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We study the problem of a buyer (aka auctioneer) who gains stochastic rewards by procuring multiple units of a service or item from a pool of heterogeneous strategic agents. The reward obtained for a single unit from an allocated agent depends on the inherent quality of the agent; the agent's quality is fixed but unknown. Each agent can only supply a limited number of units (capacity of the agent). The costs incurred per unit and capacities are private information of the agents. The auctioneer is required to elicit costs as well as capacities (making the mechanism design bidimensional) and further, learn the qualities of the agents as well, with a view to maximize her utility. Motivated by this, we design a bidimensional multi-armed bandit procurement auction that seeks to maximize the expected utility of the auctioneer subject to incentive compatibility and individual rationality while simultaneously learning the unknown qualities of the agents. We first assume that the qualities are known and propose an optimal, truthful mechanism 2D-OPT for the auctioneer to elicit costs and capacities. Next, in order to learn the qualities of the agents in addition, we provide sufficient conditions for a learning algorithm to be Bayesian incentive compatible and individually rational. We finally design a novel learning mechanism, 2D-UCB that is stochastic Bayesian incentive compatible and individually rational.

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We study the problem of training an accurate linear regression model by procuring labels from multiple noisy crowd annotators, under a budget constraint. We propose a Bayesian model for linear regression in crowdsourcing and use variational inference for parameter estimation. To minimize the number of labels crowdsourced from the annotators, we adopt an active learning approach. In this specific context, we prove the equivalence of well-studied criteria of active learning like entropy minimization and expected error reduction. Interestingly, we observe that we can decouple the problems of identifying an optimal unlabeled instance and identifying an annotator to label it. We observe a useful connection between the multi-armed bandit framework and the annotator selection in active learning. Due to the nature of the distribution of the rewards on the arms, we use the Robust Upper Confidence Bound (UCB) scheme with truncated empirical mean estimator to solve the annotator selection problem. This yields provable guarantees on the regret. We further apply our model to the scenario where annotators are strategic and design suitable incentives to induce them to put in their best efforts.

Multi-label classification is a common supervised machine learning problem where each instance is associated with multiple classes.The key challenge in this problem is learning the correlations between the classes. An additional challenge arises when the labels of the training instances are provided by noisy, heterogeneous crowdworkers with unknown qualities. We first assume labels from a perfect source and propose a novel topic model where the present as well as the absent classes generate the latent topics and hence the words. We non-trivially extend our topic model to the scenario where the labels are provided by noisy crowdworkers. Extensive experimentation on real world datasets reveals the superior performance of the proposed model. The proposed model learns the qualities of the annotators as well, even with minimal training data.