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Register a new userChallenges in Statistical Analysis of Data Collected by a Bandit Algorithm: An Empirical Exploration in Applications to Adaptively Randomized Experiments
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Multi-armed bandit algorithms have been argued for decades as useful for adaptively randomized experiments. In such experiments, an algorithm varies which arms (e.g. alternative interventions to help students learn) are assigned to participants, with the goal of assigning higher-reward arms to as many participants as possible. We applied the bandit algorithm Thompson Sampling (TS) to run adaptive experiments in three university classes. Instructors saw great value in trying to rapidly use data to give their students in the experiments better arms (e.g. better explanations of a concept). Our deployment, however, illustrated a major barrier for scientists and practitioners to use such adaptive experiments: a lack of quantifiable insight into how much statistical analysis of specific real-world experiments is impacted (Pallmann et al, 2018; FDA, 2019), compared to traditional uniform random assignment. We therefore use our case study of the ubiquitous two-arm binary reward setting to empirically investigate the impact of using Thompson Sampling instead of uniform random assignment. In this setting, using common statistical hypothesis tests, we show that collecting data with TS can as much as double the False Positive Rate (FPR; incorrectly reporting differences when none exist) and the False Negative Rate (FNR; failing to report differences when they exist)...
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Bandit algorithms are increasingly used in real-world sequential decision-making problems. Associated with this is an increased desire to be able to use the resulting datasets to answer scientific questions like: Did one type of ad lead to more purchases? In which contexts is a mobile health intervention effective? However, classical statistical approaches fail to provide valid confidence intervals when used with data collected with bandit algorithms. Alternative methods have recently been developed for simple models (e.g., comparison of means). Yet there is a lack of general methods for conducting statistical inference using more complex models on data collected with (contextual) bandit algorithms; for example, current methods cannot be used for valid inference on parameters in a logistic regression model for a binary reward. In this work, we develop theory justifying the use of M-estimators -- which includes estimators based on empirical risk minimization as well as maximum likelihood -- on data collected with adaptive algorithms, including (contextual) bandit algorithms. Specifically, we show that M-estimators, modified with particular adaptive weights, can be used to construct asymptotically valid confidence regions for a variety of inferential targets.
Adaptive collection of data is commonplace in applications throughout science and engineering. From the point of view of statistical inference however, adaptive data collection induces memory and correlation in the samples, and poses significant challenge. We consider the high-dimensional linear regression, where the samples are collected adaptively, and the sample size $n$ can be smaller than $p$, the number of covariates. In this setting, there are two distinct sources of bias: the first due to regularization imposed for consistent estimation, e.g. using the LASSO, and the second due to adaptivity in collecting the samples. We propose online debiasing, a general procedure for estimators such as the LASSO, which addresses both sources of bias. In two concrete contexts $(i)$ time series analysis and $(ii)$ batched data collection, we demonstrate that online debiasing optimally debiases the LASSO estimate when the underlying parameter $theta_0$ has sparsity of order $o(sqrt{n}/log p)$. In this regime, the debiased estimator can be used to compute $p$-values and confidence intervals of optimal size.
Learning optimal policies from historical data enables the gains from personalization to be realized in a wide variety of applications. The growing policy learning literature focuses on a setting where the treatment assignment policy does not adapt to the data. However, adaptive data collection is becoming more common in practice, from two primary sources: 1) data collected from adaptive experiments that are designed to improve inferential efficiency; 2) data collected from production systems that are adaptively evolving an operational policy to improve performance over time (e.g. contextual bandits). In this paper, we aim to address the challenge of learning the optimal policy with adaptively collected data and provide one of the first theoretical inquiries into this problem. We propose an algorithm based on generalized augmented inverse propensity weighted estimators and establish its finite-sample regret bound. We complement this regret upper bound with a lower bound that characterizes the fundamental difficulty of policy learning with adaptive data. Finally, we demonstrate our algorithms effectiveness using both synthetic data and public benchmark datasets.
Exploration policies in Bayesian bandits maximize the average reward over problem instances drawn from some distribution $mathcal{P}$. In this work, we learn such policies for an unknown distribution $mathcal{P}$ using samples from $mathcal{P}$. Our approach is a form of meta-learning and exploits properties of $mathcal{P}$ without making strong assumptions about its form. To do this, we parameterize our policies in a differentiable way and optimize them by policy gradients, an approach that is general and easy to implement. We derive effective gradient estimators and introduce novel variance reduction techniques. We also analyze and experiment with various bandit policy classes, including neural networks and a novel softmax policy. The latter has regret guarantees and is a natural starting point for our optimization. Our experiments show the versatility of our approach. We also observe that neural network policies can learn implicit biases expressed only through the sampled instances.
Statistical postprocessing techniques are nowadays key components of the forecasting suites in many National Meteorological Services (NMS), with for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS towards running ensemble Numerical Weather Prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations; the necessity to preserve space time correlation of high-dimensional corrected fields; the need to reduce the impact of model changes affecting the parameters of the corrections; the necessity for techniques to merge different types of forecasts and ensembles with different behaviors; and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues will also be discussed.
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