Forecast-Then-Optimize Deep Learning Methods

Ben Liu; Jinhang Jiang; Karthik Srinivasan; Mei Feng; Nan Wu; Xin Ji

REVIEW 4 major objections 6 minor 9 references

Forecast-Then-Optimize Deep Learning Methods

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A post-processing layer trained on historical forecast errors beat every raw deep-learning model and zero-shot foundation model tested on the M5 retail forecasting benchmark.

desk verdict A competent survey of forecast post-processing repackaged as 'FTO,' but the M5 case study does not fairly test the central claim that post-processing beats raw models. read the letter →

arxiv 2506.13036 v1 pith:KYU6IXRN submitted 2025-06-16 cs.LG

Jinhang Jiang , Nan Wu , Ben Liu , Mei Feng , Xin Ji , Karthik Srinivasan This is my paper

classification cs.LG

keywords forecast-then-optimizetimeseriesforecastingpost-processingensemblemethodsmeta-learningmodelselectionfoundationmodelsM5competition

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that Forecast-Then-Optimize (FTO) should be recognized as a distinct, high-leverage stage of forecasting pipelines: after a deep model produces a raw forecast, a separate post-processing step can refine it through ensembles, meta-learners, and uncertainty adjustments without altering the underlying model. It surveys the deep-learning forecasting literature from 2016 to 2025 and then runs an M5 retail benchmark with 30,490 SKUs to test the idea. The empirical claim is that post-adjustment methods that use historical forecasting performance, in particular TimeSpeaks with a simple linear network and a Direct Loss Estimator built on TimesFM, beat raw forecasts from advanced deep models and zero-shot foundation models on this task. If true, the practical consequence is that forecast accuracy can be improved more cheaply by optimizing outputs than by replacing or enlarging the forecasting model.

What carries the argument

The central object is the FTO post-processing layer: a model-agnostic stage that takes a pool of candidate forecasts and refines them with ensemble methods (mean, median, and quantile averaging; dynamic weighting and selection; Bayesian model averaging; hierarchical reconciliation), meta-learners (residual bias correction, Direct Loss Estimation, and model selection such as TimeSpeaks), and uncertainty adjustments (quantile forecasting and conformal prediction). The load-bearing assumption, stated by the paper, is that no matter how good finalized forecasts are, there is always room to squeeze out more accuracy. In the case study, the machinery is the M5 benchmark itself: 30,490 SKUs, ten rolling 28-day forecast windows, an input length of 56 days, and SMAPE and WRMSSE as evaluation metrics, with TimeSpeaks implemented as a fully connected linear network selecting among candidate models and DLE implemented with TimesFM as the residual predictor.

What would settle it

Rerun the M5 evaluation with outside variables included, large pretrained models fine-tuned, and TimeSpeaks using its original architecture; if any raw model then matches or beats TimeSpeaks-Linear's 30.55 SMAPE and 0.092 WRMSSE, the paper's central empirical claim would fail in that setting.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the optimization phase, not the forecasting architecture, is where the largest accuracy gains are available on a large-scale hierarchical forecasting task. On the M5 test set, TimeSpeaks-Linear reached SMAPE 30.55 and WRMSSE 0.092, DLE-TimesFM reached SMAPE 32.59 and WRMSSE 0.145, and BMA-Local reached SMAPE 36.46 and WRMSSE 0.175; among the raw models, the best was the simple NLinear at SMAPE 32.92 and WRMSSE 0.157, while the zero-shot foundation models TimesFM and Chronos landed at SMAPE 94.41/0.661 and 71.92/0.393. The paper reads these results as showing that post-adjustment techniques that exploit historical forecast performance can significantly outperform raw advanced-model forecasts, while also noting the gains are conditional: when one base model already dominates, as NLinear did, the value of post-processing shrinks.

Load-bearing premise

The benchmark conclusion rests on the assumption that the test setup is fair: the M5 dataset's outside variables were left out, the large pretrained models were used cold without fine-tuning, and TimeSpeaks was run with a simpler linear network than originally designed; if those choices handicapped some methods, the claim that post-processing beats raw deep and foundation models may not generalize.

