Title: Non-Clairvoyant Scheduling with Progress Bars
Venue: NeurIPS 2025
Accepted: yes
Keywords: online algorithms

competitive analysis

scheduling

algorithms with predictions

non-clairvoyance
Abstract: In non-clairvoyant scheduling, the goal is to minimize the
total job completion time without prior knowledge of individual
job processing times. This classical online optimization problem
has recently gained attention through the framework of
learning-augmented algorithms. We introduce a natural setting in
which the scheduler receives continuous feedback in the form of
progress bars—estimates of the fraction of each job completed over time.
We design new algorithms for both adversarial and stochastic progress bars
and prove strong competitive bounds. Our results in the adversarial case surprisingly
induce improved guarantees for learning-augmented scheduling with job size predictions.
We also introduce a general method for combining scheduling algorithms, yielding
further insights in scheduling with predictions. Finally, we propose a stochastic
model of progress bars as a more optimistic alternative to conventional worst-case
models, and present an asymptotically optimal scheduling algorithm in this setting.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper considered several settings under non-clairvoyant scheduling, namely single signal progress bar, untrusted and stochastic. In single signal progress bar, the paper introduced several algorithms and proved the consistency upper bound of these algorithm. The paper further discussed the robustness and smoothness of these algorithms, and proved that the proposed Algorithm 1 achieves a tradeoff between smoothness and robustness. The paper further proposed a lower bound of robustness.\n\nThe paper then generalized the results to untrusted setting and stochastic setting. In both setting, algorithms are introduced with corresponding consistency upper bound.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. This paper proposed a new problem setting, offline scheduling with progress bar feedback, which is theoretically interesting and practically relevant.\n\n2. Under single-signal setup, the paper discussed several strategies achieving optimal consistency and tradeoffs between robustness and smoothness. These results are new to me.\n\n3. The paper also considered stochastic progress bar, where the signals are emitted according to Poisson process. This setting is also interesting and sounds practical relevant. Meanwhile, Algorithm 3, designed for this setting, with theoretical guarantee, is also new to me.\n\nWeakness:\n\n1. In the proof of Theorem 2.5, line 586, the claim \"the algorithm processes $I_1$ and $I_2$ equivalently until time t\" requires more clarification. Since $p_j$ are different in $I_1$ and $I_2$, the time of emitting signals might be different, which might results to a different execution routine.\n\n2. Algorithm 2 looks like a direct generalization of the results in [EKMM24]. \n\n3. The presentation of this paper is not clear enough. For example, the definition of robustness and brittleness are neither presented in the paper nor referred to previous works.\n\nQUESTIONS:\nMy questions are listed below:\n\n1. What is the major technical difficulties to achieve the performance guarantees?\n\n2. For the problem described in Section 3, is there a lower bound for the total completion time?\n\nLIMITATIONS:\nLimitations are not explicitly discussed in this paper. See questions and weakness for potential limitation.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-22"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper considers the single machine non-clairvoyant scheduling to minimize the total completion time with progress bars. All jobs are available at time 0 with an unknown job size. As a job is being processed, estimates of the job's progress are received by the scheduler as progress bars, allowing for informed decisions. The progress bars may be inaccurate, meaning that they may misreport the actual fractions of the processed job. Thus, this work falls within the field of algorithms with predictions, where the algorithm is expected to use predictions so that 1) the performance is near-optimal when the predictions are perfect (consistency) and 2) the performance is bounded under arbitrarily bad predictions (robustness). The distinction of this work is that the progress bars (i.e., the predictions) are received in the process of scheduling, contrasting the existing works where predictions are static and received upfront. The authors considered various settings of the progress bars and gave solutions for each: single signal progress bars, progress bars with multiple levels, and stochastic progress bars. For each setting, a consistent and robust algorithm is proposed. Experiments were conducted to validate the proposed algorithms.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. Scheduling with predictions continuously arrived at the scheduler is a novel setting. This setting is practical so algorithmic advances along this dimension are valuable.\n\n2. The problem of scheduling with progress bars was thoroughly studied under adverbial and stochastic settings. The results are rich.\n\n3. The paper makes meaningful connections to other fields, including the classic non-clairvoyant scheduling with predictions and multi-armed bandits.\n\n\nWeaknesses:\n\nThere are two major weaknesses and a few minor ones identified. The first major one is that some statements feel like over-selling the contributions, and the second is that elaboration and clarity are needed around the computable delays.\n\n\nOverselling contributions:\n\n1. Line 204: The contribution of improving upon state-of-the-art seems a bit oversold. The parameter alpha needs to be able to choose freely for the result to hold. It is not clear if the parameter alpha can be chosen freely. It is at least not explicitly stated so.