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.

Many real-world decision-theoretic planning problems can be naturally modeled with discrete and continuous state Markov decision processes (DC-MDPs). While previous work has addressed automated decision-theoretic planning for DCMDPs, optimal solutions have only been defined so far for limited settings, e.g., DC-MDPs having hyper-rectangular piecewise linear value functions. In this work, we extend symbolic dynamic programming (SDP) techniques to provide optimal solutions for a vastly expanded class of DCMDPs. To address the inherent combinatorial aspects of SDP, we introduce the XADD — a continuous variable extension of the algebraic decision diagram (ADD) — that maintains compact representations of the exact value function. Empirically, we demonstrate an implementation of SDP with XADDs on various DC-MDPs, showing the first optimal automated solutions to DCMDPs with linear and nonlinear piecewise partitioned value functions and showing the advantages of constraint-based pruning for XADDs.
Symbolic Dynamic Programming for Discrete and Continuous State MDPs

Consider a setting where selfish agents are to be assigned to coalitions or projects from a set P. Each project k ∈ P is characterized by a valuation function; vk(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: “how should the agents divide the value that they collectively create?”. One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.
Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

A number of visual question answering approaches have been proposed recently, aiming at understanding the visual scenes by answering the natural language questions. While the image question answering has drawn significant attention, video question answering is largely unexplored. Video-QA is different from Image-QA since the information and the events are scattered among multiple frames. In order to better utilize the temporal structure of the videos and the phrasal structures of the answers, we propose two mechanisms: the re-watching and the re-reading mechanisms and combine them into the forgettable-watcher model. Then we propose a TGIF-QA dataset for video question answering with the help of automatic question generation. Finally, we evaluate the models on our dataset. The experimental results show the effectiveness of our proposed models.

The Forgettable-Watcher Model for Video Question Answering