Some label efficient learning results

We investigate the value of labels in a simple version of the standard on-line prediction model (the “experts” setting). We present algorithms and adversary arguments defining tradeoffs between the number of mistakes made and the number of labels that the learner requests. One version of this question can be viewed as a family of games whose value is given by a complicated recurrence. Although our attempts to tind a closed form for this recurrence have been unsuccessful, we show how an algorithm can efficiently compute its value, enabling it to perform optimally.