Writing study: Differentiable Model Predictive Control on the GPU

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← ICLR 2026 oral writing corpus

Emre Adabag, Marcus Greiff, John Subosits, Thomas Lew · Official ICLR 2026 oral record

Observed writing choices, not acceptance rules. This study examines the inspected manuscript version. It does not establish why the paper was accepted or that its presentation choices should be copied unchanged.

Figure, table and section ledger

Editorial contribution type: Inference, algorithms & systems efficiency (primary).

Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.

Canonical PDF

19 physical pages

Before references / appendix

≈ 9.21 page-equivalents

Main figures / tables

8 / 0

Attached appendix figures / tables

6 / 6

Attached appendix span

≈ 6.89 page-equivalents

Before references / appendix: ≈ 48.47%References / intervening material: ≈ 15.26%Attached appendix: ≈ 36.26%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Section-by-section lengths and source pages

The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.

Top-level heading	Starts on PDF page	Estimated span	Share of entire PDF
1 INTRODUCTION	1	≈ 0.91 pp.	4.79%
2 BACKGROUND ON DIFFERENTIABLE OPTIMIZATION	2	≈ 1.37 pp.	7.21%
3 DIFFERENTIABLE MODEL PREDICTIVE CONTROL ON THE GPU	3	≈ 2.78 pp.	14.63%
4 RESULTS: FASTER SOLVES AND LEARNING ON THE GPU	6	≈ 1.25 pp.	6.58%
5 APPLICATION TO DOMAIN RANDOMIZATION FOR DRIVING AT THE LIMITS	7	≈ 1.81 pp.	9.53%
6 DISCUSSION AND LIMITATIONS	9	≈ 0.58 pp.	3.05%
REFERENCES	10	≈ 2.89 pp.	15.21%
APPENDIX	13	≈ 0.03 pp.	0.16%
A SOLVER: ADDITIONAL DETAILS	13	≈ 1.29 pp.	6.79%
B RESULTS: ADDITIONAL DETAILS AND EXPERIMENTS	14	≈ 5.57 pp.	29.32%

All detected figure and table locations

Main text

• Figure 1 · p. 3
• Figure 2 · p. 6
• Figure 3 · p. 7
• Figure 4 · p. 7
• Figure 5 · p. 8
• Figure 6 · p. 8
• Figure 7 · p. 9
• Figure 8 · p. 9

Attached appendix

• Table 1 · p. 14
• Figure 10 · p. 15
• Table 2 · p. 15
• Figure 9 · p. 15
• Table 3 · p. 16
• Table 4 · p. 16
• Table 5 · p. 17
• Table 6 · p. 18
• Figure 11 · p. 18
• Figure 13 · p. 19
• Figure 12 · p. 19
• Figure 8 · p. 19

Argument and organization

1. Computational bottleneck and differentiation primer

   Explain the sequential-versus-parallel mismatch and establish forward/backward optimization roles.

2. Structure-exploiting GPU solver

   Derive SQP, implicit sensitivities, Schur systems and reusable PCG computations.

3. Microbenchmarks, learning and vehicle case study

   Escalate evidence from controlled timing to training utility and physical deployment.

Problem, claim and contribution

The introduction names a hardware-algorithm mismatch rather than claiming a generic faster optimizer. Related work separates general-purpose GPU solvers from structure-aware MPC solvers, locating the contribution at their intersection.

Sections 1–2.1, pp. 1–2. · Main paper

Argument and section order

A short implicit-differentiation primer precedes separate forward, backward and linear-system sections. The same KKT system recurs in both passes, making computation reuse a consequence of the derivation.

Sections 2.2–3.4, pp. 3–5. · Main paper

Figures, captions and visual explanation

Figure 2 places a forward/backward data-flow diagram beside two algorithms with equation cross-references. Blue/red boundaries distinguish passes, and the matrices carried between them make memory reuse visible.

Figure 2 and Algorithms 1–2, p. 6. · Main paper

Tables, comparisons and evidence

Figure 3 labels CPU/GPU and forward/backward costs separately, and its caption states that backward timings include a forward pass. Figure 4 retains convergence curves alongside the speed claim, avoiding speed-only evaluation.

Figures 3–4, p. 7. · Main paper

Appendix and reproducibility

Appendix B explains fairness-oriented baseline modifications, precision and hardware, then gives randomization distributions and controller parameters. It explicitly admits that the figure-eight hardware comparison had only one run per method.

Appendix B.1, pp. 14–16; B.3, pp. 17–19. · Main paper

What to reuse—and what not to infer

Transferable lesson: Connect a speed claim to an identifiable computational bottleneck, display what is reused, and show both controlled runtime and downstream solution quality.

Boundary: DiffMPC ignores dynamics curvature in its sensitivities, so gradients can be approximate. The physical vehicle uses OSQP rather than the training PCG solver; inequality constraints are not handled as hard constraints in the proposed MPC formulation. Single-run hardware results are illustrative, and the appendix's assertion that a JVP inherently requires a full Jacobian is too broad.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-09-19

Reading status

Full text + selected visuals inspected

Main text

Sections 1–6 and reproducibility statement, pp. 1–10; references pp. 10–12.

Appendix / supplement

Appendices A.1–A.3 and B.1–B.3, pp. 13–19: differentiation, PCG/line-search algorithms, benchmark modifications, dynamics, training and hardware details.

Visually inspected PDF pages

6, 7

• ICLR 2026 official proceedings PDF, retrieved 2026-09-19 · 19 pages