Addressing Heavy-Tailed Rewards in Reinforcement Learning with Linear Function Approximation

Core Concepts

The author addresses the challenge of heavy-tailed rewards in reinforcement learning using linear function approximation, proposing novel algorithms HEAVY-OFUL and HEAVY-LSVI-UCB.

Abstract

The content discusses the challenges of heavy-tailed rewards in reinforcement learning, introducing algorithms HEAVY-OFUL and HEAVY-LSVI-UCB. These algorithms utilize adaptive Huber regression to handle heavy-tailed noise efficiently. Theoretical regret bounds and computational complexities are analyzed, demonstrating the effectiveness of these algorithms in handling heavy-tailed rewards.
Key points include:

Introduction to the challenge of heavy-tailed rewards in reinforcement learning.
Proposal of algorithms HEAVY-OFUL and HEAVY-LSVI-UCB for efficient handling of heavy-tailed rewards.
Utilization of adaptive Huber regression for estimating reward functions and value functions.
Theoretical analysis of regret bounds and computational complexities.
Demonstration of minimax optimality in worst-case scenarios.
The results highlight the importance of addressing heavy-tailed rewards in reinforcement learning with efficient algorithms like HEAVY-OFUL and HEAVY-LSVI-UCB.

Stats

HEAVY-OFUL achieves an instance-dependent T-round regret of eO(dT1−ϵ2(1+ϵ)qPTt=1 ν2t + dT1−ϵ2(1+ϵ).
HEAVY-LVSI-UCB achieves a K-episode regret scaling as eO(d√HU∗K11+ϵ + d√HV∗K).

Quotes

"While numerous works have focused on devising efficient algorithms for reinforcement learning with uniformly bounded rewards, it remains an open question whether sample or time-efficient algorithms for RL with large state-action space exist when the rewards are heavy-tailed."
"Consequently, the performance of traditional algorithms may decline, emphasizing the need for the development of new, efficient algorithms specifically designed to handle heavy-tailed rewards."

Key Insights Distilled From

Tackling Heavy-Tailed Rewards in Reinforcement Learning with Function Approximation

by Jiayi Huang,... at arxiv.org 03-08-2024

https://arxiv.org/pdf/2306.06836.pdf

Deeper Inquiries

How can these proposed algorithms be extended to handle other types of non-standard reward distributions

The proposed algorithms, HEAVY-OFUL and HEAVY-LSVI-UCB, can be extended to handle other types of non-standard reward distributions by adapting the estimation techniques used for heavy-tailed rewards. For instance, if the rewards follow a different distribution such as asymmetric or skewed distributions, the adaptive Huber regression approach can be modified to account for these characteristics. By adjusting the parameters and constraints in the algorithm based on the properties of the specific reward distribution, it is possible to tailor the algorithms to handle a wide range of non-standard reward distributions.

What implications do these findings have on real-world applications that involve heavy-tailed reward distributions

The findings from these algorithms have significant implications for real-world applications that involve heavy-tailed reward distributions. In scenarios where traditional reinforcement learning approaches struggle with heavy-tailed rewards due to their unpredictable nature and high variance, these new algorithms offer a promising solution. Applications in finance, healthcare, marketing analytics, and other fields where outcomes exhibit heavy-tailed behavior could benefit greatly from more efficient and effective RL algorithms tailored for such distributions. Improved performance in handling heavy-tailed rewards can lead to better decision-making processes, optimized resource allocation strategies, and enhanced overall system efficiency.

How can adaptive Huber regression be further optimized or enhanced to improve its performance in handling heavy-tailed noise

To further optimize adaptive Huber regression for handling heavy-tailed noise more effectively, several enhancements can be considered:

Adaptive Parameter Tuning: Implement dynamic adjustment mechanisms for parameters like robustness parameter τt based on evolving data patterns during training.
Ensemble Methods: Explore ensemble methods by combining multiple instances of adaptive Huber regression with varying parameters or initialization conditions to improve robustness.
Regularization Techniques: Incorporate regularization techniques into adaptive Huber regression to prevent overfitting when dealing with noisy data.
Online Learning Updates: Develop online learning updates that adaptively adjust model weights based on recent observations while maintaining stability against heavy-tailed noise.
Feature Engineering: Enhance feature engineering strategies tailored specifically for handling heavy-tailed noise patterns in order to extract more relevant information from input data.

By implementing these optimizations and enhancements in adaptive Huber regression, its performance in handling heavy-tailed noise can be improved significantly across various applications requiring robust machine learning models under challenging conditions.