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.

We investigate the use of temporally abstract actions, or macro-actions, in the solution of Markov decision processes. Unlike current mod els that combine both primitive actions and macro-actions and leave the state space un changed, we propose a hierarchical model (using an abstract MDP) that works with macro-actions only, and that significantly reduces the size of the state space. This is achieved by treating macro actions as local policies that act in certain regions of state space, and by restricting states in the ab stract MDP to those at the boundaries of regions. The abstract MDP approximates the original and can be solved more efficiently. We discuss sev eral ways in which macro-actions can be gen erated to ensure good solution quality. Finally, we consider ways in which macro-actions can be reused to solve multiple, related MDPs; and we show that this can justify the computational over head of macro-action generation.
Hierarchical Solution of Markov Decision Processes using Macro-actions

Recent work has proposed several generative neural models for constituency parsing that achieve state-of-the-art results. Since direct search in these generative models is difficult, they have primarily been used to rescore candidate outputs from base parsers in which decoding is more straightforward. We first present an algorithm for direct search in these generative models. We then demonstrate that the rescoring results are at least partly due to implicit model combination rather than reranking effects. Finally, we show that explicit model combination can improve performance even further, resulting in new state-of-the-art numbers on the PTB of 94.25 F1 when training only on gold data and 94.66 F1 when using external data.
Improving Neural Parsing by Disentangling Model Combination and Reranking Effects

Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the implication problem for CI statements is decidable, given that the size of the domains of the random variables is known and fixed. We will present an approximate logical inference algorithm which combines a falsification and a novel validation algorithm. The validation algorithm represents each set of CI statements as a sparse 0-1 matrixA and validates instances of the implication problem by solving specific linear programs with constraint matrix A. We will show experimentally that the algorithm is both effective and efficient in validating and falsifying instances of the probabilistic CI implication problem.
Logical Inference Algorithms and Matrix Representations for Probabilistic Conditional Independence