# Prediction in Online Convex Optimization for Parametrizable Objective Functions

## TL;DR

This paper explores how incorporating predictions of parameter values in online convex optimization can improve dynamic regret bounds, introducing a new regularity measure and a combined prediction-optimization algorithm tested on real and simulated data.

## Contribution

It introduces a new regularity measure based on prediction accuracy and proposes a novel algorithm that jointly predicts and optimizes parametrizable objectives.

## Key findings

- Accurate predictions lead to tighter dynamic regret bounds.
- The proposed algorithm performs well on both simulated and real datasets.
- Prediction accuracy significantly impacts optimization performance.

## Abstract

Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex optimization for parametrizable objectives, i.e. optimization problems that depend solely on the value of a parameter at a given time. We introduce a new regularity for dynamic regret based on the accuracy of predicted values of the parameters and show that, under mild assumptions, accurate prediction can yield tighter bounds on dynamic regret. Inspired by recent advances on learning how to optimize, we also propose a novel algorithm to simultaneously predict and optimize for parametrizable objectives and study its performance using simulated and real data.