Stochastic Approximation with Delayed Updates: Finite-Time Rates under Markovian Sampling

Core Concepts

Non-asymptotic performance of stochastic approximation with delayed updates under Markovian sampling.

Abstract

This article explores the impact of delays on stochastic approximation schemes under Markovian sampling. It provides insights into the convergence rates of delayed SA rules and introduces a novel delay-adaptive SA scheme. The analysis includes theoretical findings on the effects of delays in various algorithms, shedding light on the interplay between delays and Markovian sampling.
Structure:

Introduction
Problem Formulation
Stochastic Approximation with Constant Delays
Stochastic Approximation with Time-Varying Delays
Delay-Adaptive Stochastic Approximation
Conclusions and Future Work

Stats

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Quotes

"Our theoretical findings shed light on the finite-time effects of delays for a broad class of algorithms."
"The delay-adaptive scheme requires no prior knowledge of the delay sequence for step-size tuning."

Key Insights Distilled From

Stochastic Approximation with Delayed Updates

by Arman Adibi,... at arxiv.org 03-27-2024

https://arxiv.org/pdf/2402.11800.pdf

Deeper Inquiries

How do delays impact the convergence rates of stochastic approximation in real-world applications

Delays can significantly impact the convergence rates of stochastic approximation in real-world applications. In the context of the study provided, delays in the updates of the stochastic approximation algorithm can lead to slower convergence rates. This is because delayed updates introduce errors in the estimation process, causing the algorithm to potentially move in suboptimal directions. As a result, the algorithm may take longer to converge to the optimal solution or fixed point. The impact of delays is particularly pronounced in settings where the delays are significant or vary over time. In such cases, the convergence rate may be further slowed down, requiring careful analysis and adaptation of the algorithm to mitigate the effects of delays.

What are the implications of delays in asynchronous multi-agent reinforcement learning

In asynchronous multi-agent reinforcement learning, delays can have several implications on the learning process and overall performance of the agents. Firstly, delays can lead to synchronization issues among the agents, causing inconsistencies in the information exchange and decision-making process. This can result in suboptimal policies, slower learning rates, and reduced overall performance of the multi-agent system. Additionally, delays can introduce uncertainty and instability in the communication network, affecting the coordination and cooperation among the agents. As a result, delays can hinder the convergence of the reinforcement learning algorithms, leading to longer training times and potentially inferior outcomes. Strategies to address delays in asynchronous multi-agent reinforcement learning are crucial to ensure efficient and effective learning in complex environments.

Can the findings on delays be extended to study robustness in other types of structured perturbations

The findings on delays in stochastic approximation can be extended to study robustness in other types of structured perturbations. By understanding how delays impact the convergence rates and performance of algorithms, researchers can apply similar analysis techniques to investigate the effects of other structured perturbations on iterative learning processes. For example, studying the robustness of algorithms to noise, sparsity, or communication constraints can benefit from the insights gained from analyzing delays. By developing a deeper understanding of how different types of perturbations affect the convergence and stability of iterative algorithms, researchers can design more resilient and efficient learning systems. This extension of the findings on delays to other structured perturbations can contribute to the development of more robust and adaptive learning algorithms in various applications.