Learning-Augmented Online Scheduling with Parsimonious Preemption

Alexander Lindermayr; Mugen Blue; Sungjin Im

arxiv: 2605.23255 · v1 · pith:LR3KILCFnew · submitted 2026-05-22 · 💻 cs.LG · cs.DS

Learning-Augmented Online Scheduling with Parsimonious Preemption

Mugen Blue , Sungjin Im , Alexander Lindermayr This is my paper

Pith reviewed 2026-05-25 04:51 UTC · model grok-4.3

classification 💻 cs.LG cs.DS

keywords learning-augmented algorithmsonline schedulingpreemptioncompetitive analysissingle machine schedulingunrelated machinesmalleable jobs

0 comments

The pith

Learning-augmented algorithms achieve O(1) competitiveness in online scheduling on single and unrelated machines while restricting each job to O(1) preemptions when predictions are accurate.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that predictions about job processing times can be used to design online scheduling algorithms that maintain constant competitive ratios while limiting preemptions to a constant number per job. This holds for single-machine and unrelated parallel-machine settings, with the preemption bound degrading only logarithmically as prediction error grows. The work extends these bounded-preemption guarantees to malleable jobs and validates the algorithms experimentally. A sympathetic reader would care because traditional online scheduling often relies on frequent preemptions that carry real system costs, and the results show how predictions can close the gap between theoretical performance and practical constraints.

Core claim

There exist O(1)-competitive learning-augmented algorithms for online scheduling on single and unrelated parallel machines that use only O(1) preemptions per job under accurate predictions, with the preemption overhead scaling logarithmically with prediction error; these constitute the first bounded-preemption guarantees for unrelated and malleable machines.

What carries the argument

Learning-augmented algorithms that exploit (possibly noisy) predictions to decide preemption points while preserving the competitive ratio.

If this is right

O(1) competitiveness holds with O(1) preemptions per job on single machines under accurate predictions.
The same O(1) competitiveness and O(1) preemption bound extend to unrelated parallel machines.
Preemption overhead grows at most logarithmically with the magnitude of prediction error.
The bounded-preemption property applies to malleable jobs as well.
Experimental evaluation confirms the algorithms behave as predicted on synthetic instances.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar prediction-driven limits on costly operations could be developed for other online problems such as routing or caching.
The logarithmic dependence on error suggests that even moderately accurate machine-learned predictors would yield near-constant preemption counts in practice.
System designers could trade off predictor quality against acceptable preemption overhead without sacrificing worst-case latency guarantees.

Load-bearing premise

The input instance supplies predictions about processing times that the algorithms can use to limit preemptions.

What would settle it

A family of instances with perfect predictions on which every O(1)-competitive algorithm for unrelated machines requires super-constant preemptions per job on average.

Figures

Figures reproduced from arXiv: 2605.23255 by Alexander Lindermayr, Mugen Blue, Sungjin Im.

**Figure 2.** Figure 2: Competitive ratio of SNAP vs. exhaustion parameter β. Performance remains stable until reaching a 100% exhaustion rate [PITH_FULL_IMAGE:figures/full_fig_p033_2.png] view at source ↗

**Figure 4.** Figure 4: Competitive ratio of the evaluated algorithms for different values of δ [PITH_FULL_IMAGE:figures/full_fig_p033_4.png] view at source ↗

read the original abstract

Learning-augmented algorithms have emerged as a powerful paradigm to surpass traditional worst-case lower bounds by integrating potentially noisy predictions. While this framework has seen success in online scheduling, existing work primarily optimizes job latency while relying on frequent, ``blind'' preemptions. This ignores the fundamental trade-off between algorithmic performance and preemption complexity. We provide the first systematic study of learning-augmented scheduling that curbs preemption while optimizing latency. We establish that the gap between theoretical latency bounds and preemption overhead can be bridged with solid analytical foundations. Our results include $O(1)$-competitive algorithms for single and unrelated parallel machines with only $O(1)$ preemptions per job under accurate predictions, with overhead scaling logarithmically with the prediction error. By providing the first bounded-preemption guarantees for unrelated and malleable machines, we extend the theoretical reach of the learning-augmented framework to more constrained and realistic settings. Finally, our algorithms are validated through experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims the first bounded-preemption results in learning-augmented online scheduling for single, unrelated, and malleable machines, with O(1) ratios when predictions are good.

