Pith. sign in

REVIEW 5 major objections 6 minor 2 cited by

Online Aggregation of Trajectory Predictors

T0 review · 5 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read A live probability vector blends trajectory predictors into a mixture that matches or beats every single model.

desk verdict Solid, clearly written application of SQUINT to trajectory predictor aggregation, but the headline regret guarantee applies to a clipped surrogate loss, not the stated loss; empirics are suggestive but under-supported. read the letter →

arxiv 2502.07178 v1 pith:JVBTONXJ submitted 2025-02-11 cs.RO

Alex Tong , Apoorva Sharma , Sushant Veer , Marco Pavone , Heng Yang This is my paper · ORCID
classification cs.RO
keywords trajectorypredictionmixtureofexpertsonlineconvexoptimizationregretminimizationSQUINTdistributionshiftautonomousdrivingexpertaggregation
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

The paper proposes that any set of trajectory predictors—neural or rule-based, trained on any data—can be treated as black-box experts and combined by a probability vector updated online with each newly observed agent state. The authors show that running the SQUINT algorithm on a loss that scores how well the current mixture predicts the revealed state yields sublinear regret in stationary environments, so the mixture converges to the best single predictor in hindsight. They extend the same update rule to a nonconvex top-$k$ displacement-error loss through differentiable surrogates, and to nonstationary environments through a discount factor. On NUSCENES city splits and the Lyft dataset, the mixture performs as well as or better than every individual model, including under out-of-distribution deployment. The significance would be a lightweight, model-agnostic route to robustness against distribution shift without retraining or data fusion.

What carries the argument

The load-bearing object is the probability vector $\alpha \in \Delta^N$ that mixes the experts' Gaussian mixture outputs into a single GMM. The update law is SQUINT: it maintains cumulative regret $R_t$ and cumulative squared regret $V_t$ relative to each expert, clips the per-round gradients with the Cutkosky rule, and reweights $\alpha$ through the potential function $\xi(R, V)$, which acts like Bayes' rule with second-order evidence. Because the per-round loss $-p(x_t \mid \Gamma(\alpha_t))$ is linear in $\alpha$, expert hedging theory applies directly, and the discount factor $\lambda$ in $R_{t+1} = \lambda R_t + r_t$, $V_{t+1} = \lambda^2 V_t + r_t \circ r_t$ adapts the same machinery to shifting environments.

What would settle it

On a held-out city split, run SQUINT with the convex probability loss, then compute the cumulative regret using the full $K$-step minADE loss instead of the one-step density; if the regret grows linearly in $T$ or the mixture fails to match the best expert on minADE$_K$, the convergence claim is falsified.

Watch

Extended reading notes

Core claim

The central claim is that online aggregation turns a collection of imperfect trajectory predictors into a mixture that is no worse than the best member, and can beat it by hedging. Given $N$ predictors that output Gaussian mixture models, the learner maintains weights $\alpha \in \Delta^N$ and at each round forms the mixture-of-experts GMM $\Gamma(\alpha)$; the true next state $x_t$ defines the loss $\ell_t(\alpha_t) = -p(x_t \mid \Gamma(\alpha_t))$, which is linear in $\alpha$, so hedging algorithms apply. SQUINT, a second-order expert-hedging algorithm with gradient clipping, gives sublinear regret, and since the loss is linear the optimal fixed comparator is one-hot, implying convergence to the best expert in hindsight. For the nonconvex minFRDE$_k$ metric, softsort and softmin make the top-$k$ selection differentiable and the same update runs; for nonstationary shifts, a discount factor on cumulative regret and regret-squared lets the weights forget stale evidence. In experiments the authors report that the mixture matches or outperforms every singular expert and, under repeated shifts, tracks the best expert in each window.

Load-bearing premise

The update rule scores only the next observed state $x_t \in \mathbb{R}^3$, while the reported metrics score full $K$-step trajectories; the paper does not specify how these connect, so the sublinear-regret guarantee may cover one-step density prediction rather than the headline trajectory errors.

