Delay-Tolerant OCO With Long-Term Constraints: Algorithm and Its Application to Network Resource Allocation
Bibliographic record
Abstract
We consider online convex optimization (OCO) with multi-slot feedback delay. An agent selects a sequence of online decisions to minimize the accumulation of time-varying convex loss functions, subject to short-term and long-term constraints that may be time-varying. Both the convex loss function and the long-term constraint function may experience multiple time slots of feedback delay to be received by the agent. Existing works on OCO under this general setting has focused on the static regret, which measures the gap of losses between an online decision sequence and a time-invariant static offline benchmark. In this work, besides the static regret, we also consider a more practically meaningful metric, the dynamic regret, where the benchmark is a time-varying online optimal decision sequence. We propose an efficient algorithm, termed Delay-Tolerant Constrained-OCO (DTC-OCO), which uses a novel double regularization together with a new penalty mechanism on the long-term constraint violation, to tackle the asynchrony between information feedback and decision updates. We obtain upper bounds for its static regret, dynamic regret, and constraint violation, proving that they are sublinear under mild conditions. Furthermore, we consider a variation of DTC-OCO with multi-step gradient descent, and show it provides improved dynamic regret and constraint violation bounds for strongly convex loss functions. For numerical demonstration, we apply DTC-OCO to a general network resource allocation problem. Our simulation results suggest substantial performance gain by DTC-OCO over the current best alternative.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".