A Variational Perturbative Approach to Planning in Graph-Based Markov Decision Processes

Coordinating multiple interacting agents to achieve a common goal is a difficult task with huge applicability. This problem remains hard to solve, even when limiting interactions to be mediated via a static interaction-graph. We present a novel approximate solution method for multi-agent Markov decision problems on graphs, based on variational perturbation theory. We adopt the strategy of planning via inference, which has been explored in various prior works. We employ a non-trivial extension of a novel high-order variational method that allows for approximate inference in large networks and has been shown to surpass the accuracy of existing variational methods. To compare our method to two state-of-the-art methods for multi-agent planning on graphs, we apply the method different standard GMDP problems. We show that in cases, where the goal is encoded as a non-local cost function, our method performs well, while state-of-the-art methods approach the performance of random guess. In a final experiment, we demonstrate that our method brings significant improvement for synchronization tasks.

ANALYTIC EQUATION OF STATE FOR EXP-6 POTENTIAL FLUID AND APPLICATION TO N2 FLUID

An analytical expression for the equation of state and thermo-physical quantities of exponential-6 ( exp- 6) fluid are derived based on the Ross variational perturbation theory. The developed formalism is applied to N 2 fluid. Comparisons of theory and simulations for exp- 6 potential fluid are presented. The agreement of numerical results of pressure and internal energy with Monte Carlo (MC) simulations show that the theoretical model is satisfactory except where a few points from metastable ones appeared in literature. The expression has been applied to fluid nitrogen and the fitting to experimental data of fluid N 2 is surprisingly good. The predictions of pressure in the range of high temperature and high density are satisfactory. It has also been found that the analytic equation of state for exp- 6 potential fluid based on RDF proposed by Sun et al. is better in a wide range of pressures and temperatures than that derived from PY expression. Comparisons show that a potential dependence on temperature and density (or volume) may be necessary for the understanding of interaction between N 2 molecules. The equation of state can also be extended to application of important real gases such as H 2, O 2, CH 4, CO and CO 2.