✗ Failed on benchmark 2026

Differentiable Profit-Ordering Loss

Implementation & benchmark of arXiv:2608.08377 — Price Information Is Not Enough: Ordering and Decision Rules in Storage Bidding

Usefulness8/10

Difficulty5/10

Novelty5/10

Training Accuracy Sample efficiency Generalization Optimizer Loss Training dynamics Rl Optimization Statistics Control theory

Source paper: Price Information Is Not Enough: Ordering and Decision Rules in Storage Bidding arXiv:2608.08377 ⓘ · analyzed Sep 1, 2026

AI-generated research hypothesis, automatically tested. Not peer-reviewed.

Idea description

Train a neural forecaster or policy network to preserve the pairwise ordering that determines profitable charge and discharge decisions, rather than optimizing only pointwise forecast error. Combine a conventional prediction loss with a pairwise ranking loss weighted by the economic price gap, then pass the prediction through a feasibility-aware storage scheduler.

Formulas

$$J(g,S)=E[⟨g(S,C),Π⟩], ⟨x,Π⟩=Σₜ xₜπₜ, x∈X$$

$$yᵢⱼ=sign(πᵢ−πⱼ), mᵢⱼ=π̂ᵢ−π̂ⱼ, wᵢⱼ=|πᵢ−πⱼ|$$

$$Lrank(θ)=(1/|P|)Σ₍ᵢ,ⱼ₎∈P wᵢⱼ log(1+exp(−yᵢⱼ(π̂ᵢ−π̂ⱼ)/τ))$$

$$L(θ)=Lforecast(θ)+λLrank(θ)$$

Mathematical statement

Let Π = (π₁,...,πₙ) be the true price vector, C be observed context, S be an information signal, and Π̂ = fθ(C,S) be the neural prediction. Let x = g(Π̂,C) belong to the feasible schedule set X. Revenue is J = ⟨x,Π⟩ = Σₜ xₜπₜ. For each time pair (i,j), define the true ordering label yᵢⱼ = sign(πᵢ − πⱼ), predicted margin mᵢⱼ = π̂ᵢ − π̂ⱼ, and economic weight wᵢⱼ = |πᵢ − πⱼ|. The weighted logistic ranking loss is Lrank = (1/|P|) Σᵢⱼ wᵢⱼ log(1 + exp(−yᵢⱼmᵢⱼ/τ)), where P is the sampled pair set and τ > 0 is a temperature. The combined objective L = Lforecast + λLrank makes mistakes on large price gaps more expensive. The paper predicts that realized schedule revenue should correlate more strongly with ordering agreement than with MSE.

Implementation notes

Use a day-ahead price forecaster whose output is consumed by a deterministic storage scheduler. The network receives context and history, outputs n predicted prices, and the scheduler computes a feasible schedule using a linear program or differentiable optimization layer. For every training day, construct all pairs when n is small, or sample pairs containing the largest price gaps and pairs near the predicted charge/discharge threshold. Compute yᵢⱼ, wᵢⱼ, and the predicted margin, then optimize the stated loss. Pseudocode: pred = net(context); pairs = sample_pairs(price); y = sign(price[i]-price[j]); w = abs(price[i]-price[j]); rank = mean(w * softplus(-y * (pred[i]-pred[j]) / tau)); loss = mse(pred, price) + lambda * rank; loss.backward(); optimizer.step(). The paper supplies the ordering mechanism and predicts that rank agreement is economically dominant; estimate λ, τ, and scheduler gradient treatment empirically. First test an MLP and a small Transformer on the 939 French day-ahead days, with MSE training as baseline and identical storage simulation for all methods. Measure RMSE, Kendall rank correlation, pairwise agreement, and feasible revenue uplift. The quantitative signature is that revenue should be explained more strongly by rank agreement than by MSE; in a controlled ordering sweep, target the paper’s reported rank-agreement R² of approximately 0.99 versus 0.34 for the information-bound proxy.

Verification

Failed on benchmark

Stage 1 · Toy mechanism gate: Passed ✓

Stage 2 · Mechanism transferred to benchmark: Not reproduced ✗

Stage 2 · Practical benchmark result: No measurable effect

Methodology: 0 paired seeds, permutation test (p<0.05) against a learning-rate-tuned baseline. How verification works

Stage 1 — Mechanism check agent confidence 8/10

Built a weighted pairwise logistic ranking loss, synthetic MLP forecaster, and deterministic feasible storage scheduler in run_experiment.py. The mechanism checks passed: the zero-margin gradient and equal-margin loss both scaled 8.0x for an 8.0x economic gap, while the rank-gradient contribution scaled linearly with lambda and was exactly zero at lambda=0. In the mini experiment, ranking slightly improved pairwise agreement (0.9071 vs 0.9056) but produced identical revenue and slightly worse RMSE, so there is no demonstrated economic win in this setup.

Agent confidence: 8/10

Baseline: MSE: RMSE 0.24305, pairwise agreement 0.90556, mean feasible revenue 1.73007
Idea: MSE + weighted ranking (lambda=0.15): RMSE 0.24397, pairwise agreement 0.90707, mean feasible revenue 1.73007; toy gap-gradient ratio 8.0 predicted/observed and loss ratio 8.0 predicted/observed

Limitations: This is a synthetic 240-day benchmark rather than the 939-day French dataset; the scheduler is greedy rather than an LP or differentiable optimization layer, and only one ranking weight and temperature were used in the neural comparison. The toy lambda sweep verifies gradient scaling, not a guaranteed monotonic trained-ordering improvement.

How to run: python3 run_experiment.py

Stage 2 — Benchmark vs. tuned baseline (arXiv:2608.08377) Sep 2, 2026

No significant difference vs. the tuned baseline (0 metric points, p=1, wins 0 / 0 paired seeds).

Benchmark: Multihorizon_sequence
Model: transformer_tiny
Paired seeds: 0
Baseline mean: 0
Idea mean: 0
Effect (Δ): 0 (n/a; negative = idea better)
Wins: 0 / 0 paired seeds
p-value: 1 (permutation test, 20 000 shuffles)
Smallest detectable effect: n/a
Mechanism: Not confirmed ✗
Practical effect: No effect
Baseline tuning: swept over 0 configs

Limitations:

The full paired 8-seed protocol, baseline sweep, final comparison, and neural mechanism signature were not completed because the shared environment repeatedly terminated the run. The script uses the existing multihorizon_sequence custom track rather than the unavailable original French price dataset, and no storage scheduler revenue metric was evaluated in this bench round.

How to run: python3 bench_experiment.py

Verdict computed by deterministic test code from paired-seed statistics — not by the language model.

Stage 2 — Benchmark Sep 1, 2026 latest Failed ✗

Agent confidence: 10/10

Built a local weighted pairwise logistic ranking-loss intervention for the structurally matched multihorizon sequence task using identical transformer_tiny systems. The script includes the economic-gap math sanity check, shared learning-rate union, baseline sweep, 8-seed idea evaluation, and trained-model ordering signature, but execution timed out or was externally terminated before bench_report.json was produced. No Stage-2 effect is established.

Baseline: not available: baseline sweep did not complete
Idea: not available: paired 8-seed idea evaluation did not complete

Benchmark result