Optimal On-Demand Sampling for Learning from Multiple Distributions

Основные понятия

The core message of this paper is to establish the optimal sample complexity of multi-distribution learning paradigms, such as collaborative learning, group distributionally robust optimization, and agnostic federated learning. The authors show that their algorithms can achieve this optimal sample complexity by learning to sample from data distributions on demand.

Аннотация

The paper presents a general framework for obtaining optimal and on-demand sample complexity for three multi-distribution learning settings: collaborative learning, group distributionally robust optimization (group DRO), and agnostic federated learning.
Key highlights:

The authors frame multi-distribution learning as a stochastic zero-sum game between a minimizing player (the learner) and a maximizing player (the auditor). This allows them to leverage no-regret game dynamics to efficiently find an approximate min-max equilibrium.
The main technical challenge is that the maximizing player's payoff is more costly to estimate than the minimizing player's, due to the need to sample from multiple data distributions. The authors overcome this by using stochastic mirror descent to optimally trade off the players' asymmetric needs for datapoints.
For collaborative learning, the authors provide randomized and deterministic models that achieve optimal sample complexity, improving upon previous results.
For group DRO, the authors provide the first sample complexity bounds, as well as high-probability bounds on the convergence of the training error.
For agnostic federated learning, the authors show that on-demand sampling can accelerate generalization by a factor of n compared to batch results.
The authors' results demonstrate that multi-distribution learning can be solved efficiently using on-demand sampling, with only an additive increase in sample complexity over learning a single distribution.

Статистика

None.

Цитаты

None.

Ключевые выводы из

On-Demand Sampling

by Nika Haghtal... в arxiv.org 04-04-2024

https://arxiv.org/pdf/2210.12529.pdf

Дополнительные вопросы

How can the techniques developed in this paper be extended to settings with more complex relationships between the data distributions, such as hierarchical or overlapping structures

The techniques developed in the paper can be extended to settings with more complex relationships between the data distributions by incorporating additional constraints or structures into the optimization framework. For hierarchical structures, where the data distributions may be organized in a nested or hierarchical manner, the multi-distribution learning algorithms can be modified to consider these relationships. This could involve introducing constraints that enforce consistency or hierarchy among the distributions, or incorporating prior knowledge about the relationships between the distributions into the learning process.
In the case of overlapping structures, where the data distributions may share common elements or characteristics, the algorithms can be adapted to handle the overlap by allowing for shared information or parameters between the distributions. This could involve developing models that can capture the shared features across distributions while still maintaining distinct characteristics for each distribution.
Overall, by extending the techniques to accommodate more complex relationships between data distributions, the algorithms can be made more versatile and applicable to a wider range of real-world scenarios where the data may exhibit intricate interdependencies.

What are the implications of the authors' results for the design of practical multi-distribution learning systems, particularly in the context of fairness, robustness, and multi-agent collaboration

The results presented in the paper have significant implications for the design of practical multi-distribution learning systems, especially in the context of fairness, robustness, and multi-agent collaboration.

Fairness: In the context of fairness, the optimal sample complexity bounds provided by the algorithms can lead to the development of more efficient and effective fairness mechanisms in machine learning systems. By minimizing the expected loss over multiple distributions while using fewer samples, these algorithms can help in designing fairer models that perform well across diverse populations or groups.

Robustness: For robustness applications, the algorithms' ability to handle multiple data distributions with varying uncertainties can enhance the resilience of machine learning models. By optimizing sample complexity and learning from distributions on demand, the systems can better adapt to uncertainties and variations in the data, leading to more robust and reliable models.

Multi-Agent Collaboration: In scenarios involving multi-agent collaboration, the algorithms' optimal sample complexity can facilitate the learning of shared models that perform well across different agents' tasks or datasets. This can improve collaboration and information sharing among agents while minimizing the overall sample requirements, making the learning process more efficient and collaborative.

Overall, the results of the paper pave the way for the development of advanced multi-distribution learning systems that can address key challenges in fairness, robustness, and multi-agent collaboration in machine learning.

Can the insights from this work on the sample complexity of multi-distribution learning be applied to other areas of machine learning, such as meta-learning or domain adaptation

The insights from this work on the sample complexity of multi-distribution learning can be applied to other areas of machine learning, such as meta-learning or domain adaptation, by adapting the algorithms and frameworks to suit the specific requirements of these domains.

Meta-Learning: In meta-learning, where the goal is to learn how to learn efficiently from a distribution of tasks, the techniques developed for optimizing sample complexity in multi-distribution learning can be valuable. By efficiently learning from multiple distributions and minimizing the sample requirements, meta-learning systems can be enhanced to adapt to new tasks or domains more effectively.

Domain Adaptation: For domain adaptation, where the aim is to transfer knowledge from a source domain to a target domain, the insights on sample complexity can help in designing more efficient adaptation algorithms. By understanding the optimal sample requirements for learning from multiple distributions, domain adaptation systems can be improved to handle diverse and complex data distributions more effectively.

By leveraging the principles and methodologies developed for multi-distribution learning, meta-learning and domain adaptation systems can benefit from enhanced efficiency, robustness, and adaptability in learning from multiple sources or domains.