In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Ex Input:
We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than other types. A positive reliable classifier is one that makes no false positive errors. The goal in the positive reliable agnostic framework is to output a hypothesis with the following properties: (i) its false positive error rate is at most ǫ, (ii) its false negative error rate is at most ǫ more than that of the best positive reliable classifier from the class. A closely related notion is fully reliable agnostic learning, which considers partial classifiers that are allowed to predict “unknown” on some inputs. The best fully reliable partial classifier is one that makes no errors and minimizes the probability of predicting “unknown”, and the goal in fully reliable learning is to output a hypothesis that is almost as good as the best fully reliable partial classifier from a class. For distribution-independent learning, the best known algorithms for PAC learning typically utilize polynomial threshold representations, while the state of the art agnostic learning algorithms use pointwise polynomial approximations. We show that one-sided polynomial approximations, an intermediate notion between polynomial threshold representations and point-wise polynomial approximations, suffice for learning in the reliable agnostic settings. We then show that majorities can be fully reliably learned and disjunctions of majorities can be positive reliably learned, through constructions of appropriate onesided polynomial approximations. Our fully reliable algorithm for majorities provides the first evidence that fully reliable learning may be strictly easier than agnostic learning. Our algorithms also satisfy strong attribute-efficiency properties, and in many cases they provide smooth tradeoffs between sample complexity and running time. University of California, Berkeley. Email: vkanade@eecs.berkeley.edu The Simons Institute for the Theory of Computing at UC Berkeley. Email: jthaler@seas.harvard.edu

Ex Output:
Distribution-Independent Reliable Learning


Ex Input:
Path planning for multiple robots is well studied in the AI and robotics communities. For a given discretized environment, robots need to find collision-free paths to a set of specified goal locations. Robots can be fully anonymous, non-anonymous, or organized in groups. Although powerful solvers for this abstract problem exist, they make simplifying assumptions by ignoring kinematic constraints, making it difficult to use the resulting plans on actual robots. In this paper, we present a solution which takes kinematic constraints, such as maximum velocities, into account, while guaranteeing a user-specified minimum safety distance between robots. We demonstrate our approach in simulation and on real robots in 2D and 3D environments.

Ex Output:
Path Planning With Kinematic Constraints For Robot Groups


Ex Input:
We improve the computational complexity of online learning algorithms that require to often recompute least squares regression estimates of parameters. We propose two stochastic gradient descent schemes with randomisation in order to efficiently track the true solutions of the regression problems achieving an O(d) improvement in complexity, where d is the dimension of the data. The first algorithm assumes strong convexity in the regression problem, and we provide bounds on the error both in expectation and high probability (the latter is often needed to provide theoretical guarantees for higher level algorithms). The second algorithm deals with cases where strong convexity of the regression problem cannot be guaranteed and uses adaptive regularisation. We again give error bounds in both expectation and high probability. We apply our approaches to the linear bandit algorithms PEGE and ConfidenceBall and demonstrate significant gains in complexity in both cases. Since strong convexity is guaranteed by the PEGE algorithm, we lose only logarithmic factors in the regret performance of the algorithm. On the other hand, in the ConfidenceBall algorithm we adaptively regularise to ensure strong convexity, and this results in an Õ(n1/5)1 deterioration of the regret.

Ex Output:

Online gradient descent for least squares regression: Non-asymptotic bounds and application to bandits


