Nearly Minimax Algorithms for Linear Bandits with Shared Representation
This work addresses the challenge of efficient learning in bandit settings with shared representations, providing improved theoretical guarantees for researchers and practitioners in reinforcement learning and online decision-making.
The paper tackles the problem of multi-task and lifelong linear bandits with shared representation by developing novel algorithms that achieve nearly minimax regret bounds, specifically $\widetilde{O}\left(d\sqrt{kMT} + kM\sqrt{T} ight)$, matching known lower bounds up to logarithmic factors.
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.