Editorial extensions

If this is right

Teams that cannot retrain or replace a legacy forecasting model can still expect accuracy gains from adding a post-processing layer, because the optimization stage is model-agnostic.
On large heterogeneous series, learned model selection can beat averaging-based ensembles: TimeSpeaks-Linear outperformed BMA-Global by roughly 9 points of SMAPE, suggesting that choosing the right candidate per series is worth more than pooling all candidates.
Simple linear raw models remain strong: NLinear beat all complex deep models and some post-adjustment methods, so FTO comparisons should always include strong simple baselines.
Zero-shot foundation models without outside variables are not safe defaults for long-horizon hierarchical retail forecasting; their autoregressive decoding accumulates error over 28-day horizons.
The benefit of post-processing is conditional on candidate-model quality and diversity; the framework adds most value when several reasonably good models have comparable performance.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the benchmark result generalizes, model leaderboards that report only raw outputs may mis-rank forecasting methods; reporting raw and post-processed accuracy separately would separate architecture quality from output-refinement quality.
The same post-processing layer could be attached to a cheaper base model, so a strong residual learner or selector plus a lightweight raw model may match an expensive foundation model at lower inference cost; the paper's numbers suggest but do not test this substitution.
Rerunning the M5 comparison with outside variables enabled and large pretrained models fine-tuned would test the scope of the conclusion; if the gap narrows, the finding is specific to zero-shot, exogenous-free settings.
The success of TimeSpeaks implemented as a simple linear network suggests model-selection gains may not require elaborate selector architectures, which would make the method easier to deploy.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things. First, this is mostly a survey of existing forecast post-processing methods, including ensembles, bias correction, residual learning, and model selection, under the new label 'Forecast-Then-Optimize.' The survey itself is solid: it covers the deep learning forecasting literature from 2016 to 2025, organizes the post-processing landscape reasonably, and cites the important prior work, including the 50-year forecast combination review and the M4 competition. Second, the M5 case study is not a fair test of the paper's headline claim. The post-processing methods receive a pool of candidate forecasts and a fitted history of their errors, while the raw deep learning and foundation model baselines get default hyperparameters, zero-shot inference, and no exogenous variables, which are especially relevant for TFT and foundation models. There is also no simple mean or median ensemble baseline, even though the paper itself notes these usually beat single models. TimeSpeaks, the best performer, is the authors' own method and is implemented with a linear network instead of its original architecture, which makes the 'FTO works' conclusion look circular. And the results have no error bars or significance tests; Table 3 is also poorly formatted, with numbers running together in the text. What the paper does well is the survey. If you want a map of post-processing techniques and a quick overview of deep forecasting architectures, this is a reasonable starting point. The case study is a preliminary benchmark, not a definitive demonstration. The authors could fix the main problems by adding simple ensemble baselines, reporting uncertainty, and either using the original TimeSpeaks or dropping it entirely. They should also soften the claim that post-processing 'significantly outperforms' raw models, since the current setup handicaps one side. Who is this for? Practitioners in enterprise forecasting and researchers wanting a survey of post-processing methods. It is not a new method or theory paper. My recommendation: send it to peer review, because the survey has real value and the empirical section is salvageable with revisions. The benchmark result should be cited with caution, not as evidence for FTO's value as-is.

Referee Report

4 major / 6 minor

Summary. The paper defines a Forecast-Then-Optimize (FTO) framework as a two-phase methodology in which a forecasting stage is followed by an optimization/post-processing stage that refines raw forecasts through ensembles, meta-learners, and uncertainty adjustments. It surveys deep learning forecasting architectures from 2016 to 2025, reviews FTO methods and their rationale, and presents a case study on the M5 dataset comparing three FTO approaches (TimeSpeaks-Linear, DLE-TimesFM, BMA-Global, BMA-Local) against raw deep learning and foundation model baselines. The central empirical claim, stated in Section 5, is that post-adjustment techniques that leverage historical forecasting performance can significantly outperform raw forecasts from advanced deep learning or foundation models.

Significance. If the central claim were fully supported, the paper would make a useful contribution by systematizing an emerging class of post-processing methods and providing a practical demonstration that forecast refinement is a high-leverage component of operational forecasting pipelines. The survey is broad and generally accurate in its coverage of deep forecasting models and post-processing techniques, and the paper is explicit about several limitations in Section 6.2. The taxonomy separating ensembles, meta-learners, and uncertainty-aware methods, together with the M5 case study, gives practitioners a useful entry point. However, the empirical demonstration as presented is not yet convincing because the benchmark comparison is asymmetric, the headline FTO method is evaluated with a simplified architecture, and the reported results lack uncertainty quantification.

major comments (4)

