Stochastic Bandit Models for Delayed Conversions (1706.09186v3)

Abstract: Online advertising and product recommendation are important domains of applications for multi-armed bandit methods. In these fields, the reward that is immediately available is most often only a proxy for the actual outcome of interest, which we refer to as a conversion. For instance, in web advertising, clicks can be observed within a few seconds after an ad display but the corresponding sale --if any-- will take hours, if not days to happen. This paper proposes and investigates a new stochas-tic multi-armed bandit model in the framework proposed by Chapelle (2014) --based on empirical studies in the field of web advertising-- in which each action may trigger a future reward that will then happen with a stochas-tic delay. We assume that the probability of conversion associated with each action is unknown while the distribution of the conversion delay is known, distinguishing between the (idealized) case where the conversion events may be observed whatever their delay and the more realistic setting in which late conversions are censored. We provide performance lower bounds as well as two simple but efficient algorithms based on the UCB and KLUCB frameworks. The latter algorithm, which is preferable when conversion rates are low, is based on a Poissonization argument, of independent interest in other settings where aggregation of Bernoulli observations with different success probabilities is required.

• The paper introduces a stochastic bandit model that manages both fully observed and censored delayed conversion data in online advertising.
• It develops UCB and KL-UCB based algorithms, using a Poissonization technique to perform well even with low conversion rates.
• Empirical results and regret lower bounds validate the approach, offering actionable insights for improved ad resource allocation.

An Expert Review of "Stochastic Bandit Models for Delayed Conversions"

The paper "Stochastic Bandit Models for Delayed Conversions" focuses on the unique challenges and opportunities presented by stochastic multi-armed bandit models in environments where rewards are subject to delays, particularly within the field of online advertising. Traditionally, in multi-armed bandit problems, immediate feedback is assumed upon action selection. However, in many applications, actual outcomes — such as conversions in advertising — are delayed. This paper proposes a novel approach to handling these delays, drawing from empirical observations in web advertising and building upon prior theoretical frameworks.

Key Contributions

1. Modeling Delayed Conversions: The authors introduce a stochastic bandit model to manage delayed rewards. This model incorporates two variations: one where all conversions are eventually observed, albeit with potentially long delays, and a censored version where observations are limited by practical constraints.
2. Algorithm Development: Two algorithms are proposed, based on Upper Confidence Bound (UCB) and KL-UCB frameworks, optimized for scenarios with delayed feedback. The KL-UCB variant, in particular, utilizes a Poissonization argument, delivering strong performance in contexts where conversion rates are low, which is a common state in online advertising.
3. Theoretical Insights: The paper provides lower bounds on the regret of any uniformly efficient algorithm in both censored and uncensored settings. This helps delineate the limitations inherent in learning in environments with delayed feedback and informs the development of more effective algorithms.
4. Empirical Evaluation: Through simulation, the paper demonstrates the efficacy of its proposed algorithms, showing that they efficiently manage the uncertainty introduced by delayed conversions and outperform naive benchmarks like discarding late feedback.

Implications for Research and Practice

The primary implication of the research is its potential to significantly improve decision-making processes in online advertising by more accurately attributing conversions to specific actions despite the inherent delays. This could lead to more efficient allocation of advertising resources and ultimately greater return on investment.

Theoretically, this work enriches the understanding of delayed feedback in reinforcement learning scenarios, providing a basis for developing algorithms that accommodate delay distributions. The practical considerations of knowing or estimating delay distributions open a path for further research into dynamic and contextual delay adaptation, which could be invaluable in various real-world applications beyond advertising, such as recommendation systems and customer relationship management.

Future Directions

Future research inspired by this work could explore:

• Dynamic Estimation of Delay Distributions:

Developing techniques to estimate delay distributions in real-time could make the proposed models more robust and adaptable to changing conditions.

• Contextual Bandit Extensions:

Incorporating context, such as user behaviors or environmental conditions, may enhance model performance by tailoring delay models for different scenarios.

• Application Across Domains:

Extending these models to other domains with delayed outcomes, exploring their use in areas like healthcare, where delayed impacts of interventions are common, could test the versatility and scalability of the approach.

In conclusion, the paper provides a significant contribution to the bandit literature by addressing the challenge of delayed feedback realistically and effectively. Its insights are bound to spark further research into not only refining these models but also expanding their applicability to a wider range of problems where delayed outcomes are a critical consideration.