Editorial extensions

If this is right

  • On the Pittsburgh split, the weights converge to the Boston-trained model, the best expert in hindsight, and the mixture's NLL and minADE approach those of an oracle model trained on Pittsburgh.
  • On the Lyft dataset, where all learned models degrade, including a rule-based expert through the nonconvex minFRDE$_k$ loss lets the mixture swing its weight to the rule-based predictor and stay competitive.
  • Under three sequential distribution shifts, discounted SQUINT re-converges to the best expert in each window without being told when a shift occurs.
  • Because the optimal fixed weight vector is one-hot, matching the best expert in hindsight is the best the stationary guarantee can promise; observed better-than-singular performance comes from the weights shifting over time.
  • The framework also extends to experts that output arbitrary sampleable distributions, by defining a linear loss on sampled trajectories and forming the mixture through importance sampling.

Reading between the lines

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

  • A testable extension is to feed the full $K$-step ground-truth trajectory into the update loss; if the regret guarantee then transfers to minADE and minFDE, the gap between the one-step update and the reported trajectory metrics would close.
  • The same aggregation scheme could apply to other sequential forecasting tasks—pedestrian intent, energy demand, weather—wherever a stream of ground-truth observations arrives and multiple black-box predictors are available.
  • The discount factor $\lambda$ is fixed in the experiments; a meta-learner that tunes $\lambda$ online from the observed shift frequency would likely make the nonstationary variant adaptive to unknown shift rates.
  • The paper assumes the expert pool is fixed; allowing experts to be added or retrained over time would turn the mixture into a lifelong learner, but would need a regret analysis against a time-varying comparator.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 6 minor

Summary. This paper proposes an online aggregation framework for trajectory prediction in which each trajectory predictor is treated as a black-box expert and a probability vector alpha_t mixes their outputs. The weights are updated online using the SQUINT algorithm with Cutkosky clipping, driven by the negative probability of the observed true state under the mixture (Eq. (5)). The authors claim that in a stationary environment SQUINT guarantees sublinear regret and convergence to the best expert in hindsight, and they propose heuristics for nonconvex minFRDE_k losses (via softsort/softmin) and for nonstationary environments (via a discount factor). Experiments on NuPlan/NUSCENES city splits and the LYFT dataset show that the mixture tracks or outperforms singular models on NLL, minADE, and minFDE metrics.

Significance. The online aggregation idea is appealing: it is model-agnostic, lightweight, and grounded in a mature online-learning literature. If the guarantees were established as stated, the method would be a practically useful tool for OOD robustness in trajectory prediction. The paper also provides a clear pseudocode implementation and a thoughtful discussion of the practical need for second-order updates. However, the central theoretical claim is currently overstated: the regret guarantee applies to a clipped surrogate objective rather than the original loss, and sublinear regret does not by itself imply weight convergence. The experimental evidence is suggestive but incomplete due to missing baselines and error bars. With careful revision, the core idea may still stand.

