Nearly Minimax Algorithms for Linear Bandits with Shared Representation

• URL: http://arxiv.org/abs/2203.15664v1
• Date: Tue, 29 Mar 2022 15:27:13 GMT
• Title: Nearly Minimax Algorithms for Linear Bandits with Shared Representation
• Authors: Jiaqi Yang, Qi Lei, Jason D. Lee, Simon S. Du
• Abstract summary: We consider the setting where we play $M$ linear bandits with dimension $d$, each for $T$ rounds, and these $M$ bandit tasks share a common $k(ll d)$ dimensional linear representation. We come up with novel algorithms that achieve $widetildeOleft(dsqrtkMT + kMsqrtTright)$ regret bounds, which matches the known minimax regret lower bound up to logarithmic factors.
• Score: 86.79657561369397
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We give novel algorithms for multi-task and lifelong linear bandits with shared representation. Specifically, we consider the setting where we play $M$ linear bandits with dimension $d$, each for $T$ rounds, and these $M$ bandit tasks share a common $k(\ll d)$ dimensional linear representation. For both the multi-task setting where we play the tasks concurrently, and the lifelong setting where we play tasks sequentially, we come up with novel algorithms that achieve $\widetilde{O}\left(d\sqrt{kMT} + kM\sqrt{T}\right)$ regret bounds, which matches the known minimax regret lower bound up to logarithmic factors and closes the gap in existing results [Yang et al., 2021]. Our main technique include a more efficient estimator for the low-rank linear feature extractor and an accompanied novel analysis for this estimator.

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