Generalized teaching dimensions and the query complexity of learning

Abstract

We investigate the query complexity of learning a concept class C over a finite domain X with membership queries, and with membership queries and equivalence queries from ahy-pothesis space H, respectively. Building on Moshkov’s work [30] done in the context of conditional tests, we give lower and upper bounds on the considered query complexities in terms of the cardinality of C and combinatorial parameters expressing the complexity of unique specification with respect to C: the extended teaching dimenston of C in the first case, and the unzque specification dimenszon of 2X \ H with respect to C in the second case. For “reasonably parametrized” classes the given bounds imply that polynomial query complexity can be achieved if and only if the corresponding specification dimensions are polynomial. We give applications of the obtained general bounds for learning geometric concepts over the discrete domain {O, 1, . . . . n– I}d, for learning deterministic finite automata with menl-bership and proper equivalence queries, for the trade-off between the number of membership and proper equivalence queries used, and for exact learning in parallel with membership and proper equivalence queries.