major comments (5)
  1. [Section III-B, Algorithm 1 (lines 3-4)] The sublinear-regret guarantee of SQUINT applies to the clipped loss vectors g_t = (g̃_t/G_t + 1)/2, not to the original losses ℓ_t defined in Eq. (5). Because G_t is time-varying, the cumulative clipped loss for expert i equals Σ_t (g̃_{t,i}/G_t + 1/2), an unequally weighted version of the original cumulative loss; early rounds receive larger weight. Consequently, the 'best expert in hindsight' under the clipped objective can differ from the best expert under Eq. (5), and the conclusion that 'SQUINT guarantees convergence to the best expert in hindsight' is not established. Please either prove a regret bound for the original losses under this clipping scheme, replace the time-varying normalizer with a fixed bound (if one exists), or clearly state that the guarantee is only for the clipped surrogate objective.
  2. [Section III-B (Eq. (5)) versus Section IV (performance metrics)] The update loss in Eq. (5) is computed from a single true state x_t ∈ R^3 revealed at time t, while the headline evaluation metrics minADE_k, minFDE_k, and trajectory NLL are defined over K-step future trajectories using ground-truth states x_t(τ), τ = 1,...,K. The manuscript never specifies how x_t relates to the K-step ground truth, so the sublinear-regret guarantee covers one-step density prediction only and does not cover the K-step trajectory metrics reported in Section IV. This temporal mismatch is load-bearing because the experimental claims are about those K-step metrics. Please clarify the relationship between x_t and x_t(τ), and either extend the analysis to K-step losses or discuss the limitation explicitly.
  3. [Section IV (Experiments)] The empirical claim that the MoE 'performs on par or better than any singular model' is not supported by the current experimental protocol. There are no error bars or multiple seeds, and no comparison to a simple baseline such as uniform weighting (α_t = 1/N) or exponentiated gradient with a tuned step size. The comparison to an 'oracle' model trained on the target city is welcome, but it does not replace a statistical comparison to natural baselines. Please add repeated trials with confidence bands and include at least a uniform-mixture baseline.
  4. [Section IV and Appendix B (dataset naming)] The abstract and the main text refer to the 'NUSCENES dataset', but the experimental section says the predictors are trained on location-based subsets of the training split of the 'NuPlan dataset [45]', and Appendix B refers to 'nuplan_mini-pittsburgh dataset from NUSCENES'. NuPlan and NUSCENES are distinct datasets with different references; this appears to be a factual error that affects reproducibility. Please correct the dataset names and references throughout.
  5. [Section III-B (conclusion after Eq. (7))] The statement that SQUINT 'guarantees convergence to the best expert in hindsight' does not follow from sublinear regret. Sublinear regret compares cumulative losses and does not imply that the probability vector α_t converges to a one-hot vector, which is the sense of 'convergence' used in the empirical weight plots of Section IV-A. Please rephrase the theoretical claim as a sublinear-regret guarantee and treat weight convergence as an empirical observation (or provide a separate proof under additional assumptions).
minor comments (6)
  1. [Section III-A] The notation x_t is introduced as a single state in R^3, but the metrics in Section IV use x_t(τ) for τ = 1,...,K; please define both notations explicitly and avoid the overloaded use of x_t.
  2. [Section IV-A, Fig. 2(a)] The figure appears to contain duplicate panels (two identical NLL curves and two identical minADE curves); please check and replace with the intended distinct plots.
  3. [Algorithm 1] The initialization of G_t is not defined; please specify G_0 (e.g., G_0 = 0) so that the clipping step is well-defined for t = 1.
  4. [Appendix A] The claim that SQUINT converges 'approximately 25 times faster' than EG is not quantified; please state the criterion used (e.g., time to reach within ε of the final weight) and report the exact ratio.
  5. [Abstract and Section IV-A] The abstract's unqualified claim that the method performs 'just as well, if not better than, any singular model' is contradicted by the nonconvex NLL result in Section IV-A, where the MoE is slightly worse than the Boston and Singapore models; please qualify the claim accordingly.
  6. [Section V (Limitations)] The limitation list does not mention the temporal mismatch between the one-step update loss and the K-step evaluation metrics, nor the surrogate nature of the clipped objective in Algorithm 1; please add these caveats.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the per-round loss is computed from observed ground truth, the regret guarantee is imported from an external theorem, and the headline comparisons are against singular models and an oracle, not fitted constants.

full rationale

The derivation chain is self-contained in the sense that matters for circularity. The per-round loss ℓ_t (Eq. 5) is evaluated at the revealed true state x_t, and the gradient (Eq. 6) measures each expert's predictive density; neither is defined in terms of the weights α_t being 'predicted.' The update (Algorithm 1) is the published SQUINT rule [15] with Cutkosky clipping [16], both external works, and the paper's claim of sublinear regret and convergence to the best expert in hindsight is a direct reading of the regret definition (1) via an external theorem, not a restatement of a fitted parameter. The headline empirical claims are benchmarked against the singular experts and an oracle (Oracle Pittsburgh), so 'on par or better' is falsifiable and not forced by construction; the MoE's NLL can beat every expert through the mixture effect, which is an empirical finding rather than a tautology. The only self-citations ([18] discount trick; [20], [31] rule-based predictor) are to published external works used as design inspiration or baselines, and the nonstationary section makes empirical rather than theoretical claims, so the citation is not load-bearing in a circular way. The weaker points — that Algorithm 1's clipped gradient sequence g_t differs from the loss-gradient sequence to which the regret bound is nominally attached, and that the update loss uses a single next state x_t while evaluation uses K-step trajectories — are rigor/transfer gaps, not circular reductions, and per the review rules they do not raise the circularity score.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard OCO theory (the SQUINT regret bound), the assumption that true states are revealed online, and two hand-built heuristics (softsort/softmin surrogates and discounted regret). The free hyperparameters beta, lambda, and k are selected without sensitivity analysis, and the sliding window lengths shape the reported curves.

