Towards minimax optimal algorithms for Active Simple Hypothesis Testing
This work addresses a specific variant of hypothesis testing for researchers in statistical learning, offering incremental improvements in computational efficiency over prior methods.
The authors tackled the Active Simple Hypothesis Testing problem by developing a computationally efficient algorithm using a game-theoretic formulation and Blackwell Approachability, which outperforms static algorithms and achieves near-optimal performance in numerical tests.
We study the Active Simple Hypothesis Testing (ASHT) problem, a simpler variant of the Fixed Budget Best Arm Identification problem. In this work, we provide novel game theoretic formulation of the upper bounds of the ASHT problem. This formulation allows us to leverage tools of differential games and Partial Differential Equations (PDEs) to propose an approximately optimal algorithm that is computationally tractable compared to prior work. However, the optimal algorithm still suffers from a curse of dimensionality and instead we use a novel link to Blackwell Approachability to propose an algorithm that is far more efficient computationally. We show that this new algorithm, although not proven to be optimal, is always better than static algorithms in all instances of ASHT and is numerically observed to attain the optimal exponent in various instances.