We consider the problem of autonomously learning robot skills under a limited practice budget for sequential tasks. We propose an active skill learning algorithm, \emph{Deliberate Practice (DP)}, that computes a provably \emph{budget-optimal} allocation---practicing skills that maximize expected cumulative reward while being learnable within the budget. DP estimates both the time needed to master skills and the cumulative reward of the task plans that the skills unlock. Computing a budget-optimal allocation is challenging as it requires reasoning about combinatorially many skill plans over a large practice budget. Our key contribution is a bilinear program that can compute this exactly using off-the-shelf solvers. Through simulated and real-world experiments on long-horizon manipulation tasks, we show that our approach allows robots to optimally use limited practice time to acquire useful policies and improve long-horizon planning.

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