# Predictive Online Convex Optimization

## TL;DR

This paper introduces a predictive step in online convex optimization that uses future gradient estimates to improve performance, especially in demand response scenarios, with proven regret bounds and empirical validation.

## Contribution

It proposes a novel predictive update method for online convex optimization that leverages future gradient estimates without assuming environment predictability.

## Key findings

- Predictive updates outperform standard methods in demand response tasks.
- Regret bounds are established for the proposed algorithms.
- Empirical results show improved performance over traditional online convex optimization.

## Abstract

We incorporate future information in the form of the estimated value of future gradients in online convex optimization. This is motivated by demand response in power systems, where forecasts about the current round, e.g., the weather or the loads' behavior, can be used to improve on predictions made with only past observations. Specifically, we introduce an additional predictive step that follows the standard online convex optimization step when certain conditions on the estimated gradient and descent direction are met. We show that under these conditions and without any assumptions on the predictability of the environment, the predictive update strictly improves on the performance of the standard update. We give two types of predictive update for various family of loss functions. We provide a regret bound for each of our predictive online convex optimization algorithms. Finally, we apply our framework to an example based on demand response which demonstrates its superior performance to a standard online convex optimization algorithm.