Online Stochastic Linear Optimization under One-bit Feedback
This work addresses computational inefficiency in generalized linear bandits for real-world problems like online recommendation, though it is incremental as it builds on existing methods.
The paper tackles online stochastic linear optimization with one-bit feedback, common in applications like online advertising, by developing an efficient algorithm that achieves a regret bound of O(d√T), matching the optimal result for stochastic linear bandits.
In this paper, we study a special bandit setting of online stochastic linear optimization, where only one-bit of information is revealed to the learner at each round. This problem has found many applications including online advertisement and online recommendation. We assume the binary feedback is a random variable generated from the logit model, and aim to minimize the regret defined by the unknown linear function. Although the existing method for generalized linear bandit can be applied to our problem, the high computational cost makes it impractical for real-world problems. To address this challenge, we develop an efficient online learning algorithm by exploiting particular structures of the observation model. Specifically, we adopt online Newton step to estimate the unknown parameter and derive a tight confidence region based on the exponential concavity of the logistic loss. Our analysis shows that the proposed algorithm achieves a regret bound of $O(d\sqrt{T})$, which matches the optimal result of stochastic linear bandits.