free parameters (4)
  • softmin temperature beta = 10
    Set in Appendix B for the smooth approximation of the minFRDE_k loss; no sensitivity analysis is reported.
  • discount factor lambda = 0.9999
    Set in Appendix B for the nonstationary discounted SQUINT; controls the effective memory of past losses and is not swept.
  • top-k mode count k = 10
    Set in Appendix B for the minFRDE_k, minADE_k, and minFDE_k metrics and the softsort surrogate; no sensitivity analysis is reported.
  • sliding window lengths for metric averaging = 500 (stationary), 5000 (nonstationary)
    Used in Section IV to smooth performance curves; chosen for visualization and could affect reported trends.
assumptions (6)
  • standard math SQUINT attains sublinear regret against the best expert for bounded losses (Theorem 4 of [15]).
    Section III-B invokes this theorem to claim convergence to the best expert in hindsight.
  • domain assumption The expert GMM parameters (p, mu, Sigma) are fixed when updating alpha; only alpha changes.
    Section III-A/B defines the MoE with fixed expert distributions per round; the gradient in (6) treats them as constants.
  • domain assumption The true agent state x_t is revealed each round before the next alpha update.
    Section III-B sets up the OCO game with x_t revealed online; this is essential for the loss (5) and the claimed online adaptation.
  • standard math Gradient clipping via Cutkosky preserves the hedging or regret guarantees.
    Algorithm 1 lines 3-4 cite [16]; the paper relies on this to keep losses bounded for SQUINT.
  • ad hoc to paper Softsort and softmin surrogates provide practically useful gradients for the nonsmooth minFRDE_k loss.
    Section III-C introduces these surrogates to apply SQUINT to a nonconvex, nonsmooth objective; no regret guarantee is given.
  • ad hoc to paper The discounted update (11) converts a stationary online learner into a nonstationary one.
    Section III-D borrows a result from [18] and applies it to SQUINT as a heuristic; no theoretical analysis specific to this setting is provided.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Online Aggregation of Trajectory Predictors." pith.science (2026). https://pith.science/paper/JVBTONXJ

@misc{pith2026250207178,
  author       = {Pith},
  title        = {Pith review of: Online Aggregation of Trajectory Predictors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JVBTONXJ}},
  note         = {Machine review of arXiv:2502.07178}
}
read the original abstract

Trajectory prediction, the task of forecasting future agent behavior from past data, is central to safe and efficient autonomous driving. A diverse set of methods (e.g., rule-based or learned with different architectures and datasets) have been proposed, yet it is often the case that the performance of these methods is sensitive to the deployment environment (e.g., how well the design rules model the environment, or how accurately the test data match the training data). Building upon the principled theory of online convex optimization but also going beyond convexity and stationarity, we present a lightweight and model-agnostic method to aggregate different trajectory predictors online. We propose treating each individual trajectory predictor as an "expert" and maintaining a probability vector to mix the outputs of different experts. Then, the key technical approach lies in leveraging online data -- the true agent behavior to be revealed at the next timestep -- to form a convex-or-nonconvex, stationary-or-dynamic loss function whose gradient steers the probability vector towards choosing the best mixture of experts. We instantiate this method to aggregate trajectory predictors trained on different cities in the NUSCENES dataset and show that it performs just as well, if not better than, any singular model, even when deployed on the out-of-distribution LYFT dataset.

Figures

Figures reproduced from arXiv: 2502.07178 by the authors.

