Universal value iteration networks: When spatially-invariant is not universal

In this paper, we first formally define the problem set of spatially invariant Markov Decision Processes (MDPs), and show that Value Iteration Networks (VIN) and its extensions are computationally bounded to it due to the use of the convolution kernel. To generalize VIN to spatially variant MDPs, we propose Universal Value Iteration Networks (UVIN). In comparison with VIN, UVIN automatically learns a flexible but compact network structure to encode the transition dynamics of the problems and support the differentiable planning module. We evaluate UVIN with both spatially invariant and spatially variant tasks, including navigation in regular maze, chessboard maze, and Mars, and Minecraft item syntheses. Results show that UVIN can achieve similar performance as VIN and its extensions on spatially invariant tasks, and significantly outperforms other models on more general problems.