Exploration via Linearly Perturbed Loss Minimisation: A Study on Bandit Algorithms

Core Concepts

The authors introduce EVILL as a method for structured stochastic bandit problems, providing insights into the effectiveness of random reward perturbations. EVILL offers a new approach to exploration by minimizing loss functions perturbed with random linear components.

Abstract

The study introduces EVILL as a method for structured stochastic bandit problems, comparing it to perturbed history exploration (PHE). The research focuses on the effectiveness of random reward perturbations and their impact on bandit algorithms. By proposing data-dependent perturbations, EVILL matches the performance of parameter-perturbation methods like Thompson sampling. The study highlights the importance of exploring when and why additive reward perturbations can be successful in different bandit settings. It also addresses challenges faced by PHE in certain scenarios and demonstrates how EVILL remains performant. Overall, the research extends the literature on randomised exploration in stochastic bandits by introducing a novel method that simplifies implementation while maintaining competitive performance.

Stats

We propose data-dependent perturbations not present in previous PHE-type methods. The scaling of data-dependent perturbations arises naturally from considering a quadratic approximation to the loss. In self-concordant generalised linear bandits, the regret of EVILL enjoys guarantees similar to those available for Thompson sampling.

Quotes

"We propose a new way of inducing exploration, EVILL, which adds a random linear term to the model-fitting loss." "EVILL is equivalent to PHE with additive perturbations in generalised linear bandits but is also applicable in settings where PHE is not well-defined or is inconsistent."

Key Insights Distilled From

Exploration via linearly perturbed loss minimisation

by Davi... at arxiv.org 03-07-2024

https://arxiv.org/pdf/2311.07565.pdf

Deeper Inquiries

How does EVILL's approach to exploration compare with traditional methods like Thompson sampling

EVILL's approach to exploration differs from traditional methods like Thompson sampling in the way it introduces random perturbations. While Thompson sampling samples parameters from a posterior distribution and selects actions based on these samples, EVILL adds linear perturbations to the loss function during model fitting. This perturbation induces optimism by ensuring that the mean reward for the best arm under the random parameter exceeds that under the true model parameter with some probability bounded away from zero uniformly.

What are the implications of data-dependent perturbations introduced by EVILL for other machine learning applications

The data-dependent perturbations introduced by EVILL have significant implications for other machine learning applications, particularly in scenarios where exploration is crucial for optimizing long-term rewards while interacting with environments. By incorporating linearly perturbed loss minimization, EVILL provides a simple yet effective method of inducing optimism in models without complex modifications. These data-dependent perturbations can enhance exploration strategies across various domains such as reinforcement learning, contextual bandits, and optimization problems.

How might the findings of this study impact future research on stochastic bandit algorithms

The findings of this study are likely to influence future research on stochastic bandit algorithms by offering a new perspective on structured stochastic bandit problems. The development of EVILL as an alternative exploration method opens up avenues for exploring different approaches to balancing exploitation and exploration efficiently. Researchers may further investigate how linearly perturbed loss minimization can be adapted or extended to more complex models or real-world applications beyond generalised linear bandits. Additionally, understanding when and why additive reward perturbations induce optimal levels of exploration could lead to advancements in algorithm design and performance evaluation within stochastic environments.