Analyzing the Effectiveness of Local Updates for Decentralized Learning under Data Heterogeneity

Core Concepts

Incorporating multiple local updates can reduce communication complexity in decentralized learning under data heterogeneity.

Abstract

The article discusses the effectiveness of local updates in decentralized learning under data heterogeneity. It explores two fundamental methods, Decentralized Gradient Tracking (DGT) and Decentralized Gradient Descent (DGD), demonstrating how increasing local update steps can reduce communication complexity. The study reveals a tradeoff between communication and computation, showing that more local updates can lower costs when data heterogeneity is low and network connectivity is strong. The impact of gradient heterogeneity on convergence is analyzed, along with the benefits of employing local updates in different settings. The article also delves into over-parameterization scenarios and compares DGT and DGD algorithms in reducing communication costs.
Index:

Introduction to Decentralized Optimization
Algorithms for Collaborative Learning
Impact of Data Heterogeneity on Communication Costs
Over-parameterization Regime Analysis
Comparison of DGT and DGD Algorithms

Stats

We proved that local DGT achieves communication complexity O(LµK + δµ(1−ρ) + ρ(1−ρ)2L+δµ).
For arbitrary bound δ, it takes local DGD O(LµK + δ2/µ2(1−ρ)) communication rounds to reach the minimizer.
Our result shows that increasing K can significantly reduce communication overhead when network connectivity is strong.

Quotes

"Increasing K can effectively reduce communication costs when data heterogeneity is low."
"Our result reveals a tradeoff between communication and computation."

Key Insights Distilled From

The Effectiveness of Local Updates for Decentralized Learning under Data Heterogeneity

by Tongle Wu,Yi... at arxiv.org 03-26-2024

https://arxiv.org/pdf/2403.15654.pdf

Deeper Inquiries

How does network connectivity impact the effectiveness of local updates?

In the context of decentralized learning algorithms like DGT and DGD, network connectivity plays a crucial role in determining the effectiveness of local updates. The experiments conducted in the provided context demonstrate that network connectivity directly impacts how beneficial increasing the number of local updates can be in reducing communication costs.

High Network Connectivity: When the network is well-connected (high ρ), increasing the number of local updates per communication round can significantly reduce communication overhead. In this scenario, more frequent local computations before communicating with network neighbors prove to be effective in accelerating optimization processes and reducing overall communication complexity.

Low Network Connectivity: Conversely, when there is poor network connectivity (low ρ), additional local updates may not offer significant benefits in terms of reducing communication costs. In such cases, unnecessary computation costs may outweigh any potential gains from increased local updates.
Therefore, high network connectivity enhances the efficiency and effectiveness of incorporating multiple local update steps by effectively reducing communication overhead.

How do over-parameterization scenarios affect the choice between DGT and DGD algorithms?

In over-parameterization scenarios where models have a large number of parameters allowing them to perfectly interpolate training data, both DGT and DGD algorithms exhibit unique characteristics:

DGT Algorithm:

Effectiveness: Local Distributed Gradient Tracking (DGT) algorithm actively aligns each agent's descent direction with average gradient using gradient tracking techniques.
Convergence Guarantee: Under certain conditions like strong convexity or Polyak-Łojasiewicz condition for average loss function f, Local DGT converges linearly to an ε-optimal solution while correcting for gradient heterogeneity.
Communication Complexity Reduction: Increasing K (number of local update steps) can significantly reduce communication overhead when data heterogeneity is low and networks are well-connected.

DGD Algorithm:

Automatic Convergence: Local Distributed Gradient Descent (DGD) algorithm automatically converges to exact minimizer due to shared minimums among all agents' loss functions under over-parameterized settings.
Communication Efficiency: While still achieving exact convergence without bias correction even with multiple local updates but without as much reduction in communication complexity as seen with Local DDT under similar conditions.
The choice between these two algorithms depends on factors such as data heterogeneity levels, degree of second-order derivatives differences among individual loss functions fi compared to average loss f, level of model parameter overfitting due to interpolation capacity relative to sample size N vs dimensionality d ratio etc., which ultimately determine which algorithm would be more suitable based on specific problem requirements.