# Online Learning with Local Permutations and Delayed Feedback

arXiv: https://arxiv.org/abs/1703.04274 · HTML: https://mlsanity.com/paper/1703.04274/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2017.

## Built on by (most cited first, 10 of 10)

- [Nonstochastic Bandits with Composite Anonymous Feedback](https://mlsanity.com/paper/2112.02866/) (2021)
- [Online Strongly Convex Optimization with Unknown Delays](https://mlsanity.com/paper/2103.11354/) (2021)
- [Online Optimization with Feedback Delay and Nonlinear Switching Cost](https://mlsanity.com/paper/2111.00095/) (2021)
- [Is Stochastic Mirror Descent Vulnerable to Adversarial Delay Attacks? A Traffic Assignment Resilience Study](https://mlsanity.com/paper/2304.01161/) (2023)
- [Projection-free Online Learning with Arbitrary Delays](https://mlsanity.com/paper/2204.04964/) (2022)
- [Robust Learning for Smoothed Online Convex Optimization with Feedback Delay](https://mlsanity.com/paper/2310.20098/) (2023)
- [ConformalShift: Targeted Event Reordering Against Adaptive ECG Monitoring](https://mlsanity.com/paper/2608.03628/) (2026)
- [Learning from Delayed Feedback in Games via Extra Prediction](https://mlsanity.com/paper/2509.22426/) (2025)
- [Linear Convergence in Games with Delayed Feedback via Extra Prediction](https://mlsanity.com/paper/2602.17486/) (2026)
- [CFR without Unbiasedness: Deterministic Guarantees for Persistent Public-Chance Schedules](https://mlsanity.com/paper/2608.14761/) (2026)

## Abstract (arXiv)

We propose an Online Learning with Local Permutations (OLLP) setting, in which the learner is allowed to slightly permute the order of the loss functions generated by an adversary. On one hand, this models natural situations where the exact order of the learner's responses is not crucial, and on the other hand, might allow better learning and regret performance, by mitigating highly adversarial loss sequences. Also, with random permutations, this can be seen as a setting interpolating between adversarial and stochastic losses. In this paper, we consider the applicability of this setting to convex online learning with delayed feedback, in which the feedback on the prediction made in round t arrives with some delay τ. With such delayed feedback, the best possible regret bound is well-known to be O(√τ T). We prove that by being able to permute losses by a distance of at most M (for M≥ τ), the regret can be improved to O(√T(1+√τ2/M)), using a Mirror-Descent based algorithm which can be applied for both Euclidean and non-Euclidean geometries. We also prove a lower bound, showing that for M<τ/3, it is impossible to improve the standard O(√τ T) regret bound by more than constant factors. Finally, we provide some experiments validating the performance of our algorithm.