Importance weighting without importance weights: An efficient algorithm for combinatorial semi-bandits
This addresses computational efficiency challenges in online learning for combinatorial decision-making, though it is incremental as it builds on existing methods like FPL.
The paper tackles the problem of online combinatorial optimization under semi-bandit feedback by proposing Geometric Resampling (GR) as an efficient alternative to importance weighting, achieving performance guarantees with high probability and improving regret bounds for Follow-the-Perturbed-Leader in full feedback settings.
We propose a sample-efficient alternative for importance weighting for situations where one only has sample access to the probability distribution that generates the observations. Our new method, called Geometric Resampling (GR), is described and analyzed in the context of online combinatorial optimization under semi-bandit feedback, where a learner sequentially selects its actions from a combinatorial decision set so as to minimize its cumulative loss. In particular, we show that the well-known Follow-the-Perturbed-Leader (FPL) prediction method coupled with Geometric Resampling yields the first computationally efficient reduction from offline to online optimization in this setting. We provide a thorough theoretical analysis for the resulting algorithm, showing that its performance is on par with previous, inefficient solutions. Our main contribution is showing that, despite the relatively large variance induced by the GR procedure, our performance guarantees hold with high probability rather than only in expectation. As a side result, we also improve the best known regret bounds for FPL in online combinatorial optimization with full feedback, closing the perceived performance gap between FPL and exponential weights in this setting.