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:
<lb>We consider a situation in which we see samples Xn R drawn i.i.d. from some<lb>distribution with mean zero and unknown covariance A. We wish to compute the<lb>top eigenvector of A in an incremental fashion with an algorithm that maintains<lb>an estimate of the top eigenvector in O(d) space, and incrementally adjusts the<lb>estimate with each new data point that arrives. Two classical such schemes are<lb>due to Krasulina (1969) and Oja (1983). We give finite-sample convergence rates<lb>for both.

Ex Output:
The Fast Convergence of Incremental PCA

Ex Input:
This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies. Inference is shown to be PEXP-complete, and variational methods are designed so as to exploit logical inference whenever possible.

Ex Output:
Complexity Analysis and Variational Inference for Interpretation-based Probabilistic Description Logics

Ex Input:
Transferring knowledge across a sequence of related tasks is an important challenge in reinforce-<lb>ment learning. Despite much encouraging empirical evidence that shows benefits of transfer, there<lb>has been very little theoretical analysis. In this paper, we study a class of lifelong reinforcement-<lb>learning problems: the agent solves a sequence of tasks modeled as finite Markov decision processes<lb>(MDPs), each of which is from a finite set of MDPs with the same state/action spaces and different<lb>transition/reward functions. Inspired by the need for cross-task exploration in lifelong learning, we<lb>formulate a novel online discovery problem and give an optimal learning algorithm to solve it. Such<lb>results allow us to develop a new lifelong reinforcement-learning algorithm, whose overall sample<lb>complexity in a sequence of tasks is much smaller than that of single-task learning, with high prob-<lb>ability, even if the sequence of tasks is generated by an adversary. Benefits of the algorithm are<lb>demonstrated in a simulated problem.

Ex Output:
The Online Discovery Problem and Its Application to Lifelong Reinforcement Learning