Abstract
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.
Highlights
Adaptive decision-making is often modeled, within the framework of reinforcement learning, as a process of generating actions associated with a high expected reward signal, or value [1]
We first modelled the dynamics of a naive mouse as it swims around the circular tank
We added a damping term to model water viscosity and additive Gaussian noise to allow for randomness in the trajectories. We refer to this model of mouse motion as the naive or uncontrolled mouse model as it does not contain any information about the location of the platform. It can be expressed in state-space notation by the following linear-time-invariant stochastic dynamical system: x_ðtÞ 1⁄4 AxðtÞ þ xðtÞ; ð1Þ
Summary
Goal directed learning typically involves the computation of complex sequences of actions. Computational frameworks such as reinforcement learning focus on optimizing the reward, or value, associated with action sequences while ignoring their complexity cost. We develop a complexity-limited optimal control model of 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
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