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Exploring Viable Algorithmic Options for Learning from Demonstration (LfD): A Parameterized Complexity Approach

The key to reconciling the polynomial-time intractability of many machine learning tasks in the worst case with the surprising solvability of these tasks by heuristic algorithms in practice seems to be exploiting restrictions on real-world data sets. One approach to investigating such restrictions is to analyze why heuristics perform well under restrictions. A complementary approach would be to systematically determine under which sets of restrictions efficient and reliable machine learning algorithms do and do not exist. In this paper, we show how such a systematic exploration of algorithmic options can be done using parameterized complexity analysis, As an illustrative example, we give the first parameterized complexity analysis of batch and incremental policy inference under Learning from Demonstration (LfD). Relative to a basic model of LfD, we show that none of our problems can be solved efficiently either in general or relative to a number of (often simultaneous) restrictions on environments, demonstrations, and policies. We also give the first known restrictions under which efficient solvability is possible and discuss the implications of our solvability and unsolvability results for both our basic model of LfD and more complex models of LfD used in practice.