Thompson Sampling for Stochastic Bandits with Noisy Contexts: An Information-Theoretic Regret Analysis

Core Concepts

Designing a Thompson Sampling algorithm for stochastic bandits with noisy contexts to minimize Bayesian cumulative regret.

Abstract

The article discusses the development of a modified Thompson Sampling algorithm for stochastic linear contextual bandits with Gaussian context noise. It aims to approximate the action policy of a Bayesian oracle using information-theoretic tools. The analysis shows that delayed true contexts lead to lower regret, and empirical performance against baselines is demonstrated.

Introduction

Decision-making under uncertainty is a common challenge in various domains.
Contextual bandits capture sequential decision-making incorporating side information.

Motivation and Problem Setting

Addressing noisy context settings in contextual bandits.
Developing algorithms tailored to handle noisy contexts effectively.

Challenges and Novelty

Proposing a fully Bayesian Thompson Sampling algorithm.
De-noising approach to estimate predictive distribution from noisy contexts.

Data Extraction

"Our information-theoretic analysis shows that the Bayesian cumulative regret scales as O(d √ T), where T is the horizon."

Quotations

"Different from existing works that developed UCB-based algorithms, we propose a fully Bayesian TS algorithm..."

Further Questions

How can the proposed algorithm be adapted to handle non-Gaussian noise distributions?
What are the practical implications of delayed true contexts on real-world applications?
How might the concept of de-noising be applied in other machine learning algorithms?

Stats

"Our information-theoretic analysis shows that the Bayesian cumulative regret scales as O(d √ T), where T is the horizon."

Quotes

"Different from existing works that developed UCB-based algorithms, we propose a fully Bayesian TS algorithm..."

Key Insights Distilled From

Thompson Sampling for Stochastic Bandits with Noisy Contexts

by Sharu Theres... at arxiv.org 03-26-2024

https://arxiv.org/pdf/2401.11565.pdf

Deeper Inquiries

How can the proposed algorithm be adapted to handle non-Gaussian noise distributions

To adapt the proposed algorithm to handle non-Gaussian noise distributions, we can modify the denoising step in Algorithm 1. Instead of assuming Gaussian noise channels, we can consider different parametric or non-parametric models for the noise distribution. For instance, if the noise follows a Laplace distribution or a Poisson distribution, we would need to adjust the calculations for evaluating the predictive posterior distribution accordingly. The key lies in accurately modeling the noise characteristics and incorporating them into the algorithm's framework while ensuring that it aligns with the underlying assumptions of Thompson Sampling.

What are the practical implications of delayed true contexts on real-world applications

Delayed true contexts have significant practical implications in real-world applications. One major implication is that agents can make more informed decisions by leveraging delayed context information received after observing rewards. This delay allows for better understanding of contextual patterns and relationships before making subsequent decisions. In scenarios like online recommendation systems or personalized marketing campaigns, delayed true contexts enable more accurate user profiling and tailored recommendations based on comprehensive historical data rather than just immediate observations.

How might the concept of de-noising be applied in other machine learning algorithms

The concept of de-noising can be applied in various machine learning algorithms beyond contextual bandits. In supervised learning tasks such as image classification or speech recognition, de-noising techniques like autoencoders can help remove irrelevant features or noisy inputs from data samples before feeding them into neural networks for training. Similarly, in reinforcement learning settings where noisy observations may impact policy optimization, de-noising methods could enhance decision-making processes by filtering out irrelevant information and focusing on essential signals to improve overall performance and efficiency.