Online learning and on-line convex optimization (online learning and online convex optimization)-FTL algorithm 5

The most natural learning rule is to use any vector that has the least loss in the past rounds. This is the same spirit as the consistent algorithm, which is commonly referred to as follow-the-leaderin online convex optimization, minimizing cumulative losses.

For any t:

　　　　　　　　　　　

　　

We talked about the ability to minimize cumulative losses that cannot be explained by this algorithm in an online learning scenario that is valid and we need to explore the algorithm of regret bound:

　　

Using inductive method to prove:

　　

Example 1:Online quadratic optimization

　　

Example 2:Online Linear Optimization

　　

Not finished, to be continued ...

The next section describes the Ftrl algorithm

　　

Online learning and on-line convex optimization (online learning and online convex optimization)-FTL algorithm 5