Discrete Prediction Games with Arbitrary Feedback and Loss (Extended Abstract) [chapter]

Antonio Piccolboni, Christian Schindelhauer
2001 Lecture Notes in Computer Science  
We investigate the problem of predicting a sequence when the information about the previous elements (feedback) is only partial and possibly dependent on the predicted values. This setting can be seen as a generalization of the classical multi-armed bandit problem and accommodates as a special case a natural bandwidth allocation problem. According to the approach adopted by many authors, we give up any statistical assumption on the sequence to be predicted. We evaluate the performance against
more » ... e best constant predictor (regret), as it is common in iterated game analysis. We show that for any discrete loss function and feedback function only one of two situations can occur: either there is a prediction strategy that achieves in Ì rounds a regret of at most Ç´Ì ¿ ´ÐÒ Ì µ ½ ¾ µ or there is a sequence which cannot be predicted by any algorithm without incurring a regret of ª´Ì µ. We prove both sides constructively, that is when the loss and feedback functions satisfy a certain condition, we present an algorithm that generates predictions with the claimed performance; otherwise we show a sequence that no algorithm can predict without incurring a linear regret with probability at least ½ ¾.
doi:10.1007/3-540-44581-1_14 fatcat:5jltob57fbegrlrp2zs3q7suaa