On Elimination Strategies for Bandit Fixed-Confidence Identification
This addresses a computational bottleneck for researchers and practitioners in bandit algorithms, offering a more efficient approach without sacrificing adaptivity, though it is incremental in combining existing ideas.
The paper tackles the computational inefficiency of fully-adaptive strategies in bandit fixed-confidence identification by modifying them to incorporate elimination, resulting in algorithms that remain fully adaptive, maintain or improve sample complexity, and reduce computational complexity significantly in experiments like best-arm identification in linear bandits.
Elimination algorithms for bandit identification, which prune the plausible correct answers sequentially until only one remains, are computationally convenient since they reduce the problem size over time. However, existing elimination strategies are often not fully adaptive (they update their sampling rule infrequently) and are not easy to extend to combinatorial settings, where the set of answers is exponentially large in the problem dimension. On the other hand, most existing fully-adaptive strategies to tackle general identification problems are computationally demanding since they repeatedly test the correctness of every answer, without ever reducing the problem size. We show that adaptive methods can be modified to use elimination in both their stopping and sampling rules, hence obtaining the best of these two worlds: the algorithms (1) remain fully adaptive, (2) suffer a sample complexity that is never worse of their non-elimination counterpart, and (3) provably eliminate certain wrong answers early. We confirm these benefits experimentally, where elimination improves significantly the computational complexity of adaptive methods on common tasks like best-arm identification in linear bandits.