Characterizing perceptual decision-making is an important goal of systems neuroscience. Recent work has shown that animal decision-making behavior is not stationary, but exhibits switches between discrete latent states within a single experimental session. However, fitting these complex models requires large amounts of data, a crucial impediment to progress. Here we propose to overcome this obstacle by introducing active learning methods for discrete latent variable models of decision-making. Active learning seeks to improve the efficiency of experiments by selecting highly informative stimuli on each trial. However, past work has largely overlooked active learning for latent variable models (LVMs). To address this gap, we propose a novel framework for "infomax" stimulus selection in discrete latent variable regression models. Our approach relies on sampling of the joint distribution over latents and model parameters to evaluate information gain, which we use to select the maximally informative stimulus on each trial. We begin with an application to a simple "mixture of linear regressions" (MLR) model; although it is well known that active learning confers no advantage in standard linear regression settings, we show that for mixtures of linear regressions, our method can provide dramatic gains. We then proceed with an application to Input-Output Hidden Markov Models (IO-HMMs), a family of highly expressive regression models for time series data, which have proven useful in diverse applications including perceptual decision-making. We show that our method substantially reduces the number of trials needed to learn the parameters of these models. We expect this method to have broad applicability for improving experimental efficiency in neuroscience and beyond.