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.

Example Input: As a general and thus popular model for autonomous systems, partially observable Markov decision process (POMDP) can capture uncertainties from different sources like sensing noises, actuation errors, and uncertain environments. However, its comprehensiveness makes the planning and control in POMDP difficult. Traditional POMDP planning problems target to find the optimal policy to maximize the expectation of accumulated rewards. But for safety critical applications, guarantees of system performance described by formal specifications are desired, which motivates us to consider formal methods to synthesize supervisor for POMDP. With system specifications given by Probabilistic Computation Tree Logic (PCTL), we propose a supervisory control framework with a type of deterministic finite automata (DFA), za-DFA, as the controller form. While the existing work mainly relies on optimization techniques to learn fixed-size finite state controllers (FSCs), we develop an L∗ learning based algorithm to determine both space and transitions of za-DFA. Membership queries and different oracles for conjectures are defined. The learning algorithm is sound and complete. An example is given in detailed steps to illustrate the supervisor synthesis algorithm.
Example Output: Supervisor Synthesis of POMDP based on Automata Learning

Example Input: Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.
Example Output: Robust Spectral Detection of Global Structures in the Data by Learning a Regularization

Example Input: -This study proposes a framework of Uncertainty-based Group Decision Support System (UGDSS). It provides a platform for multiple criteria decision analysis in six aspects including (1) decision environment, (2) decision problem, (3) decision group, (4) decision conflict, (5) decision schemes and (6) group negotiation. Based on multiple artificial intelligent technologies, this framework provides reliable support for the comprehensive manipulation of applications and advanced decision approaches through the design of an integrated multi-agents architecture.
Example Output:
Towards a Reliable Framework of Uncertainty-based Group Decision Support System