Figure 1
Figure 1. Online aggregation of trajectory predictors. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Performance of MoE in a stationary distribution shift [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Performance of MoE in nonstationary distribution [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (3 more)
Figure 6
Figure 6. Figure 6: More results on the performance of MoE in a [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 5
Figure 5. Figure 5: shows the evolution of the probability vector αt over time for (a) EG and (b) SQUINT. Notably, SQUINT converges approximately 25 times faster than EG, demonstrating a significant improvement in adaptation speed. 0 5000 10000 15000 20000 25000 Timesteps 0.1 0.2 0.3 0.4 …
Figure 7
Figure 7. Figure 7: minFDE performance metric in a nonstationary [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Self-Adaptive Learning and Model Predictive Control for Tracking Unknown Dynamics with No Regret

    cs.RO 2026-07 conditional novelty 6.0 of 10

    A self-adaptive MPC with multiple online-learned RFF predictors and Hedge-based selection achieves O(T^{3/4}) expected regret for tracking unknown, switching target dynamics.

  2. GEMINUS: Dual-aware Global and Scene-Adaptive Mixture-of-Experts for End-to-End Autonomous Driving

    cs.CV 2025-07 conditional novelty 5.0 of 10

    GEMINUS reports state-of-the-art closed-loop driving scores on Bench2Drive with a monocular camera by routing each situation to either a global expert or a scene-specialized expert based on scenario confidence.

Reference graph

Works this paper leans on

47 extracted references · 35 canonical work pages · cited by 2 Pith papers

  1. [45]

    Nuplan: A closed-loop ml- based planning benchmark for autonomous vehicles,

    H. Caesar, J. Kabzan, K. S. Tan, W. K. Fong, E. Wolff, A. Lang, L. Fletcher, O. Beijbom, and S. Omari, “Nuplan: A closed-loop ml- based planning benchmark for autonomous vehicles,” 2022

    work page 2022

  2. [1]

    Liability, ethics, and culture-aware behavior specification using rulebooks,

    A. Censi, K. Slutsky, T. Wongpiromsarn, D. Yershov, S. Pendleton, J. Fu, and E. Frazzoli, “Liability, ethics, and culture-aware behavior specification using rulebooks,” in 2019 International Conference on Robotics and Automation (ICRA) . IEEE, 2019, pp. 8536–8542

    work page 2019

  3. [2]

    Receding horizon planning with rule hierarchies for autonomous vehicles,

    S. Veer, K. Leung, R. K. Cosner, Y . Chen, P. Karkus, and M. Pavone, “Receding horizon planning with rule hierarchies for autonomous vehicles,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2023, pp. 1507–1513

    work page 2023

  4. [3]

    The reasonable crowd: Towards evidence-based and interpretable models of driving behavior,

    B. Helou, A. Dusi, A. Collin, N. Mehdipour, Z. Chen, C. Lizarazo, C. Belta, T. Wongpiromsarn, R. D. Tebbens, and O. Beijbom, “The reasonable crowd: Towards evidence-based and interpretable models of driving behavior,” in 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) . IEEE, 2021, pp. 6708–6715

    work page 2021

  5. [4]

    Tra- jectron++: Dynamically-feasible trajectory forecasting with hetero- geneous data,

    T. Salzmann, B. Ivanovic, P. Chakravarty, and M. Pavone, “Tra- jectron++: Dynamically-feasible trajectory forecasting with hetero- geneous data,” in European Conf. on Computer Vision (ECCV) . Springer, 2020, pp. 683–700

    work page 2020

  6. [5]

    Scept: Scene-consistent, policy- based trajectory predictions for planning,

    Y . Chen, B. Ivanovic, and M. Pavone, “Scept: Scene-consistent, policy- based trajectory predictions for planning,” in IEEE Conf. on Computer Vision and Pattern Recognition (CVPR) , 2022, pp. 17 103–17 112

    work page 2022

  7. [6]

    Agentformer: Agent- aware transformers for socio-temporal multi-agent forecasting,

    Y . Yuan, X. Weng, Y . Ou, and K. M. Kitani, “Agentformer: Agent- aware transformers for socio-temporal multi-agent forecasting,” in Proceedings of the IEEE/CVF International Conference on Computer Vision, 2021, pp. 9813–9823

    work page 2021

  8. [7]

