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The Prophet Inequality and Pandora's Box problems are fundamental stochastic problem with applications in Mechanism Design, Online Algorithms, Stochastic Optimization, Optimal Stopping, and Operations Research. A usual assumption in these works is that the probability distributions of the n underlying random variables are given as input to the algorithm. Since in practice these distributions need to be learned under limited feedback, we initiate the study of such stochastic problems in the Multi-Armed Bandits model. In the Multi-Armed Bandits model we interact with n unknown distributions over T rounds: in round t we play a policy x(t) and only receive the value of x(t) as feedback. The goal is to minimize the regret, which is the difference over T rounds in the total value of the optimal algorithm that knows the distributions vs. the total value of our algorithm that learns the distributions from the limited feedback. Our main results give near-optimal Õ (poly (n) √T) total regret algorithms for both Prophet Inequality and Pandora's Box. Our proofs proceed by maintaining confidence intervals on the unknown indices of the optimal policy. The exploration-exploitation tradeoff prevents us from directly refining these confidence intervals, so the main technique is to design a regret upper bound function that is learnable while playing low-regret Bandit policies.
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Active Search using Meta-Bandits
There are many applications where positive instances are rare but important to identify. For example, in NLP, positive sentences for a given relation are rare in a large corpus. Positive data are more informative for learning in these applications, but before one labels a certain amount of data, it is unknown where to find the rare positives. Since random sampling can lead to significant waste in labeling effort, previous ”active search” methods use a single bandit model to learn about the data distribution (exploration) while sampling from the regions potentially containing more positives (exploitation). Many bandit models are possible and a sub-optimal model reduces labeling efficiency, but the optimal model is unknown before any data are labeled. We propose Meta-AS (Meta Active Search) that uses a meta-bandit to evaluate a set of base bandits and aims to label positive examples efficiently, comparing to the optimal base bandit with hindsight. The meta-bandit estimates the mean and variance of the performance of the base bandits, and selects a base bandit to propose what data to label next for exploration or exploitation. The feedback in the labels updates both the base bandits and the meta-bandit for the next round. Meta-AS can accommodate a diverse set of base bandits to explore assumptions about the dataset, without over-committing to a single model before labeling starts. Experiments on five datasets for relation extraction demonstrate that Meta-AS labels positives more efficiently than the base bandits and other bandit selection strategies.
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- PAR ID:
- 10184358
- Date Published:
- Journal Name:
- The 29th ACM International Conference on Information and Knowledge Management (CIKM'2020)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3340531.3417409
