A General Framework for Robust Interactive Learning *
We propose a general framework for interactively learning models, such as (binary or non-binary) classifiers, orderings/rankings of items, or clusterings of data points. Our framework is based on a generalization of Angluin's equivalence query model and Littlestone's online learning model: in each iteration, the algorithm proposes a model, and the user either accepts it or reveals a specific mistake in the proposal. The feedback is correct only with probability p > 1 2 (and adversarially incorrect with probability 1 − p), i.e., the algorithm must be able to learn in the presence of arbitrary noise. The algorithm's goal is to learn the ground truth model using few iterations. Our general framework is based on a graph representation of the models and user feedback. To be able to learn efficiently, it is sufficient that there be a graph G whose nodes are the models, and (weighted) edges capture the user feedback, with the property that if s, s * are the proposed and target models, respectively, then any (correct) user feedback s must lie on a shortest s-s * path in G. Under this one assumption, there is a natural algorithm, reminiscent of the Multiplicative Weights Update algorithm, which will efficiently learn s * even in the presence of noise in the user's feedback. From this general result, we rederive with barely any extra effort classic results on learning of classifiers and a recent result on interactive clustering; in addition, we easily obtain new interactive learning algorithms for ordering/ranking.
The paper proposes a general framework for interactive learning. In the framework, the machine learning models are represented as the nodes in a graph G and the user feedback are represented as weighted edges in G. Under the assumption of “if s, s* are the proposed and target models, then any (correct) user feedback s’ must lie on the shortest s-s* path in G”, the author showed that the Multiplicative Weights Update algorithm can efficiently learn the target model. The framework can be applied to three important machine learning tasks: ranking, clustering, and classification. The problem investigated in the paper is interesting and important. The theoretical results of the paper is convincing. However, these results are not empirically verified on real tasks. My comments on the paper are listed as follows:
Pros.
1.	A interactive learning framework which models the models and user feedback with graph. The framework can learn the target model in the presence of random noise in the user’s feedback. 
2.	The framework is really general and can be applied to major machine learning tasks such as classification, clustering and ranking. 
Cons.
1.	My major concern on the paper comes from the absence of empirical evaluation of the proposed framework. The major assumption of the framework is “any (correct) user feedback s’ must lie on the shortest s-s* path in G”. Also, the authors claimed that the proposed framework is robust, which can learn the correct s* even in the presence of random noise in user’s feedback. It is necessary to verify the correctness of these assumption and conclusions based on real data and real tasks. The framework is applied to the tasks of ranking, clustering, and classification, achieving the interactive ranking, interactive clustering, and interactive classification models. It is necessary to compare these derived models with state-of-the-arts models to show the effectiveness of these models. Currently, the authors only showed the theoretical results.  
2.	There is no conclusion section in the paper. It is better to conclude the contributions of the paper in the last section.