Forced Exploration in Bandit Problems
This addresses a practical issue for practitioners who struggle with distribution assumptions in non-stationary bandit problems, though it is incremental as it builds on existing forced exploration strategies.
The paper tackles the problem of designing a multi-armed bandit algorithm that does not require prior knowledge of reward distributions, achieving substantial regret upper bounds for stationary and piecewise-stationary settings.
The multi-armed bandit(MAB) is a classical sequential decision problem. Most work requires assumptions about the reward distribution (e.g., bounded), while practitioners may have difficulty obtaining information about these distributions to design models for their problems, especially in non-stationary MAB problems. This paper aims to design a multi-armed bandit algorithm that can be implemented without using information about the reward distribution while still achieving substantial regret upper bounds. To this end, we propose a novel algorithm alternating between greedy rule and forced exploration. Our method can be applied to Gaussian, Bernoulli and other subgaussian distributions, and its implementation does not require additional information. We employ a unified analysis method for different forced exploration strategies and provide problem-dependent regret upper bounds for stationary and piecewise-stationary settings. Furthermore, we compare our algorithm with popular bandit algorithms on different reward distributions.