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We introduce a method for constructing skills capable of solving tasks drawn from a distribution of parameterized reinforcement learning problems. The method draws example tasks from a distribution of interest and uses the corresponding learned policies to estimate the topology of the lower-dimensional piecewise-smooth manifold on which the skill policies lie. This manifold models how policy parameters change as task parameters vary. The method identifies the number of charts that compose thearXiv:1206.6398v2 fatcat:mgvk6rxgyzfi5cdrnauawa6rsm