This paper establishes central limit theorems for Polyak-Ruppert averaged Q-learning under asynchronous updates. We present a non-asymptotic central limit theorem, where the convergence rate in Wasserstein distance explicitly reflects the dependence on the number of iterations, state-action space size, the discount factor, and the quality of exploration. In addition, we derive a functional central limit theorem, showing that the partial-sum process converges weakly to a Brownian motion.

Commonsense knowledge acquisition and reasoning have long been a core artificial intelligence problem. However, in the past, there has been a lack of scalable methods to collect commonsense knowledge. In this paper, we propose to develop principles for collecting commonsense knowledge based on selectional preference. We generalize the definition of selectional preference from one-hop linguistic syntactic relations to higher-order relations over linguistic graphs. Unlike previous commonsense knowledge definition (e.g., ConceptNet), the selectional preference (SP) knowledge only relies on statistical distribution over linguistic graphs, which can be efficiently and accurately acquired from the unlabeled corpus with modern tools. Following this principle, we develop a large-scale eventuality (a linguistic term covering activity, state, and event)-based knowledge graph ASER, where each eventuality is represented as a dependency graph, and the relation between them is a discourse relation defined in shallow discourse parsing. The higher-order selectional preference over collected linguistic graphs reflects various kinds of commonsense knowledge. Moreover, motivated by the observation that humans understand events by abstracting the observed events to a higher level and can thus transferring their knowledge to new events, we propose a conceptualization module to significantly boost the coverage of ASER. In total, ASER contains 438 million eventualities and 648 million edges between eventualities. After conceptualization with Probase, a selectional preference based concept-instance relational knowledge base, our concept graph contains 15 million conceptualized eventualities and 224 million edges between them. Detailed analysis is provided to demonstrate its quality. All the collected data, APIs, and tools are available at https://github.com/HKUST-KnowComp/ASER.