  Online learning is the process of answering a sequence of questions based on
the correct answers to the previous questions. It is studied in many research
areas such as game theory, information theory and machine learning. There are
two main components of online learning framework. First, the learning algorithm
also known as the learner and second, the hypothesis class which is essentially
a set of functions which learner uses to predict answers to the questions.
Sometimes, this class contains some functions which have the capability to
provide correct answers to the entire sequence of questions. This case is
called realizable case. And when hypothesis class does not contain such
functions is called unrealizable case. The goal of the learner, in both the
cases, is to make as few mistakes as that could have been made by most powerful
functions in hypothesis class over the entire sequence of questions.
Performance of the learners is analysed by theoretical bounds on the number of
mistakes made by them. This paper proposes three algorithms to improve the
mistakes bound in the unrealizable case. Proposed algorithms perform highly
better than the existing ones in the long run when most of the input sequences
presented to the learner are likely to be realizable.
