Value-complexity tradeoff explains mouse navigational learning

We introduce a novel methodology for describing animal behavior as a tradeoff between value and complexity, using the Morris Water Maze navigation task as a concrete example. We develop a dynamical system model of the Water Maze navigation task, solve its optimal control under varying complexity constraints, and analyze the learning process in terms of the value and complexity of swimming trajectories. The value of a trajectory is related to its energetic cost and is correlated with swimming time. Complexity is a novel learning metric which measures how unlikely is a trajectory to be generated by a naive animal. Our model is analytically tractable, provides good fit to observed behavior and reveals that the learning process is characterized by early value optimization followed by complexity reduction. Furthermore, complexity sensitively characterizes behavioral differences between mouse strains.Author summary: Goal directed learning typically involves the computation of complex sequences of actions. However, computational frameworks such as reinforcement learning focus on optimizing the reward, or value, associated with action sequences while ignoring their complexity cost. Here we develop a complexity-limited optimal control model of a the Morris Water Maze navigation task: a widely used tool for characterizing the effects of genetic and other experimental manipulations in animal models. Our proposed complexity metric provides new insights on the dynamics of navigational learning and reveals behavioral differences between mouse strains.