Learning to Solve Single Variable Linear Equations by Universal Search with Probabilistic Program Graphs

Abstract

The motivation for general AI is to overcome the problem of specificity in traditional AI approaches. Universal search guarantees to solve this problem with asymptotic optimality. However, the constant factor associated with the search time exponentially depends on solution size and can be immensely large. Evidently this reduces practical interest. Transfer learning can help reducing this constant factor for a series of related problems. We propose a dataflow graph-based programming model which evidently helps improving transfer learning between related tasks. We built a universal search based agent using our programming model which learned to solve single variable linear equations with minimal prior knowledge about list operations and arithmetic expression evaluation. The agent returned the solution as a program graph and was able to find general solution for a set of equations. Experimental results reveal the efficiency of the agent. The experiments demonstrate how universal search can be deployed in solving some practical problems like algebra equations.