    On the opportunities and risks of foundation models,

    R. Bommasani, D. A. Hudson, E. Adeli, R. Altman, S. Arora, S. von Arx, M. S. Bernstein, J. Bohg, A. Bosselut, E. Brunskill et al. , “On the opportunities and risks of foundation models,” arXiv preprint arXiv:2108.07258, 2021

    arXiv 2021

Show all 47 references
  1. [8]

    Decodingtrust: A compre- hensive assessment of trustworthiness in gpt models,

    B. Wang, W. Chen, H. Pei, C. Xie, M. Kang, C. Zhang, C. Xu, Z. Xiong, R. Dutta, R. Schaeffer et al. , “Decodingtrust: A compre- hensive assessment of trustworthiness in gpt models,” arXiv preprint arXiv:2306.11698, 2023

    2023 arXiv

  2. [9]

    On the out of distribution robustness of foundation models in medical image segmentation,

    D. M. H. Nguyen, T. N. Pham, N. T. Diep, N. Q. Phan, Q. Pham, V . Tong, B. T. Nguyen, N. H. Le, N. Ho, P. Xie et al. , “On the out of distribution robustness of foundation models in medical image segmentation,” arXiv preprint arXiv:2311.11096 , 2023

    2023 arXiv

  3. [10]

    A survey on hallucination in large vision-language models,

    H. Liu, W. Xue, Y . Chen, D. Chen, X. Zhao, K. Wang, L. Hou, R. Li, and W. Peng, “A survey on hallucination in large vision-language models,” arXiv preprint arXiv:2402.00253 , 2024

    2024 arXiv

  4. [11]

    A brief introduction to boosting,

    R. E. Schapire et al. , “A brief introduction to boosting,” in Ijcai, vol. 99, no. 999. Citeseer, 1999, pp. 1401–1406

    1999

  5. [12]

    An introduction to boosting and leveraging,

    R. Meir and G. Rätsch, “An introduction to boosting and leveraging,” in Advanced Lectures on Machine Learning: Machine Learning Sum- mer School 2002 Canberra, Australia, February 11–22, 2002 Revised Lectures. Springer, 2003, pp. 118–183

    2002

  6. [13]

    A modern introduction to online learning,

    F. Orabona, “A modern introduction to online learning,” arXiv preprint arXiv:1912.13213, 2019

    1912 arXiv

  7. [14]

    Improving adaptive online learning using refined discretization,

    Z. Zhang, H. Yang, A. Cutkosky, and I. C. Paschalidis, “Improving adaptive online learning using refined discretization,” in International Conference on Algorithmic Learning Theory . PMLR, 2024, pp. 1208– 1233

    2024

  8. [15]

    Second-order quantile methods for experts and combinatorial games,

    W. M. Koolen and T. van Erven, “Second-order quantile methods for experts and combinatorial games,” 2015

    2015

  9. [16]

    Artificial constraints and lipschitz hints for uncon- strained online learning,

    A. Cutkosky, “Artificial constraints and lipschitz hints for uncon- strained online learning,” arXiv preprint arXiv:1902.09013 , 2019

    1902 arXiv

  10. [17]

    Stochastic optimiza- tion of sorting networks via continuous relaxations,

    A. Grover, E. Wang, A. Zweig, and S. Ermon, “Stochastic optimiza- tion of sorting networks via continuous relaxations,” arXiv preprint arXiv:1903.08850, 2019

    1903 arXiv

  11. [18]

    Discounted adaptive online learning: Towards better regularization,

    Z. Zhang, D. Bombara, and H. Yang, “Discounted adaptive online learning: Towards better regularization,” in Intl. Conf. on Machine Learning (ICML) , 2024

    2024

  12. [19]

    nuscenes: A multimodal dataset for autonomous driving,

    H. Caesar, V . Bankiti, A. H. Lang, S. V ora, V . E. Liong, Q. Xu, A. Krishnan, Y . Pan, G. Baldan, and O. Beijbom, “nuscenes: A multimodal dataset for autonomous driving,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , 2020, pp. 11 621–11 631

    2020

  13. [20]

    Multi-predictor fusion: Combin- ing learning-based and rule-based trajectory predictors,

    S. Veer, A. Sharma, and M. Pavone, “Multi-predictor fusion: Combin- ing learning-based and rule-based trajectory predictors,” in Conference on Robot Learning (CoRL) , 2023

