This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning algorithm is if it is allowed a one-step look-ahead into the future. We show that given stability, bounded forward regret is equivalent to bounded regret. We also show that the existence of an algorithm with bounded regret implies the existence of a stable algorithm with bounded regret and bounded forward regret. The equivalence results apply to general, possibly non-convex problems. To the best of our knowledge, our analysis provides the first general connection between stability and regret in the online setting that is not restricted to a particular class of algorithms. Our stability-regret connection provides a simple recipe for analyzing regret incurred by any online learning algorithm. Using our framework, we analyze several existing online learning algorithms as well as the "approximate" versions of algorithms like RDA that solve an optimization problem at each iteration. Our proofs are simpler than existing analysis for the respective algorithms, show a clear trade-off between stability and forward regret, and provide tighter regret bounds in some cases. Furthermore, using our recipe, we analyze "approximate" versions of several algorithms such as follow-the-regularized-leader (FTRL) that requires solving an optimization problem at each step.

We present a new method for automatically providing feedback for introductory programming problems. In order to use this method, we need a reference implementation of the assignment, and an error model consisting of potential corrections to errors that students might make. Using this information, the system automatically derives minimal corrections to student's incorrect solutions, providing them with a quantifiable measure of exactly how incorrect a given solution was, as well as feedback about what they did wrong. We introduce a simple language for describing error models in terms of correction rules, and formally define a rule-directed translation strategy that reduces the problem of finding minimal corrections in an incorrect program to the problem of synthesizing a correct program from a sketch. We have evaluated our system on thousands of real student attempts obtained from 6.00 and 6.00x. Our results show that relatively simple error models can correct on average 65% of all incorrect submissions.

Interest in online education is surging, as dramatized bythe success of Khan Academy and recent Stanford online courses, but the technology for online education isin its infancy. Crowdsourcing mechanisms will likelybe essential in order to reach the full potential of thismedium. This paper sketches some of the challengesand directions we hope HCOMP researchers will address.

In this paper, we study the problem of large-scale Kernel Logistic Regression (KLR). A straightforward approach is to apply stochastic approximation to KLR. We refer to this approach as non-conservative online learning algorithm because it updates the kernel classifier after every received training example, leading to a dense classifier. To improve the sparsity of the KLR classifier, we propose two conservative online learning algorithms that update the classifier in a stochastic manner and generate sparse solutions. With appropriately designed updating strategies, our analysis shows that the two conservative algorithms enjoy similar theoretical guarantee as that of the non-conservative algorithm. Empirical studies on several benchmark data sets demonstrate that compared to batch-mode algorithms for KLR, the proposed conservative online learning algorithms are able to produce sparse KLR classifiers, and achieve similar classification accuracy but with significantly shorter training time. Furthermore, both the sparsity and classification accuracy of our methods are comparable to those of the online kernel SVM.

In this paper we promote introducing software verification and control flow graph similarity measurement in automated evaluation of students' programs. We present a new grading framework that merges results obtained by combination of these two approaches with results obtained by automated testing, leading to improved quality and precision of automated grading. These two approaches are also useful in providing a comprehensible feedback that can help students to improve the quality of their programs We also present our corresponding tools that are publicly available and open source. The tools are based on LLVM low-level intermediate code representation, so they could be applied to a number of programming languages. Experimental evaluation of the proposed grading framework is performed on a corpus of university students' programs written in programming language C. Results of the experiments show that automatically generated grades are highly correlated with manually determined grades suggesting that the presented tools can find real-world applications in studying and grading.

Kernel-based online learning has often shown state-of-the-art performance for many online learning tasks. It, however, suffers from a major shortcoming, that is, the unbounded number of support vectors, making it non-scalable and unsuitable for applications with large-scale datasets. In this work, we study the problem of bounded kernel-based online learning that aims to constrain the number of support vectors by a predefined budget. Although several algorithms have been proposed in literature, they are neither computationally efficient due to their intensive budget maintenance strategy nor effective due to the use of simple Perceptron algorithm. To overcome these limitations, we propose a framework for bounded kernel-based online learning based on an online gradient descent approach. We propose two efficient algorithms of bounded online gradient descent (BOGD) for scalable kernel-based online learning: (i) BOGD by maintaining support vectors using uniform sampling, and (ii) BOGD++ by maintaining support vectors using non-uniform sampling. We present theoretical analysis of regret bound for both algorithms, and found promising empirical performance in terms of both efficacy and efficiency by comparing them to several well-known algorithms for bounded kernel-based online learning on large-scale datasets.

We study the tracking problem, namely, estimating the hidden state of an object over time, from unreliable and noisy measurements. The standard framework for the tracking problem is the generative framework, which is the basis of solutions such as the Bayesian algorithm and its approximation, the particle filters. However, these solutions can be very sensitive to model mismatches. In this paper, motivated by online learning, we introduce a new framework for tracking. We provide an efficient tracking algorithm for this framework. We provide experimental results comparing our algorithm to the Bayesian algorithm on simulated data. Our experiments show that when there are slight model mismatches, our algorithm outperforms the Bayesian algorithm.

Learning theory has largely focused on two main learning scenarios: the classical statistical setting where instances are drawn i.i.d. from a fixed distribution, and the adversarial scenario whereby at every time step the worst instance is revealed to the player. It can be argued that in the real world neither of these assumptions is reasonable. We define the minimax value of a game where the adversary is restricted in his moves, capturing stochastic and non-stochastic assumptions on data. Building on the sequential symmetrization approach, we define a notion of distribution-dependent Rademacher complexity for the spectrum of problems ranging from i.i.d. to worst-case. The bounds let us immediately deduce variation-type bounds. We study a smoothed online learning scenario and show that exponentially small amount of noise can make function classes with infinite Littlestone dimension learnable.

We propose an online prediction version of submodular set cover with connections to ranking and repeated active learning. In each round, the learning algorithm chooses a sequence of items. The algorithm then receives a monotone submodular function and suffers loss equal to the cover time of the function: the number of items needed, when items are selected in order of the chosen sequence, to achieve a coverage constraint. We develop an online learning algorithm whose loss converges to approximately that of the best sequence in hindsight. Our proposed algorithm is readily extended to a setting where multiple functions are revealed at each round and to bandit and contextual bandit settings.

Most online algorithms used in machine learning today are based on variants of mirror descent or follow-the-leader. In this paper, we present an online algorithm based on a completely different approach, which combines ``random playout'' and randomized rounding of loss subgradients. As an application of our approach, we provide the first computationally efficient online algorithm for collaborative filtering with trace-norm constrained matrices. As a second application, we solve an open question linking batch learning and transductive online learning.