Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Abstract: We study Byzantine collaborative learning, where $n$ nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and $f < n$ nodes can behave arbitrarily. We prove that collaborative learning is equivalent to a new form of agreement, which we call averaging agreement. In this problem, nodes start each with an initial vector and seek to approximately agree on a common vector, which is close to the average of honest nodes' initial vectors. We present two asynchronous solutions to averaging agreement, each we prove optimal according to some dimension. The first, based on the minimum-diameter averaging, requires $ n \geq 6f+1$, but achieves asymptotically the best-possible averaging constant up to a multiplicative constant. The second, based on reliable broadcast and coordinate-wise trimmed mean, achieves optimal Byzantine resilience, i.e., $n \geq 3f+1$. Each of these algorithms induces an optimal Byzantine collaborative learning protocol. In particular, our equivalence yields new impossibility theorems on what any collaborative learning algorithm can achieve in adversarial and heterogeneous environments.

Byzantine Collaborative Learning in Decentralized Environments

The paper titled "Collaborative Learning in the Jungle" addresses the complex issue of Byzantine collaborative learning in decentralized, heterogeneous, asynchronous environments with non-convex loss functions. This research examines scenarios where nodes in a network strive to collaboratively learn from locally stored data, despite the presence of up to $f$ of $n$ nodes exhibiting arbitrary Byzantine behaviors.

Problem Space and Contributions

The authors initiate their investigation by formulating the problem of decentralized collaborative learning under Byzantine conditions as "averaging agreement". This abstract concept involves nodes that must converge to a common vector that closely represents the average of honest nodes' initial vectors. To solve this, the paper introduces two algorithms, both optimal under different criterions.

1. Minimum-Diameter Averaging (MDA): Requires $n \geq 6f+1$ nodes for operation. This algorithm is asymptotically optimal with respect to the correctness of averaging, using the smallest possible averaging constant relative to data heterogeneity when nearly all nodes are honest.

2. Reliable Broadcast - Trimmed Mean (RB-TM): Achieves optimal Byzantine resilience requiring $n \geq 3f+1$ nodes. This method employs a reliable broadcasting mechanism to prevent Byzantine nodes from tampering with honest nodes' data, ensuring that the agreement reflects a version of trimmed mean despite adversarial interference.

The equivalency between collaborative learning and averaging agreement underpins the authors' contributions, providing tight reductions that facilitate both impossibility results and optimal solutions derivations for collaborative learning.

Theoretical Insights

The research presents critical theoretical findings showing the limits and possibilities within Byzantine collaborative learning:

• Averaging Agreement Equivalence: Collaborative learning is reduced to the averaging agreement problem, providing a novel perspective that simplifies the analysis of Byzantine resilience in distributed learning.

• Limitations of Byzantine Resistance: The paper presents strong theoretical bounds, such as the lower resilience limit where no solution exists if $n \leq 3f$. These bounds highlight critical thresholds for practical implementations of the distributed algorithms.

The theoretical analysis is detailed through various lemmas, propositions, and proofs, offering rigorous mathematical formulations to support claims of algorithmic efficiency and resilience.

Practical Implications and Future Speculations

The proposed algorithms are evaluated empirically, notably demonstrating resilience in environments with different data distributions. The paper implements these algorithms on models ranging from simple neural networks to complex ones like ResNet.

This research has profound implications on distributed machine learning, particularly in federated and edge computation scenarios where security concerns against Byzantine adversaries persist. While the current study suggests optimal configurations and resilience levels, future research could explore adaptability to dynamic Byzantine behaviors or further optimize the communication overhead inherent in these solutions.

In summary, this paper advances understanding of collaborative learning in hostile, decentralized environments, presenting robust solutions that should influence future developments addressing scalability and security in distributed AI systems.