    2023

  14. [21]

    One thousand and one hours: Self-driving motion prediction dataset,

    J. Houston, G. Zuidhof, L. Bergamini, Y . Ye, L. Chen, A. Jain, S. Omari, V . Iglovikov, and P. Ondruska, “One thousand and one hours: Self-driving motion prediction dataset,” in Conference on Robot Learning. PMLR, 2021, pp. 409–418

    2021

  15. [22]

    Vehicle trajec- tory prediction based on motion model and maneuver recognition,

    A. Houenou, P. Bonnifait, V . Cherfaoui, and W. Yao, “Vehicle trajec- tory prediction based on motion model and maneuver recognition,” in 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2013, pp. 4363–4369

    2013

  16. [23]

    Social lstm: Human trajectory prediction in crowded spaces,

    A. Alahi, K. Goel, V . Ramanathan, A. Robicquet, L. Fei-Fei, and S. Savarese, “Social lstm: Human trajectory prediction in crowded spaces,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , 2016, pp. 961–971

    2016

  17. [24]

    Pre- dictionnet: Real-time joint probabilistic traffic prediction for planning, control, and simulation,

    A. Kamenev, L. Wang, O. B. Bohan, I. Kulkarni, B. Kartal, A. Molchanov, S. Birchfield, D. Nistér, and N. Smolyanskiy, “Pre- dictionnet: Real-time joint probabilistic traffic prediction for planning, control, and simulation,” 2022

    2022

  18. [25]

    Social GAN: Socially acceptable trajectories with generative adversarial networks,

    A. Gupta, J. Johnson, L. Fei-Fei, S. Savarese, and A. Alahi, “Social GAN: Socially acceptable trajectories with generative adversarial networks,” in IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), 2018, pp. 2255–2264

    2018

  19. [26]

    Can language beat numerical regres- sion? language-based multimodal trajectory prediction,

    I. Bae, J. Lee, and H.-G. Jeon, “Can language beat numerical regres- sion? language-based multimodal trajectory prediction,” arXiv preprint arXiv:2403.18447, 2024

    2024 arXiv

  20. [27]

    Learning to predict vehicle trajectories with model-based planning,

    H. Song, D. Luan, W. Ding, M. Y . Wang, and Q. Chen, “Learning to predict vehicle trajectories with model-based planning,” 2021

    2021

  21. [28]

    Planning-inspired hierarchical trajectory prediction for autonomous driving,

    D. Li, Q. Zhang, Z. Xia, K. Zhang, M. Yi, W. Jin, and D. Zhao, “Planning-inspired hierarchical trajectory prediction for autonomous driving,” 2023

    2023

  22. [29]

    Differentiable logic layer for rule guided trajectory prediction,

    X. Li, G. Rosman, I. Gilitschenski, J. DeCastro, C.-I. Vasile, S. Karaman, and D. Rus, “Differentiable logic layer for rule guided trajectory prediction,” in Proceedings of the 2020 Conference on Robot Learning , ser. Proceedings of Machine Learning Research, J. Kober, F. Ramo...

    2020

  23. [30]

    On complementing end-to-end human behavior predictors with planning,

    L. Sun, X. Jia, and A. D. Dragan, “On complementing end-to-end human behavior predictors with planning,” 2021

    2021

  24. [31]

    Rulefuser: Injecting rules in evidential networks for robust out-of-distribution trajectory prediction,

    J. Patrikar, S. Veer, A. Sharma, M. Pavone, and S. Scherer, “Rulefuser: Injecting rules in evidential networks for robust out-of-distribution trajectory prediction,” arXiv preprint arXiv:2405.11139 , 2024

    2024 arXiv

  25. [32]

    Online control with adversarial disturbances,

    N. Agarwal, B. Bullins, E. Hazan, S. Kakade, and K. Singh, “Online control with adversarial disturbances,” in International Conference on Machine Learning . PMLR, 2019, pp. 111–119

    2019

  26. [33]

    Introduction to online nonstochastic control,

    E. Hazan and K. Singh, “Introduction to online nonstochastic control,” arXiv preprint arXiv:2211.09619 , 2022

    2022 arXiv

  27. [34]

