{'fraction_non_alphanumeric': 0.024189114898295765, 'fraction_numerical': 0.0, 'mean_word_length': 5.275862068965517, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Asynchronous algorithms for approximate distributed constraint optimization with quality bounds

Distributed Constraint Optimization (DCOP) is a popular framework for cooperative multi-agent decision making. DCOP is NP-hard, so an important line of work focuses on developing fast incomplete solution algorithms for large-scale applications. One of the few incomplete algorithms to provide bounds on solution quality is k-size optimality, which defines a local optimality criterion based on the size of the group of deviating agents. Unfortunately, the lack of a general-purpose algorithm and the commitment to forming groups based solely on group size has limited the use of k-size optimality. 
 
This paper introduces t-distance optimality which departs from k-size optimality by using graph distance as an alternative criteria for selecting groups of deviating agents. This throws open a new research direction into the tradeoffs between different group selection and coordination mechanisms for incomplete DCOP algorithms. We derive theoretical quality bounds for t-distance optimality that improve known bounds for k-size optimality. In addition, we develop a new efficient asynchronous local search algorithm for finding both k-size and t-distance optimal solutions --- allowing these concepts to be deployed in real applications. Indeed, empirical results show that this algorithm significantly outperforms the only existing algorithm for finding general k-size optimal solutions, which is also synchronous. Finally, we compare the algorithmic performance of k-size and t-distance optimality using this algorithm. We find that t-distance consistently converges to higher-quality solutions in the long run, but results are mixed on convergence speed; we identify cases where k-size and t-distance converge faster.