Experimental Design for Regret Minimization in Linear Bandits
This work addresses the challenge of suboptimal regret in bandit algorithms for researchers and practitioners in machine learning, offering a new approach that improves performance in specific feedback regimes.
The paper tackles the problem of minimizing regret in online stochastic linear and combinatorial bandits by proposing a novel experimental design-based algorithm that balances information gain and reward, overcoming the limitations of optimism-based methods, and it provides state-of-the-art finite time regret guarantees with computational efficiency in semi-bandit settings.
In this paper we propose a novel experimental design-based algorithm to minimize regret in online stochastic linear and combinatorial bandits. While existing literature tends to focus on optimism-based algorithms--which have been shown to be suboptimal in many cases--our approach carefully plans which action to take by balancing the tradeoff between information gain and reward, overcoming the failures of optimism. In addition, we leverage tools from the theory of suprema of empirical processes to obtain regret guarantees that scale with the Gaussian width of the action set, avoiding wasteful union bounds. We provide state-of-the-art finite time regret guarantees and show that our algorithm can be applied in both the bandit and semi-bandit feedback regime. In the combinatorial semi-bandit setting, we show that our algorithm is computationally efficient and relies only on calls to a linear maximization oracle. In addition, we show that with slight modification our algorithm can be used for pure exploration, obtaining state-of-the-art pure exploration guarantees in the semi-bandit setting. Finally, we provide, to the best of our knowledge, the first example where optimism fails in the semi-bandit regime, and show that in this setting our algorithm succeeds.