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We formalize the problem of selecting the optimal set of options for planningas that of computing the smallest set of options so that planning converges inless than a given maximum of value-iteration passes. We first show that theproblem is NP-hard, even if the task is constrained to be deterministic---thefirst such complexity result for option discovery. We then present the firstpolynomial-time boundedly suboptimal approximation algorithm for this setting,and empirically evaluate it against both the optimal options and arepresentative collection of heuristic approaches in simple grid-based domainsincluding the classic four-rooms problem.

Finding Options that Minimize Planning Time