Using More Data to Speed-up Training Time

In many recent applications, data is plentiful. By now, we have a rather clear understanding of how more data can be used to improve the accuracy of learning algorithms. Recently, there has been a growing interest in understanding how more data can be leveraged to reduce the required training runtime. In this paper, we study the runtime of learning as a function of the number of available training examples, and underscore the main high-level techniques. We provide the first formal positive result showing that even in the unrealizable case, the runtime can decrease exponentially while only requiring a polynomial growth of the number of examples. Our construction corresponds to a synthetic learning problem and an interesting open question is whether the tradeoff can be shown for more natural learning problems. We spell out several interesting candidates of natural learning problems for which we conjecture that there is a tradeoff between computational and sample complexity.