We investigate theory and algorithms for pool-based active learning for multiclass classification using multinomial logistic regression. Using finite sample analysis, we establish both upper and lower bounds for the excess risk of unlabeled samples. We prove that the Fisher Information Ratio (FIR) lower and upper bounds the excess risk. Based on our theoretical analysis, we propose a novel active learning algorithm that employs regret minimization to minimize the FIR. To verify our derived exces…