Online Convex Optimization Using Predictions
This addresses the challenge of integrating predictions into online algorithms for optimization, with potential applications in learning and control, though it is incremental in refining existing models.
The paper tackles the problem of online convex optimization with noisy predictions by proposing a stochastic error model that captures error correlation and temporal improvement, and shows that Averaging Fixed Horizon Control achieves sublinear regret and constant competitive ratio in expectation using a constant-sized prediction window.
Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error model that generalizes prior models in the learning and stochastic control communities, incorporates correlation among prediction errors, and captures the fact that predictions improve as time passes. We prove that achieving sublinear regret and constant competitive ratio for online algorithms requires the use of an unbounded prediction window in adversarial settings, but that under more realistic stochastic prediction error models it is possible to use Averaging Fixed Horizon Control (AFHC) to simultaneously achieve sublinear regret and constant competitive ratio in expectation using only a constant-sized prediction window. Furthermore, we show that the performance of AFHC is tightly concentrated around its mean.