Transferring Information Across Causally Abstracted Multi-armed Bandits

Khái niệm cốt lõi

This work introduces the problem of Causally Abstracted Multi-armed Bandits (CAMABs), where decision-making problems are modeled at different levels of resolution and related via causal abstraction. The authors propose algorithms to learn across these related models and analyze their regret.

Tóm tắt

The paper introduces the problem of Causally Abstracted Multi-armed Bandits (CAMABs), where decision-making problems are modeled at different levels of resolution and related via causal abstraction. The key insights are:

Rewriting the title to be more informative and honest.
The content is categorized as Causal Inference.
The main topic is Causally Abstracted Multi-armed Bandits.
The core message is that the authors introduce the CAMAB problem, where decision-making problems are modeled at different levels of resolution and related via causal abstraction, and propose algorithms to learn across these related models.

The paper first provides background on Structural Causal Models (SCMs) and Causal Multi-armed Bandits (CMABs). It then defines the CAMAB problem, where two CMABs are related via a causal abstraction. The authors introduce measures to quantify the quality of the abstraction, such as interventional consistency error and reward discrepancy.
The paper then studies three representative scenarios for transferring information in CAMABs:

Transferring the optimal action from the base CMAB to the abstracted CMAB. The authors show that this is not guaranteed to work, even with an exact abstraction.
Transferring the actions taken in the base CMAB to the abstracted CMAB. The authors analyze the trade-off between confidence and regret in this approach.
Transferring the expected values of rewards from the base CMAB to the abstracted CMAB. The authors propose an algorithm (TExp) that uses this approach and analyze its regret.

Finally, the authors showcase their algorithms on a realistic online advertising scenario and discuss connections to related work.

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Thông tin chi tiết chính được chắt lọc từ

Causally Abstracted Multi-armed Bandits

by Fabio Massim... lúc arxiv.org 04-29-2024

https://arxiv.org/pdf/2404.17493.pdf

Yêu cầu sâu hơn

How can the causal abstraction be learned in an efficient and data-driven way, rather than being provided as prior knowledge

In order to learn causal abstraction in an efficient and data-driven manner, one can leverage techniques from causal inference and machine learning. Here are some approaches:

Causal Discovery Algorithms: Utilize causal discovery algorithms such as PC Algorithm, GES, or FCI to learn the causal relationships from observational data. These algorithms can help identify the causal structure of the variables in the system.

Interventional Data: Collect intervention data where specific variables are manipulated or intervened upon. By analyzing the outcomes of these interventions, one can infer causal relationships and build the causal abstraction map.

Counterfactual Reasoning: Incorporate counterfactual reasoning to estimate the causal effects of interventions. By comparing the outcomes of actual interventions with counterfactual scenarios, one can learn the causal relationships between variables.

Machine Learning Models: Use machine learning models, such as causal inference algorithms or deep learning models, to learn the causal relationships from data. These models can capture complex causal structures and provide insights into the causal abstraction.

Transfer Learning: Apply transfer learning techniques to transfer causal knowledge from related domains or tasks. By leveraging knowledge from similar contexts, one can enhance the learning of causal abstractions in new environments.

By combining these approaches and leveraging data-driven methods, one can efficiently learn causal abstractions from data without relying solely on prior knowledge.

What are the implications of the CAMAB framework for other structured bandit problems, such as linear or contextual bandits

The CAMAB framework has implications for other structured bandit problems, such as linear or contextual bandits, in the following ways:

Structured Bandit Algorithms: CAMAB can inspire the development of structured bandit algorithms that incorporate causal relationships into decision-making. By considering the causal structure of the problem, algorithms can make more informed decisions and optimize rewards efficiently.

Transfer Learning in Bandits: The transfer learning aspect of CAMAB can be extended to other structured bandit problems. By transferring knowledge and insights from one structured bandit problem to another, algorithms can adapt and improve performance in new environments.

Optimal Intervention Strategies: CAMAB can provide insights into optimal intervention strategies in structured bandit problems. By understanding the causal relationships between actions and rewards, algorithms can prioritize interventions that lead to the most significant rewards.

Generalization to Different Bandit Settings: The principles of CAMAB, such as abstraction mapping and information transfer, can be generalized to different structured bandit settings, allowing for a more comprehensive approach to decision-making in complex environments.

Overall, the CAMAB framework can enhance the understanding and optimization of structured bandit problems by incorporating causal relationships and transfer learning principles.

How can the CAMAB framework be extended to handle more complex causal structures, such as cyclic or latent variable models

To extend the CAMAB framework to handle more complex causal structures, such as cyclic or latent variable models, several considerations and approaches can be taken:

Cyclic Causal Models: For cyclic causal structures, specialized algorithms and techniques from cyclic causal inference can be applied. Methods like cyclic causal discovery algorithms or cyclic causal effect estimation can help in modeling and understanding the causal relationships in cyclic structures.

Latent Variable Models: In the case of latent variable models, techniques like structural equation modeling (SEM) or latent variable modeling can be employed to uncover the hidden causal factors influencing the observed variables. By incorporating latent variables into the abstraction map, the CAMAB framework can account for these hidden influences.

Bayesian Networks: Bayesian networks are effective tools for modeling complex causal structures, including cyclic and latent variable models. By representing the causal relationships in a probabilistic graphical model, the CAMAB framework can utilize Bayesian networks to capture and analyze intricate causal dependencies.

Probabilistic Programming: Probabilistic programming languages like Pyro or Stan can be used to model complex causal structures and infer causal relationships. By encoding the causal relationships in a probabilistic programming framework, the CAMAB framework can handle the uncertainty and complexity of cyclic or latent variable models.

By integrating these approaches and adapting the CAMAB framework to accommodate more intricate causal structures, researchers and practitioners can address the challenges posed by cyclic and latent variable models in decision-making problems.