read the letter

The main takeaway is that this work adds a limit on preemptions to the learning-augmented scheduling setting and still gets constant competitive ratios when the predictions are accurate. The overhead grows only logarithmically with prediction error, and they extend the guarantees to unrelated parallel machines and malleable machines, which prior learning-augmented papers had not handled with bounded preemptions. That is the concrete advance over earlier work that treated preemptions as free. The abstract also notes experiments for validation, which helps tie the theory to practice. The approach makes sense: use the predictions to decide preemptions sparingly instead of the usual blind frequent switches. The soft spot is that only the abstract is available here, so there is no way to inspect the actual proofs or the experimental setup. The O(1) bounds and the logarithmic scaling could have hidden assumptions about how the predictions are generated or how the machine models interact with the preemption limit. Without those details it is hard to judge whether the analysis closes or whether the experiments actually stress the error scaling. This paper is aimed at people working on online scheduling or learning-augmented algorithms who care about practical constraints like preemption cost. A reader in that area would get value from the new machine-model results if the proofs hold. It deserves a serious referee because the claimed extension to more realistic settings is worth checking in detail.

Referee Report

2 major / 1 minor

Summary. The paper introduces learning-augmented online scheduling algorithms that explicitly trade off latency against preemption count. It claims O(1)-competitive algorithms for single-machine and unrelated parallel-machine settings that use only O(1) preemptions per job when predictions are accurate, with preemption overhead growing logarithmically in the prediction error; the same framework is extended to malleable machines, and the algorithms are evaluated experimentally.

Significance. If the stated competitive ratios and preemption bounds are rigorously established, the work supplies the first bounded-preemption guarantees inside the learning-augmented model for unrelated and malleable machines. This directly addresses a practical constraint that prior learning-augmented scheduling results largely ignored, thereby widening the framework's applicability to realistic systems.

major comments (2)

[Abstract] Abstract and §1: the central claim that O(1) competitiveness is retained while restricting each job to O(1) preemptions (logarithmic in error) is load-bearing for the entire contribution, yet the provided context contains no proof sketches, potential-function arguments, or reduction steps that would allow verification of the claimed bounds.
The manuscript asserts the first bounded-preemption results for unrelated and malleable machines, but without the algorithmic descriptions or competitive-analysis sections it is impossible to confirm that the preemption restriction does not introduce additional competitive-ratio factors that would invalidate the O(1) guarantee.

minor comments (1)

[Abstract] The abstract refers to 'solid analytical foundations' and 'experiments' without naming the sections that contain the formal statements or the experimental setup; explicit section references would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the review and for recognizing the practical relevance of bounded-preemption guarantees in the learning-augmented scheduling model. Below we respond point-by-point to the major comments.

read point-by-point responses

Referee: [Abstract] Abstract and §1: the central claim that O(1) competitiveness is retained while restricting each job to O(1) preemptions (logarithmic in error) is load-bearing for the entire contribution, yet the provided context contains no proof sketches, potential-function arguments, or reduction steps that would allow verification of the claimed bounds.

Authors: The abstract and §1 are intentionally concise. The algorithmic descriptions, preemption rules, and competitive analyses (including potential-function arguments and the reduction showing that the O(1)-preemption constraint adds only a logarithmic factor in the prediction error) appear in full in Sections 3 (single machine), 4 (unrelated machines), and 5 (malleable machines). We will add a one-paragraph proof sketch to the introduction in the revision to make the high-level argument more immediately verifiable from the front matter. revision: partial
Referee: The manuscript asserts the first bounded-preemption results for unrelated and malleable machines, but without the algorithmic descriptions or competitive-analysis sections it is impossible to confirm that the preemption restriction does not introduce additional competitive-ratio factors that would invalidate the O(1) guarantee.

Authors: Sections 4 and 5 contain the complete algorithmic descriptions for the unrelated and malleable cases together with the competitive analyses. These sections explicitly show that the per-job O(1)-preemption bound (logarithmic in error) does not inflate the competitive ratio beyond O(1); any extra cost is charged against the prediction-error term already present in the objective. The “first such guarantees” claim is supported by the literature review in §2. The sections were part of the submitted manuscript; if they were not visible we can resupply the relevant excerpts. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and context describe a theoretical contribution establishing O(1)-competitive algorithms with bounded preemptions under the learning-augmented framework. No equations, definitions, or claims are visible that reduce by construction to fitted parameters, self-referential inputs, or load-bearing self-citations. The derivation relies on standard competitive analysis adapted to predictions about job instances, remaining self-contained against external benchmarks without any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no concrete free parameters, axioms, or invented entities; therefore the ledger is empty.

pith-pipeline@v0.9.0 · 5695 in / 1079 out tokens · 24376 ms · 2026-05-25T04:51:40.675040+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

PMLF maintains FIFO queues Qi; job j starts in queue ⌊log_{1+δ} ˆp_j⌋ and advances when processed (1+δ)^{i+1} units (Theorem 2.1). SNAP runs PF rates per epoch then rounds to non-preemptive schedule, charging preemptions to checkpoint exhaustions (Theorems 3.3–3.4).
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Competitive ratios 2+ε (single), 14.48(1+ε) (unrelated), 27e/(e−1)(1+ε) (malleable) obtained via delay decomposition and super-additivity of non-preemptive optimum.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

