Blessings of Multiple Good Arms in Multi-Objective Linear Bandits
This work addresses fairness and efficiency challenges in multi-objective decision-making for applications like recommendation systems, though it is incremental in extending implicit exploration to new settings.
The paper tackles the complexity of multi-objective linear bandits by showing that when multiple good arms exist, they enable implicit exploration, allowing simple greedy algorithms to achieve strong performance with theoretical and empirical results, such as improved regret bounds.
The multi objective bandit setting has traditionally been regarded as more complex than the single objective case, as multiple objectives must be optimized simultaneously. In contrast to this prevailing view, we demonstrate that when multiple good arms exist for multiple objectives, they can induce a surprising benefit, implicit exploration. Under this condition, we show that simple algorithms that greedily select actions in most rounds can nonetheless achieve strong performance, both theoretically and empirically. To our knowledge, this is the first study to introduce implicit exploration in both multi objective and parametric bandit settings without any distributional assumptions on the contexts. We further introduce a framework for effective Pareto fairness, which provides a principled approach to rigorously analyzing fairness of multi objective bandit algorithms.