We consider the online linear optimization problem, where at every step the algorithm plays a point x_t in the unit ball, and suffers loss for some cost vector c_t that is then revealed to the algorithm. Recent work showed that if an algorithm receives a "hint" h_t that has non-trivial correlation with c_t before it plays x_t, then it can achieve a logarithmic regret guarantee, improving on the classical sqrt(T) bound. In this work, we study the question of whether an algorithm really requires a hint at every time step. Somewhat surprisingly, we show that an algorithm can obtain logarithmic regret with just O(sqrt(T)) hints under a natural query model. We give two applications of our result, to the well-studied setting of optimistic regret bounds and to the problem of online learning with abstention.
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Bandit Online Linear Optimization with Hints and Queries
We study variants of the online linear optimization (OLO) problem with bandit feedback, where the algorithm has access to external information about the unknown cost vector. Our motivation is the recent body of work on using such “hints” towards improving regret bounds for OLO problems in the full-information setting. Unlike in the full-information OLO setting, with bandit feedback, we first show that one cannot improve the standard regret bounds of O(\sqrt{T}) by using hints, even if they are always well-correlated with the cost vector. In contrast, if the algorithm is empowered to issue queries and if all the responses are correct, then we show O(\log(T)) regret is achievable. We then show how to make this result more robust — when some of the query responses can be adversarial — by using a little feedback on the quality of the responses.
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- Award ID(s):
- 2211718
- PAR ID:
- 10486613
- Publisher / Repository:
- ICML
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- ISSN:
- 2640-3498
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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