Multi-Objective Non-parametric Sequential Prediction
This work addresses multi-objective prediction for online learning applications where dependencies exist, but it is incremental as it builds on prior i.i.d. methods.
The paper tackles the problem of multi-objective online learning by extending it from i.i.d. to stationary and ergodic processes, allowing dependencies among observations, and presents an algorithm that achieves the optimal solution while meeting continuous and convex constraints.
Online-learning research has mainly been focusing on minimizing one objective function. In many real-world applications, however, several objective functions have to be considered simultaneously. Recently, an algorithm for dealing with several objective functions in the i.i.d. case has been presented. In this paper, we extend the multi-objective framework to the case of stationary and ergodic processes, thus allowing dependencies among observations. We first identify an asymptomatic lower bound for any prediction strategy and then present an algorithm whose predictions achieve the optimal solution while fulfilling any continuous and convex constraining criterion.