[1]

slow down

Let ⪯ denote the total over all available jobs that corresponds to the lexicographic order of those tuples. Schedule the first at mostmjobs of⪯. • If a jobj∈Q i has received a total processing equal to(1 +δ)i+1 at time t, remove it from Qi and place it at the end ofQi+1. We show the following theorem, which matches the guarantees of our single machine res...

work page
[2]

We chargeW to the total completion time of these jobs, which increases the competitive ratio by a factor of Θ(1/ν)

The last sub-epochH of epoch k completes at least(ν/4)|JH | jobs. We chargeW to the total completion time of these jobs, which increases the competitive ratio by a factor of Θ(1/ν). This charging is done “locally” within the same epoch, ensuring no overcharging

work page
[3]

Otherwise, let k′ > k be the latest epoch such that at least(ν/4)|JH | jobs are completed during epochsk+ 1, k+ 2, . . . , k ′. (a) If any of the epochsk + 1, k + 2, . . . , k′ − 1has a sub-epoch—say k′′ is the earliest epoch having a sub-epoch—then there must exist at leastν(1 −ν/ 2)|JH | jobs that arrive during epochk′′. Each of these jobs has an arriva...

work page
[4]

Formally, y(k) is the solution to (CP(J)) max X j∈J wj ·log(y j) s.t

Compute PF Rates.We compute the PF ratesy(k) for the jobsJk. Formally, y(k) is the solution to (CP(J)) max X j∈J wj ·log(y j) s.t. X j∈J bd j·y j ≤1∀d∈[D] yj ≥0∀j∈J 2.Compute Next Checkpoints.For each jobj∈J k, we define the remaining processing requirement to reach its next checkpoint asuj,k = (1 + δ)h+1 −q j(ek), where h∈N s.t. (1 +δ) h ≤max{q j(ek),ˆpj...

work page
[5]

The targeted processing requirement for each job j∈J k is thenv j,k = min{uj,k, lky(k) j }

Determine the Simulation Duration.Let lk denote the length of the shortest time interval such that, if jobs are processed at ratesy(k) during the time interval, at least⌈βnk⌉ jobs from Jk reach their next checkpoint. The targeted processing requirement for each job j∈J k is thenv j,k = min{uj,k, lky(k) j }

work page
[6]

completion time

Convert to aO(1)-Preemptive Schedule.We now compute anα-approximate O(1)- preemptive schedule (cf. Definition 4.1) for jobsJk with processing requirementsvj,k for each j∈J k. If we start this schedule at timeek, it will complete by time at mostek+1 ≤e k + αlk. Then, Epochkends and we start Epochk+ 1if not all jobs have been completed yet. Theorem E.1.The ...

work page
[7]

While a machinei could technically idle after meeting the specific processing targets vj,k for its assigned jobs, such idling results in an unnecessary loss of efficiency

SNAP(coupled with PMLF): Recall that the SNAP algorithm aims to process each jobj by vj,k units in epochk. While a machinei could technically idle after meeting the specific processing targets vj,k for its assigned jobs, such idling results in an unnecessary loss of efficiency. 31 Therefore, we introduce an engineering adaptation: while jobs are assigned ...

work page
[8]

The algorithm is equivalent to that of [AGK12] assuming that pj = ˆpj for all jobsj

Blind Algorithm: This policy is non-migratory, ensuring that no job is ever processed on multiple machines throughout its duration. The algorithm is equivalent to that of [AGK12] assuming that pj = ˆpj for all jobsj. The algorithm operates under the assumption of100% trust in the provided predictions. Lett denote the current time andqj(t)represent the vol...

work page
[9]

If a job’s actual processing time exceeds this estimate, we double the predicted size (i.e.,ˆpj ← 2ˆpj)

Doubling(Coupled With Immediate-Dispatch): Initially, each job’s size is assumed to be equal to its predicted sizeˆpj. If a job’s actual processing time exceeds this estimate, we double the predicted size (i.e.,ˆpj ← 2ˆpj). In this event, we treat the original job as completed and consider a new copy of the job to have arrived. This copy is dispatched to ...

work page
[10]

Jobs in Group 1 are dispatched to machines using the Doubling strategy

Hybrid SNAP: Initially, all jobs are initially in Group 1. Jobs in Group 1 are dispatched to machines using the Doubling strategy. To loosely emulate the Blind strategy, we utilize large milestones: {c(1 + δ)iˆpj |i≥ 1} for a large parameterc≥ 1. Any job that reaches its first milestone permanently migrates to Group 2. Group 2 jobs are assigned to machine...

