Dynamic Regret with Untrusted Decision Predictions via Heterogeneous Expert Aggregation

Wentao Zhang

Abstract: We study online convex optimization with dynamic regret, where the learner has access to untrusted decision predictions about the per-round minimizers. Existing methods either exploit only gradient feedback, achieving $O(\sqrt{T(1+P\_T)})$ dynamic regret but remaining unable to benefit from predictions, or follow predictions blindly, obtaining regret proportional to the prediction error but with no worst-case safeguard. We propose a framework based on heterogeneous expert aggregation that simultaneously adapts to both the environment non-stationarity, characterized by path length $P\_T$, and prediction quality, measured by cumulative error $\bar{E}\_T$, without prior knowledge of either. The framework maintains a diverse pool of experts, which includes a gradient-based expert utilizing Online Gradient Descent, a prediction-based expert following predictions, and a new hybrid subroutine called Online Anchor Mirror Descent. These experts are aggregated by AdaHedge, whose small-loss property is critical to our results. We prove that our strongest variant achieves dynamic regret that smoothly interpolates between $O(GD\log\log T)$ when predictions are accurate and $O(R^\*)$ when predictions are adversarial, where $R^\*$ $= O(G\sqrt{T(D^2+2DP\_T)})$ is the optimal prediction-free rate. The small-loss bound of AdaHedge ensures that the aggregation overhead depends on the best expert's loss rather than on $T$, enabling a qualitative improvement over the $\Omega(\sqrt{T})$ floor of prediction-free methods. We further introduce an instance-dependent refinement of the new hybrid subroutine that can strictly improve the guarantee on favorable trajectories. Experiments on synthetic benchmarks validate all theoretical predictions: our methods achieve near-constant regret under accurate predictions, degrade gracefully under adversarial predictions, and outperform baselines by up to $26\times$ in non-stationary environments.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Julian_Zimmert1

Submission Number: 8046