a range of regression and classification datasets show that ensembles of gradient boosting models yield improved predictive performance, and measures of uncertainty successfully enable detection of out-of-domain inputs.