TL;DR#
Adversarial multi-armed bandit (MAB) problems are a significant challenge in online learning, where limited feedback makes finding optimal algorithms difficult. Previous research suggested fundamental limitations of Prod-family algorithms, a class of simple arithmetic update rules, in MAB settings, favoring more complex methods like online mirror descent (OMD). These complex methods often require solving computationally expensive optimization problems.
This research challenges the established view. By leveraging the interpretation of Prod as a first-order OMD approximation, it presents modified Prod variants that achieve optimal regret guarantees in adversarial MAB problems. Furthermore, it introduces a surprisingly simple, importance-weighting-free version that maintains optimal performance. The work offers a significant improvement over prior state-of-the-art, specifically in incentive-compatible bandit settings where the experts’ incentives must be carefully managed.
Key Takeaways#
Why does it matter?#
This paper challenges existing beliefs about the limitations of Prod-family algorithms in online learning, demonstrating their surprising efficacy for multi-armed bandit problems. It introduces novel variants achieving optimal regret bounds and best-of-both-worlds guarantees, simplifying existing algorithms and advancing the state-of-the-art in incentive-compatible bandits. This has implications for various online learning applications requiring efficient and robust solutions.
Visual Insights#
Full paper#
