可进化性不一定意味着可学习性
Evolvability need not imply learnability
摘要：
我们证明了，如果假设大小保持不变，则可表示为单调析取范式的布尔函数在布尔立方体上的均匀分布下是PAC-可演化的。我们进一步表明，这一结果是不足以证明的PAC可学习的单调布尔函数，从而证明了一个反例，最近声称相反。我们进一步讨论的情况下，进化性和可学习性将一致，以及他们不同的情况下。后一种情况下学习的前景在复杂的假设空间的影响进行了简要的研究。
英文摘要：
We show that Boolean functions expressible as monotone disjunctive normal forms are PAC-evolvable under a uniform distribution on the Boolean cube if the hypothesis size is allowed to remain fixed. We further show that this result is insufficient to prove the PAC-learnability of monotone Boolean functions, thereby demonstrating a counter-example to a recent claim to the contrary. We further discuss scenarios wherein evolvability and learnability will coincide as well as scenarios under which they differ. The implications of the latter case on the prospects of learning in complex hypothesis spaces is briefly examined.
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