Policies with Sparse Inter-Agent Dependencies in Dynamic Games: A Dynamic Programming Approach

Common feedback strategies in multi-agent dynamic games require all players' state information to compute control strategies. However, in real-world scenarios, sensing and communication limitations between agents make full state feedback expensive or impractical, and such strategies can become fragile when state information from other agents is inaccurate. To this end, we propose a regularized dynamic programming approach for finding sparse feedback policies that selectively depend on the states of a subset of agents in dynamic games. The proposed approach solves convex adaptive group Lasso problems to compute sparse policies approximating Nash equilibrium solutions. We prove the regularized solutions' asymptotic convergence to a neighborhood of Nash equilibrium policies in linear-quadratic (LQ) games. We extend the proposed approach to general non-LQ games via an iterative algorithm. Empirical results in multi-robot interaction scenarios show that the proposed approach effectively computes feedback policies with varying sparsity levels. When agents have noisy observations of other agents' states, simulation results indicate that the proposed regularized policies consistently achieve lower costs than standard Nash equilibrium policies by up to 77% for all interacting agents whose costs are coupled with other agents' states.

Measuring Multi-Source Redundancy in Factor Graphs

Factor graphs are a ubiquitous tool for multi-source inference in robotics and multi-sensor networks. They allow for heterogeneous measurements from many sources to be concurrently represented as factors in the state posterior distribution, so that inference can be conducted via sparse graphical methods. Adding measurements from many sources can supply robustness to state estimation, as seen in distributed pose graph optimization. However, adding excessive measurements to a factor graph can also quickly degrade their performance as more cycles are added to the graph. In both situations, the relevant quality is the redundancy of information. Drawing on recent work in information theory on partial information decomposition (PID), we articulate two potential definitions of redundancy in factor graphs, both within a common axiomatic framework for redundancy in factor graphs. This is the first application of PID to factor graphs, and only one of a few presenting quantitative measures of redundancy for them.