Learning Across Bandits in High Dimension via Robust Statistics

Decision-makers often face the "many bandits" problem, where one must simultaneously learn across related but heterogeneous contextual bandit instances. For instance, a large retailer may wish to dynamically learn product demand across many stores to solve pricing or inventory problems, making it desirable to learn jointly for stores serving similar customers; alternatively, a hospital network may wish to dynamically learn patient risk across many providers to allocate personalized interventions, making it desirable to learn jointly for hospitals serving similar patient populations. We study the setting where the unknown parameter in each bandit instance can be decomposed into a global parameter plus a sparse instance-specific term. Then, we propose a novel two-stage estimator that exploits this structure in a sample-efficient way by using a combination of robust statistics (to learn across similar instances) and LASSO regression (to debias the results). We embed this estimator within a bandit algorithm, and prove that it improves asymptotic regret bounds in the context dimension $d$; this improvement is exponential for data-poor instances. We further demonstrate how our results depend on the underlying network structure of bandit instances. Finally, we illustrate the value of our approach on synthetic and real datasets

Meta Dynamic Pricing: Transfer Learning Across Experiments

We study the problem of learning shared structure across a sequence of dynamic pricing experiments for related products. We consider a practical formulation in which the unknown demand parameters for each product come from an unknown distribution (prior) that is shared across products. We then propose a meta dynamic pricing algorithm that learns this prior online while solving a sequence of Thompson sampling pricing experiments (each with horizon T) for N different products. Our algorithm addresses two challenges: (i) balancing the need to learn the prior (meta-exploration) with the need to leverage the estimated prior to achieve good performance (meta-exploitation) and (ii) accounting for uncertainty in the estimated prior by appropriately “widening” the estimated prior as a function of its estimation error. We introduce a novel prior alignment technique to analyze the regret of Thompson sampling with a misspecified prior, which may be of independent interest. Unlike prior-independent approaches, our algorithm’s meta regret grows sublinearly in N, demonstrating that the price of an unknown prior in Thompson sampling can be negligible in experiment-rich environments (large N). Numerical experiments on synthetic and real auto loan data demonstrate that our algorithm significantly speeds up learning compared with prior-independent algorithms. This paper was accepted by George J. Shanthikumar, Management Science Special Section on Data-Driven Prescriptive Analytics. </jats:p

Efficient and targeted COVID-19 border testing via reinforcement learning

Throughout the coronavirus disease 2019 (COVID-19) pandemic, countries have relied on a variety of ad hoc border control protocols to allow for non-essential travel while safeguarding public health, from quarantining all travellers to restricting entry from select nations on the basis of population-level epidemiological metrics such as cases, deaths or testing positivity rates(1,2). Here we report the design and performance of a reinforcement learning system, nicknamed Eva. In the summer of 2020, Eva was deployed across all Greek borders to limit the influx of asymptomatic travellers infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and to inform border policies through real-time estimates of COVID-19 prevalence. In contrast to country-wide protocols, Eva allocated Greece&apos;s limited testing resources on the basis of incoming travellers&apos; demographic information and testing results from previous travellers. By comparing Eva&apos;s performance against modelled counterfactual scenarios, we show that Eva identified 1.85 times as many asymptomatic, infected travellers as random surveillance testing, with up to 2-4 times as many during peak travel, and 1.25-1.45 times as many asymptomatic, infected travellers as testing policies that utilize only epidemiological metrics. We demonstrate that this latter benefit arises, at least partially, because population-level epidemiological metrics had limited predictive value for the actual prevalence of SARS-CoV-2 among asymptomatic travellers and exhibited strong country-specific idiosyncrasies in the summer of 2020. Our results raise serious concerns on the effectiveness of country-agnostic internationally proposed border control policies(3) that are based on population-level epidemiological metrics. Instead, our work represents a successful example of the potential of reinforcement learning and real-time data for safeguarding public health. A study reports the design and performance of a reinforcement learning algorithm that enabled efficient and targeted SARS-CoV-2 testing of passengers travelling to Greece in the summer of 2020