[Section 5, Table 3] The benchmark does not isolate the contribution of the FTO machinery. Every post-adjustment method receives a pool of candidate forecasts plus a fitted history of their errors, while the raw deep-learning and foundation-model baselines receive none of that support: base-model hyperparameters are left at defaults, foundation models are evaluated zero-shot, and M5 exogenous variables are deliberately excluded. Section 3.3.1 itself notes that even equally weighted averages typically beat single models, yet Table 3 includes no mean or median ensemble baseline. Consequently, the TimeSpeaks result of 30.55 SMAPE and 0.092 WRMSSE cannot be attributed to the specific FTO mechanisms; a simple average of the same candidate pool might achieve comparable performance. The authors should add simple ensemble baselines and a controlled comparison in which raw models receive the same candidate-pool support or the FTO methods are restricted to the same information as the baselines.
[Section 5, TimeSpeaks implementation] Section 3.3.2 describes TimeSpeaks as a generative approach that uses a Transformer-based architecture to select forecasting models, but Section 5 states that 'for simplicity, we implemented TimeSpeaks with a fully connected linear network.' This substitution is load-bearing because TimeSpeaks is the headline FTO method and the paper's central empirical claim rests heavily on its performance. The manuscript provides no evidence that a linear network preserves the model-selection behavior of the original BiLSTM/Transformer implementation. The authors should either use the original TimeSpeaks architecture or validate and explicitly label the linear variant as a distinct simplified method whose results do not directly transfer to the published TimeSpeaks approach.
[Section 5, Table 3] The reported results have no error bars, confidence intervals, or significance tests. Table 3 presents a single set of numbers for each method, yet the text concludes that post-adjustment techniques 'can significantly outperform raw forecasts.' The experimental design involves ten sequential forecast windows, so per-window or repeated-run results could support paired significance tests or at least report variability. Without such evidence, 'significantly outperform' is not supported by the data shown. The authors should add standard errors, confidence intervals, or paired tests (e.g., Wilcoxon or Diebold-Mariano-type tests) across the evaluation windows.
[Section 5, exogenous variables and zero-shot baselines] The decision to exclude M5 exogenous variables is described as intentional, and this is reasonable for a controlled FTO benchmark. However, the subsequent conclusion that foundation models 'may struggle to generalize effectively for long horizon forecasting' is overgeneralized because Chronos and TimesFM are evaluated zero-shot and without covariates, while the FTO methods receive fitted error histories and a candidate pool. This asymmetry should be acknowledged in the concluding interpretation, or the experiment should include a variant where TFT and the foundation models receive the same exogenous inputs, so that the comparison speaks to the actual value of FTO rather than to the handicap of the baselines.

minor comments (6)

[Section 3.1] There is a typo in 'FTO eextends' that should read 'extends.'
[Table 3] The table formatting is broken for several entries, with values such as '59.2659.0867.4444.0494.41 71.92' lacking separators. The table needs a clean layout with distinct columns for each method.
[Section 3.1] The term 'Forecast-Then-Optimize' is used here to mean forecast post-processing, which differs from the standard Predict-Then-Optimize (PTO) meaning where forecasts are inputs to a decision optimization model. The paper should clarify this terminology early to avoid confusion with the SPO framework cited in Section 1.
[Section 4.1.1] There are typos and ungrammatical phrases, including 'Gated Recurrent Unity' (should be 'Unit') and 'Recent research has empirically validated Compared to transformer-based models,' which should be rewritten.
[Abstract and Section 4.2.5] The abstract claims that 'deep learning and large language models have established superiority over traditional parametric forecasting models for most enterprise applications,' but this is inconsistent with Section 3.2 and Section 4.2.5, which cite evidence that linear models can outperform transformers and that LLM-based forecasting has not delivered corresponding accuracy improvements. The framing should be reconciled.
[Section 6.3] There is a typo in 'domain adaption' which should be 'domain adaptation.'

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the FTO case study is a new benchmark on M5, and the self-cited TimeSpeaks component is not load-bearing.

full rationale

The paper's central empirical claim, that post-adjustment techniques leveraging historical forecasting performance can outperform raw deep learning and foundation model forecasts, is supported by a new case study on the M5 dataset rather than by a derivation that reduces to its inputs. The post-processing methods (BMA, DLE, TimeSpeaks) are fitted on historical windows and then evaluated on the M5 test set, as stated: 'For methods dependent on historical forecasting data, specifically BMA, DLE, and TimeSpeaks, forecasts were simulated across these historical windows to provide the requisite performance insights.' This is a train/validation/test split, not a fitted parameter being renamed as a prediction. The survey's broader FTO claims are grounded in external literature on forecast combinations and the M4/M5 competitions, including Makridakis et al. (2018) and X. Wang et al. (2022). The only self-referential component is TimeSpeaks, introduced in the authors' prior work (Jiang et al. 2025) and used as the headline FTO method in Table 3. However, the case study does not borrow the prior paper's numerical results; it computes new results with a simplified linear implementation. Thus the self-citation is not load-bearing for the empirical conclusion. Concerns about experimental fairness, such as excluding M5 exogenous variables, using zero-shot foundation models, keeping default hyperparameters, and omitting a simple ensemble baseline, are correctness or experimental-design risks rather than circularity. No equation or fitted value is shown to be equivalent by construction to an input, so the derivation chain is not circular.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The paper makes no formal derivation; its central empirical claim rests on a single benchmark. The ledger therefore lists the fitted models in the case study as free parameters and the representativeness/simplification assumptions as axioms. The conceptual label FTO is a re-framing of existing post-processing methods rather than an invented entity.

