Leveraging correlations in utility learning

We present two approaches for leveraging correlations in learning the utilities of non-cooperative agents' competing in a game: correlation and coalition utility learning. In the former, we estimate the correlations between agents using constrained Feasible Generalized Least Squares with noise estimation and then use the estimated correlations to generate a correlation utility function for each agent which is a weighted sum of its own estimated utility function and all the agents' estimated utilities that are highly correlated with them. We then optimize the weights to boost the performance of the estimators. In the latter, we use a small amount of training data to estimate the correlations between players and form coalitions between agents that are positively correlated. We then estimate the parameters of the utility functions for each coalition where agents in a coalition jointly optimize their utilities. The correlation utility learning method outperforms existing schemes while the coalition utility learning method is simple enough to be adapted to an online framework after an initial training phase, yet it matches the performance of much more complex schemes. To demonstrate the efficacy of the estimation schemes, we apply them to data collected from a social game framework for incentivizing more efficient shared resource consumption in smart buildings.