    Fast trac: A parameter-free optimizer for lifelong reinforcement learning,

    A. Muppidi, Z. Zhang, and H. Yang, “Fast trac: A parameter-free optimizer for lifelong reinforcement learning,” Advances in Neural Information Processing Systems , vol. 37, pp. 51 169–51 195, 2024

    2024

  28. [35]

    Adaptive conformal inference under dis- tribution shift,

    I. Gibbs and E. Candes, “Adaptive conformal inference under dis- tribution shift,” Advances in Neural Information Processing Systems , vol. 34, pp. 1660–1672, 2021

    2021

  29. [36]

    Improved online conformal prediction via strongly adaptive online learning,

    A. Bhatnagar, H. Wang, C. Xiong, and Y . Bai, “Improved online conformal prediction via strongly adaptive online learning,” in Inter- national Conference on Machine Learning . PMLR, 2023, pp. 2337– 2363

    2023

  30. [37]

    Wayformer: Motion forecasting via simple & efficient atten- tion networks,

    N. Nayakanti, R. Al-Rfou, A. Zhou, K. Goel, K. S. Refaat, and B. Sapp, “Wayformer: Motion forecasting via simple & efficient atten- tion networks,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2023, pp. 2980–2987

    2023

  31. [38]

    Mtr++: Multi-agent motion prediction with symmetric scene modeling and guided intention query- ing,

    S. Shi, L. Jiang, D. Dai, and B. Schiele, “Mtr++: Multi-agent motion prediction with symmetric scene modeling and guided intention query- ing,” IEEE Transactions on Pattern Analysis and Machine Intelligence , 2024

    2024

  32. [39]

    A decision-theoretic generalization of on-line learning and an application to boosting,

    Y . Freund and R. E. Schapire, “A decision-theoretic generalization of on-line learning and an application to boosting,” Journal of Computer and System Sciences , vol. 55, no. 1, pp. 119–139, 1997

    1997

  33. [40]

    Understanding the exploding gradient problem,

    R. Pascanu, T. Mikolov, and Y . Bengio, “Understanding the exploding gradient problem,” CoRR, abs/1211.5063 , vol. 2, no. 417, p. 1, 2012

    2012 arXiv

  34. [41]

    Stochastic optimization with heavy-tailed noise via accelerated gradient clipping,

    E. Gorbunov, M. Danilova, and A. Gasnikov, “Stochastic optimization with heavy-tailed noise via accelerated gradient clipping,” Advances in Neural Information Processing Systems , vol. 33, pp. 15 042–15 053, 2020

    2020

  35. [42]

    Why are adaptive methods good for attention models?

    J. Zhang, S. P. Karimireddy, A. Veit, S. Kim, S. Reddi, S. Kumar, and S. Sra, “Why are adaptive methods good for attention models?” Advances in Neural Information Processing Systems , vol. 33, pp. 15 383–15 393, 2020

    2020

  36. [43]

    R. T. Rockafellar, Convex Analysis. Princeton University Press, 1970

    1970

  37. [44]

    Softsort: A continuous relaxation for the argsort operator,

    S. Prillo and J. M. Eisenschlos, “Softsort: A continuous relaxation for the argsort operator,” 2020

    2020

  38. [46]

    Scene transformer: A unified architecture for predicting multiple agent tra- jectories,

    J. Ngiam, B. Caine, V . Vasudevan, Z. Zhang, H.-T. L. Chiang, J. Ling, R. Roelofs, A. Bewley, C. Liu, A. Venugopal et al. , “Scene transformer: A unified architecture for predicting multiple agent tra- jectories,” arXiv preprint arXiv:2106.08417 , 2021

    2021 arXiv

  39. [47]

    Lecture 10: Exponentiated gradient descent,

    University of Washington, “Lecture 10: Exponentiated gradient descent,” 2012, cSE 599S: Special Topics in Theoretical Computer Science, Spring 2012. [Online]. Available: https://courses. cs.washington.edu/courses/cse599s/12sp/scribes/lecture10.pdf APPENDIX A. Exponentiated Gra...

    2012

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.