work page arXiv

[1] [1]

slow down

Let ⪯ denote the total over all available jobs that corresponds to the lexicographic order of those tuples. Schedule the first at mostmjobs of⪯. • If a jobj∈Q i has received a total processing equal to(1 +δ)i+1 at time t, remove it from Qi and place it at the end ofQi+1. We show the following theorem, which matches the guarantees of our single machine res...

work page

[2] [2]

We chargeW to the total completion time of these jobs, which increases the competitive ratio by a factor of Θ(1/ν)

The last sub-epochH of epoch k completes at least(ν/4)|JH | jobs. We chargeW to the total completion time of these jobs, which increases the competitive ratio by a factor of Θ(1/ν). This charging is done “locally” within the same epoch, ensuring no overcharging

work page

[3] [3]

Otherwise, let k′ > k be the latest epoch such that at least(ν/4)|JH | jobs are completed during epochsk+ 1, k+ 2, . . . , k ′. (a) If any of the epochsk + 1, k + 2, . . . , k′ − 1has a sub-epoch—say k′′ is the earliest epoch having a sub-epoch—then there must exist at leastν(1 −ν/ 2)|JH | jobs that arrive during epochk′′. Each of these jobs has an arriva...

work page

[4] [4]

Formally, y(k) is the solution to (CP(J)) max X j∈J wj ·log(y j) s.t

Compute PF Rates.We compute the PF ratesy(k) for the jobsJk. Formally, y(k) is the solution to (CP(J)) max X j∈J wj ·log(y j) s.t. X j∈J bd j·y j ≤1∀d∈[D] yj ≥0∀j∈J 2.Compute Next Checkpoints.For each jobj∈J k, we define the remaining processing requirement to reach its next checkpoint asuj,k = (1 + δ)h+1 −q j(ek), where h∈N s.t. (1 +δ) h ≤max{q j(ek),ˆpj...

work page

[5] [5]

The targeted processing requirement for each job j∈J k is thenv j,k = min{uj,k, lky(k) j }

Determine the Simulation Duration.Let lk denote the length of the shortest time interval such that, if jobs are processed at ratesy(k) during the time interval, at least⌈βnk⌉ jobs from Jk reach their next checkpoint. The targeted processing requirement for each job j∈J k is thenv j,k = min{uj,k, lky(k) j }

work page

[6] [6]

completion time

Convert to aO(1)-Preemptive Schedule.We now compute anα-approximate O(1)- preemptive schedule (cf. Definition 4.1) for jobsJk with processing requirementsvj,k for each j∈J k. If we start this schedule at timeek, it will complete by time at mostek+1 ≤e k + αlk. Then, Epochkends and we start Epochk+ 1if not all jobs have been completed yet. Theorem E.1.The ...

work page

[7] [7]

While a machinei could technically idle after meeting the specific processing targets vj,k for its assigned jobs, such idling results in an unnecessary loss of efficiency

SNAP(coupled with PMLF): Recall that the SNAP algorithm aims to process each jobj by vj,k units in epochk. While a machinei could technically idle after meeting the specific processing targets vj,k for its assigned jobs, such idling results in an unnecessary loss of efficiency. 31 Therefore, we introduce an engineering adaptation: while jobs are assigned ...

work page

[8] [8]

The algorithm is equivalent to that of [AGK12] assuming that pj = ˆpj for all jobsj

Blind Algorithm: This policy is non-migratory, ensuring that no job is ever processed on multiple machines throughout its duration. The algorithm is equivalent to that of [AGK12] assuming that pj = ˆpj for all jobsj. The algorithm operates under the assumption of100% trust in the provided predictions. Lett denote the current time andqj(t)represent the vol...

work page

[9] [9]

If a job’s actual processing time exceeds this estimate, we double the predicted size (i.e.,ˆpj ← 2ˆpj)

Doubling(Coupled With Immediate-Dispatch): Initially, each job’s size is assumed to be equal to its predicted sizeˆpj. If a job’s actual processing time exceeds this estimate, we double the predicted size (i.e.,ˆpj ← 2ˆpj). In this event, we treat the original job as completed and consider a new copy of the job to have arrived. This copy is dispatched to ...

work page

[10] [10]

Jobs in Group 1 are dispatched to machines using the Doubling strategy

Hybrid SNAP: Initially, all jobs are initially in Group 1. Jobs in Group 1 are dispatched to machines using the Doubling strategy. To loosely emulate the Blind strategy, we utilize large milestones: {c(1 + δ)iˆpj |i≥ 1} for a large parameterc≥ 1. Any job that reaches its first milestone permanently migrates to Group 2. Group 2 jobs are assigned to machine...

work page arXiv