Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including Weighted Constraint Programs (WCSPs), Distributed Constraint Optimization (DCOP), as well as optimization in stochastic variants such as the tasks of finding the most probable explanation (MPE) in belief networks. Inference-based algorithms are powerful techniques for solving discrete optimization problems, which can be used independently or in combination with other techniques. However, their applicability is often limited by their compute intensive nature and their space requirements. This paper proposes the design and implementation of a novel inference-based technique, which exploits modern massively parallel architectures, such as those found in Graphical Processing Units (GPUs), to speed up the resolution of exact and approximated inference-based algorithms for discrete optimization. The paper studies the proposed algorithm in both centralized and distributed optimization contexts. The paper demonstrates that the use of GPUs provides significant advantages in terms of runtime and scalability, achieving up to two orders of magnitude in speedups and showing a considerable reduction in execution time (up to 345 times faster) with respect to a sequential version.
In the distributed constraint optimization context, GPU parallelism has been applied to speed up several DCOP solving techniques. Fioretto @cite_10 proposed a multi-variable agent decomposition strategy to solve DCOPs with complex local subproblems, which makes use of GPUs to implement a search-based and a sampling-based algorithm to speed up the agents' local subproblems resolution. Le @cite_12 studied a GPU accelerated algorithm in the context of stochastic DCOPs---DCOPs where the values of the cost tables are stochastic. The authors used SIMT-style parallelism on a DP-based approach, which resulted in a speedup of up to two orders of magnitude. Recently, a combination of GPUs with (MCMC) sampling algorithms has been proposed in the context of solving DCOPs @cite_24 , where the authors adopted GPUs to accelerate the computation of the normalization constants used in the MCMC sampling process as well as to compute several samples in parallel, resulting in a speedup of up to one order of magnitude.
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The field of Distributed Constraint Optimization (DCOP) has gained momentum in recent years, thanks to its ability to address various applications related to multi-agent coordination. Nevertheless, solving DCOPs is computationally challenging. Thus, in large scale, complex applications, incomplete DCOP algorithms are necessary. Recently, researchers have introduced a promising class of incomplete DCOP algorithms, based on sampling. However, this paradigm requires a multitude of samples to ensure convergence. This paper exploits the property that sampling is amenable to parallelization, and introduces a general framework, called Distributed MCMC (DMCMC), that is based on a dynamic programming procedure and uses Markov Chain Monte Carlo (MCMC) sampling algorithms to solve DCOPs. Additionally, DMCMC harnesses the parallel computing power of Graphical Processing Units (GPUs) to speed-up the sampling process. The experimental results show that DMCMC can find good solutions up to two order of magnitude faster than other incomplete DCOP algorithms. The application of DCOP models to large problems faces two main limitations: (i) Modeling limitations, as each agent can handle only a single variable of the problem; and (ii) Resolution limitations, as current approaches do not exploit the local problem structure within each agent. This paper proposes a novel Multi-Variable Agent (MVA) DCOP decomposition technique, which: (i) Exploits the co-locality of each agent's variables, allowing us to adopt efficient centralized techniques within each agent; (ii) Enables the use of hierarchical parallel models and proposes the use of GPUs; and (iii) Reduces the amount of computation and communication required in several classes of DCOP algorithms. Distributed Constraint Optimization Problems (DCOPs) have been used to model a number of multi-agent coordination problems. In DCOPs, agents are assumed to have complete information about the utility of their possible actions. However, in many real-world applications, such utilities are stochastic due to the presence of exogenous events that are beyond the direct control of the agents. This paper addresses this issue by extending the standard DCOP model to Expected Regret DCOP (ER-DCOP) for DCOP applications with uncertainty in constraint utilities. Different from other approaches, ER-DCOPs aim at minimizing the overall expected regret of the problem. The paper proposes the ER-DPOP algorithm for solving ER-DCOPs, which is complete and requires a linear number of messages with respect to the number of agents in the problem. We further present two implementations of ER-DPOP---GPU- and ASP-based implementations---that orthogonally exploit the problem structure and present their evaluations on random networks and power network problems.