\n\n2. Line 267 claims that a near-perfect consistency and robustness could be simultaneously achievable, but it is a bit oversold as it requires specific problem instances, e.g., max_i p_i = o(n^{-5/3} OPT).\n\n\nComputable delays:\n\n1. The need for computable delays is not explicitly in the proof of Theorem 3.1. What would happen to which part of the proof if the algorithms do not have computable delays?\n\n2. Corollary 3.2 requires algorithms (A^{(h)})_h to have computable delays to use Theorem 3.1. This was not shown, which may affect the correctness of the corollary. Are mutual delays of these algorithms functions in progress levels alpha and beta?\n\n\nMinor issues:\n\n1. Line 241: typo OPT = \\Omega not \\omega.\n\n2. Line 612: formula 2mn p_{max} is missing.\n\n3. Line 617: all with variance factor m p^2_{\\max}.\n\n\nDespite the issues identified, I have an overall positive feeling about the paper. The contributions are sufficient for NeurIPS, conditional on that the Corollary 3.2 is correctly proved, where I have a few questions in the Question section.\n\nQUESTIONS:\n1. Regarding Line 204, the claimed contribution of improving upon the state-of-the-art seems a bit oversold. The parameter alpha must be chosen arbitrarily for the results to hold. Can you please justify this point?\n\n2. How are computable delays used in the proof of Theorem 3.1? Corollary 3.2 requires the algorithms to have computable delays, which were not shown. This may affect the correctness of the corollary. Can authors explain this point? The validity of the correctness may affect my evaluation. For example, if the result is not correctly proved, my evaluation may be lowered.\n\n3. Line 341. It is not clear that the delayed predictions have performance which is highly sensitive to errors. It seems that the performance deviation is small. Can you please explain this?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel model for non-clairvoyant scheduling enhanced with progress bars. The proposed framework interpolates between non-clairvoyant and clairvoyant settings by providing online feedback about job completion percentages, simulating real-world scenarios like system profiling or machine learning training. Three models of progress bars have been studied, including single signal progress bar, untrusted progress bar, stochastic progress bar. Besides, this paper combines worst-case competitive analysis with insights from learning-augmented algorithms and stochastic modeling. The authors design algorithms for each model and prove competitive ratio bounds. They also show how combining multiple scheduling strategies can improve performance and robustness.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths.**\n1. This paper presents a novel and natural model (scheduling with progress bars) for incorporating dynamic feedback into scheduling, which seems reasonable in some real-world scenarios. This broadens the algorithmic design space for the learning-augmented job scheduling problem.\n2. The assumptions are well-justified and analyzed in both stochastic and adversarial settings.\n3. This paper achieves an improved tradeoff (over time-sharing) compared with the SOTA learning-augmented scheduling algorithms.\n4. The theoretical analysis is well-founded and clearly structured, which I appreciate.\n5. The algorithm *Repeated Explore-Then-Commit* is intuitive and well motivated.\n\n**Weaknesses.**\n1. The new algorithm design is motivated by real-world phenomena (e.g., profiling and ML training in which multi-round progressive information can be obtained), but not evaluated using real-world job traces.\n2. The empirical performance of the combining algorithm appears to be unstable and only shows clear advantages when $n$ is large. This limits its applicability, as it is uncommon for a large number of jobs to be queued on a single machine, particularly when such jobs, like those with progress bars, are typically ML training jobs discussed in this paper.\n\nQUESTIONS:\n* Can the algorithms be applied to job scheduling scenarios with online, time-varying job arrivals?\n\nLIMITATIONS:\nThis paper does not have any negative societal impact.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper considers online scheduling problems where job sizes are unknown a priori but estimations about their remaining processing times are gradually revealed and refined. Online non-clairvoyant scheduling has been extensively studied in the literature. Recently, there has been a flurry of activities in online scheduling with predictions. Unlike these works, however, this paper studies the setup in which the scheduler starts with limited information although it is possible to get a better understanding via the means of progress bars. The paper considers three different progress bar models, for which efficient competitive algorithms are designed.

STRENGTHS AND WEAKNESSES:
Strengths
- This paper introduces a novel framework for online scheduling via the idea of progress bars. The framework is closely aligned with modern machine learning systems, where the decision-maker can obtain more refined information by analyzing more data sets. The paper proposes three models of progress bars, for which efficient algorithms have been devised. 
- The paper provides strong theoretical guarantees in terms of strong competitive ratios that depend on the parameters of progress bar models.
- Numerical experiments demonstrate the computational performance of the algorithms.

Weaknesses
- As opposed to non-clairvoyant scheduling with predictions, the framework of this paper seems qualitatively different. However, formal comparisons are missing.

QUESTIONS:
- Can the framework of progress bars incorporate recent online machine learning schemes, such as multi-armed bandits, scheduling with testing, and queuing bandits?
- Progress bars allow more flexibility in comparison with scheduling with predictions. Is it possible to compare them in a more formal way?

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-03