No abstract

No abstract

We study the problem of inverse reinforcement learning (IRL) with the added twist that the learner is assisted by a helpful teacher. More formally, we tackle the following algorithmic question: How could a teacher provide an informative sequence of demonstrations to an IRL learner to speed up the learning process? We present an interactive teaching framework where a teacher adaptively chooses the next demonstration based on learner's current policy. In particular, we design teaching algorithms for two concrete settings: an omniscient setting where a teacher has full knowledge about the learner's dynamics and a blackbox setting where the teacher has minimal knowledge. Then, we study a sequential variant of the popular MCE-IRL learner and prove convergence guarantees of our teaching algorithm in the omniscient setting. Extensive experiments with a car driving simulator environment show that the learning progress can be speeded up drastically as compared to an uninformative teacher.

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learning dynamics of the students can teach a target concept to the entire classroom using O min {d, N } log 1 examples, where d is the ambient dimension of the problem, N is the number of learners, and is the accuracy parameter. We show the robustness of our teaching strategy when the teacher has limited knowledge of the learners' internal dynamics as provided by a noisy oracle. Further, we study the trade-off between the learners' workload and the teacher's cost in teaching the target concept. Our experiments validate our theoretical results and suggest that appropriately partitioning the classroom into homogenous groups provides a balance between these two objectives.

Differential privacy provides strong privacy guarantees simultaneously enabling useful insights from sensitive datasets. However, it provides the same level of protection for all elements (individuals and attributes) in the data. There are practical scenarios where some data attributes need more/less protection than others. In this paper, we consider dX -privacy, an instantiation of the privacy notion introduced in [6], which allows this flexibility by specifying a separate privacy budget for each pair of elements in the data domain. We describe a systematic procedure to tailor any existing differentially private mechanism that assumes a query set and a sensitivity vector as input into its dX -private variant, specifically focusing on linear queries. Our proposed meta procedure has broad applications as linear queries form the basis of a range of data analysis and machine learning algorithms, and the ability to define a more flexible privacy budget across the data domain results in improved privacy/utility tradeoff in these applications. We propose several dX -private mechanisms, and provide theoretical guarantees on the trade-off between utility and privacy. We also experimentally demonstrate the effectiveness of our procedure, by evaluating our proposed dX -private Laplace mechanism on both synthetic and real datasets using a set of randomly generated linear queries.