We present two variants of a multi-agent reinforcement learning algorithm based on evolutionary game theoretic considerations. The intentional simplicity of one variant enables us to prove results on its relationship to a system of ordinary differential equations of replicator-mutator dynamics type, allowing us to present proofs on the algorithm's convergence conditions in various settings via its ODE counterpart. The more complicated variant enables comparisons to Q-learning based algorithms. We compare both variants experimentally to WoLF-PHC and frequency-adjusted Q-learning on a range of settings, illustrating cases of increasing dimensionality where our variants preserve convergence in contrast to more complicated algorithms. The availability of analytic results provides a degree of transferability of results as compared to purely empirical case studies, illustrating the general utility of a dynamical systems perspective on multi-agent reinforcement learning when addressing questions of convergence and reliable generalisation.

Computational models have become a powerful tool in the quantitative sciences to understand the behaviour of complex systems that evolve in time. However, they often contain a potentially large number of free parameters whose values cannot be obtained from theory but need to be inferred from data. This is especially the case for models in the social sciences, economics, or computational epidemiology. Yet many current parameter estimation methods are mathematically involved and computationally slow to run. In this paper we present a computationally simple and fast method to retrieve accurate probability densities for model parameters using neural differential equations. We present a pipeline comprising multi-agent models acting as forward solvers for systems of ordinary or stochastic differential equations, and a neural network to then extract parameters from the data generated by the model. The two combined create a powerful tool that can quickly estimate densities on model parameters, even for very large systems. We demonstrate the method on synthetic time series data of the SIR model of the spread of infection, and perform an in-depth analysis of the Harris-Wilson model of economic activity on a network, representing a non-convex problem. For the latter, we apply our method both to synthetic data and to data of economic activity across Greater London. We find that our method calibrates the model orders of magnitude more accurately than a previous study of the same dataset using classical techniques, while running between 195 and 390 times faster.

A recent novel extension of multi-output Gaussian processes handles heterogeneous outputs assuming that each output has its own likelihood function. It uses a vector-valued Gaussian process prior to jointly model all likelihoods' parameters as latent functions drawn from a Gaussian process with a linear model of coregionalisation covariance. By means of an inducing points framework, the model is able to obtain tractable variational bounds amenable to stochastic variational inference. Nonetheless, the strong conditioning between the variational parameters and the hyper-parameters burdens the adaptive gradient optimisation methods used in the original approach. To overcome this issue we borrow ideas from variational optimisation introducing an exploratory distribution over the hyper-parameters, allowing inference together with the variational parameters through a fully natural gradient optimisation scheme. We show that our optimisation scheme can achieve better local optima solution with higher test performance rates than adaptive gradient methods or an hybrid strategy that partially use natural gradients in cooperation with the Adam method. We compare the performance of the different methods over toy and real databases.