free parameters (3)

TimeSpeaks-linear model weights = not reported
Fitted on M5 historical windows to select among candidate forecasts; the case study's headline SMAPE 30.55 depends on this trained model.
TimesFM-based DLE residual model weights = not reported
A separate TimesFM model is fitted to predict the loss of each candidate model; its parameters are not disclosed.
BMA Local/Global per-SKU weights = not reported
Weights computed from historical forecast accuracy; no prior, regularization lambda, or weight values are given.

assumptions (3)

domain assumption M5 without exogenous variables is a representative operations-management forecasting benchmark.
The paper extrapolates from this single benchmark to broad claims about FTO's role in supply chain, healthcare, energy, and finance in Sections 5 and 6, even though M5's calendar and price covariates were deliberately removed.
ad hoc to paper The simplified TimeSpeaks-linear implementation preserves the behavior of the original BiLSTM/Transformer TimeSpeaks.
Section 5 states 'we implemented TimeSpeaks with a fully connected linear network'; no validation or ablation is given to show the simplification retains the method's model-selection capability.
domain assumption Keeping all base deep models at default hyperparameters yields fair baselines.
Section 5 says 'architecture-related parameters of each model was kept default'; without tuning, strong base models like NLinear may be underpowered, which directly affects the comparison between FTO methods and single models.

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Cite this review

Pith. "Pith review of Forecast-Then-Optimize Deep Learning Methods." pith.science (2026). https://pith.science/paper/KYU6IXRN

@misc{pith2026250613036,
  author       = {Pith},
  title        = {Pith review of: Forecast-Then-Optimize Deep Learning Methods},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KYU6IXRN}},
  note         = {Machine review of arXiv:2506.13036}
}

read the original abstract

Time series forecasting underpins vital decision-making across various sectors, yet raw predictions from sophisticated models often harbor systematic errors and biases. We examine the Forecast-Then-Optimize (FTO) framework, pioneering its systematic synopsis. Unlike conventional Predict-Then-Optimize (PTO) methods, FTO explicitly refines forecasts through optimization techniques such as ensemble methods, meta-learners, and uncertainty adjustments. Furthermore, deep learning and large language models have established superiority over traditional parametric forecasting models for most enterprise applications. This paper surveys significant advancements from 2016 to 2025, analyzing mainstream deep learning FTO architectures. Focusing on real-world applications in operations management, we demonstrate FTO's crucial role in enhancing predictive accuracy, robustness, and decision efficacy. Our study establishes foundational guidelines for future forecasting methodologies, bridging theory and operational practicality.

Figures

Figures reproduced from arXiv: 2506.13036 by the authors.

**Figure 1.** An illustration of the FTO Framework 3.2 Rationale Purely model-driven forecasts, even those utilizing advanced architectures like Transformers, often encounter challenges in effectively capturing complex temporal dependencies and inherent patterns in time series data. Recent studies have highlighted that simpler linear models can outperform these sophisticated models, particularly in long-term forecasting scenarios… view at source ↗

**Figure 2.** The Timeline of Select Deep Time Series Algorithms [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

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Reference graph

Works this paper leans on

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Reviewed August 7, 2026 · model on record in the stance chip above.

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Li S, Zhou Y, Yi J, Gall J (2021) Spatial-Temporal Consistency Network for Low-Latency Trajectory Forecasting. ICCV Li Y, Yu R, Shahabi C, Liu Y (2018) Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. 6th International Conference on Learning Representations, ICLR 2018 - Conference Track Proceedings Li Y, Zhang S, Hu R, Lu...

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Tedesco P, Rabault J, Sætra ML, Kristensen NM, Aarnes OJ, Breivik Ø, Mauritzen C, Sætra Ø (2023) Bias Correction of Operational Storm Surge Forecasts Using Neural Networks

Tang P, Zhang W (2024) Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting. Tedesco P, Rabault J, Sætra ML, Kristensen NM, Aarnes OJ, Breivik Ø, Mauritzen C, Sætra Ø (2023) Bias Correction of Operational Storm Surge Forecasts Using Neural Networks. Thomson ME, Pollock AC, Önkal D, Gönül MS (2019) Combining forecasts: Perfor...

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