Multi-Objective Non-parametric Sequential Prediction

TL;DR

This paper extends multi-objective online learning to stationary and ergodic processes, providing an optimal prediction algorithm that handles multiple objectives with constraints in dependent data settings.

Contribution

It introduces a framework for multi-objective sequential prediction in dependent data environments and proposes an optimal algorithm respecting convex constraints.

Findings

Established an asymptotic lower bound for prediction strategies.

Developed an algorithm achieving the optimal solution under constraints.

Extended the multi-objective framework beyond i.i.d. data to ergodic processes.

Abstract

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.