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.

Input: Consider Input: There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their solutions. This paper introduces effective and compact, complete symmetry breaking constraints for small graph search. Enumerating with these symmetry breaks generates all and only non-isomorphic solutions. For small search problems, with up to 10 vertices, we compute instance independent symmetry breaking constraints. For small search problems with a larger number of vertices we demonstrate the computation of instance dependent constraints which are complete. We illustrate the application of complete symmetry breaking constraints to extend two known sequences from the OEIS related to graph enumeration.

Output: Breaking Symmetries in Graph Search with Canonizing Sets


Input: Consider Input: Deep reinforcement learning (RL) can acquire complex behaviors from low-level inputs, such as images. However, real-world applications of such methods require generalizing to the vast variability of the real world. Deep networks are known to achieve remarkable generalization when provided with massive amounts of labeled data, but can we provide this breadth of experience to an RL agent, such as a robot? The robot might continuously learn as it explores the world around it, even while it is deployed and performing useful tasks. However, this learning requires access to a reward function, to tell the agent whether it is succeeding or failing at its task. Such reward functions are often hard to measure in the real world, especially in domains such as robotics and dialog systems, where the reward could depend on the unknown positions of objects or the emotional state of the user. On the other hand, it is often quite practical to provide the agent with reward functions in a limited set of situations, such as when a human supervisor is present, or in a controlled laboratory setting. Can we make use of this limited supervision, and still benefit from the breadth of experience an agent might collect in the unstructured real world? In this paper, we formalize this problem setting as semisupervised reinforcement learning (SSRL), where the reward function can only be evaluated in a set of “labeled” MDPs, and the agent must generalize its behavior to the wide range of states it might encounter in a set of “unlabeled” MDPs, by using experience from both settings. Our proposed method infers the task objective in the unlabeled MDPs through an algorithm that resembles inverse RL, using the agent’s own prior experience in the labeled MDPs as a kind of demonstration of optimal behavior. We evaluate our method on challenging, continuous control tasks that require control directly from images, and show that our approach can improve the generalization of a learned deep neural network policy by using experience for which no reward function is available. We also show that our method outperforms direct supervised learning of the reward.

Output: GENERALIZING SKILLS WITH SEMI-SUPERVISED REINFORCEMENT LEARNING


Input: Consider Input: We can program a Real-Time (RT) music improvisation system in C++ without a formal semantic or we can model it with process calculi such as the Non-deterministic Timed Concurrent Constraint (ntcc) calculus. “A Concurrent Constraints Factor Oracle (FO) model for Music Improvisation” (Ccfomi) is an improvisation model specified on ntcc. Since Ccfomi improvises non-deterministically, there is no control on choices and therefore little control over the sequence variation during the improvisation. To avoid this, we extended Ccfomi using the Probabilistic Non-deterministic Timed Concurrent Constraint calculus. Our extension to Ccfomi does not change the time and space complexity of building the FO, thus making our extension compatible with RT. However, there was not a ntcc interpreter capable of RT to execute Ccfomi. We developed Ntccrt –a RT capable interpreter for ntcc– and we executed Ccfomi on Ntccrt. In the future, we plan to extend Ntccrt to execute our extension to Ccfomi.


Output: Probabilistic Extension to the Concurrent Constraint Factor Oracle Model for Music Improvisation