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# Finding Options that Minimize Planning Time

*Proceedings of the 36th International Conference on Machine Learning*, PMLR 97:3120-3129, 2019.

#### Abstract

We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem is $\NP$-hard, even if the task is constrained to be deterministicâ€”the first such complexity result for option discovery. We then present the first polynomial-time boundedly suboptimal approximation algorithm for this setting, and empirically evaluate it against both the optimal options and a representative collection of heuristic approaches in simple grid-based domains.