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REVIEW 3 major objections 7 minor 36 references

Inverse Mixed Strategy Games with Generative Trajectory Models

T0 review · 3 major / 7 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read This paper shows that an inverse mixed-strategy game, with each agent's trajectory distribution represented by a conditional variational autoencoder, infers Nash-optimal robot actions from noisy multi-agent demonstrations without access…

desk verdict A useful new algorithmic combination - CVAE as nominal mixed strategy with end-to-end cost learning - but the MLE justification is shaky at Eq. (23), and the authors should address that gap before publication. read the letter →

arxiv 2502.03356 v1 pith:P2K3BRBL submitted 2025-02-05 cs.RO

Max Muchen Sun , Pete Trautman , Todd Murphey This is my paper · ORCID
classification cs.RO
keywords inversegamemixedstrategyNashequilibriumconditionalvariationalautoencodertrajectorypredictionmulti-agentinteractionsocialnavigationdifferentiablesolver
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

Coordinating robots with people requires knowing the objectives behind other agents' behavior, but observed trajectories are noisy and rarely reflect a single deterministic optimal choice. This paper proposes to solve that inverse problem by modeling each agent's behavior as a mixed strategy—a probability distribution over trajectories—and representing one piece of that distribution with a conditional variational autoencoder trained on offline demonstrations. It then learns a neural-network inter-agent cost function by backpropagating through a differentiable solver for the forward mixed-strategy game, so the inferred equilibrium matches the demonstrations. In a simulated five-agent navigation benchmark with unknown agent cost weights and added measurement noise, the resulting robot actions are comparable to those of the ground-truth model and an oracle that knows the true problem structure, and they clearly beat non-game baselines. The practical upshot is that a robot can recover interaction-aware behavior from imperfect data without privileged knowledge of other agents' objectives.

What carries the argument

The central object is the generalized mixed-strategy trajectory game whose objective for agent $i$ is $J_{i,[\theta,\phi]}=\sum_{j\ne i} l_\theta(x_i,x_j)+\log(p_i/q_{i,\phi})$, with equilibrium condition (11) balancing expected inter-agent cost against KL divergence from the nominal strategy $q_{i,\phi}$. The nominal strategy is a conditional variational autoencoder that produces multi-modal future-trajectory distributions conditioned on past observations and a goal; it supplies the sample set for the forward solve. The forward equilibrium is computed by the Bayesian recursive Nash equilibrium (BRNE) algorithm, an iterative, fully differentiable sample-weight update, and the inverse problem is solved by backpropagating through this solver to update $l_\theta$. The tractability hinge is Eq. (23), which replaces the intractable log-likelihood of the equilibrium distribution with a weighted squared error between the demonstrated future trajectory and the CVAE samples.

What would settle it

An experiment could evaluate the surrogate directly: fix a set of cost parameters, generate mixed-strategy equilibria from the CVAE nominal strategies, and compare the ordering of the true log-likelihood (Eq. 20) with the weighted squared-error surrogate (Eq. 23) across parameter values. If the surrogate improves while the true likelihood worsens, the learned cost function is biased by construction rather than by data.

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Extended reading notes

Core claim

The central claim is that the inverse mixed-strategy game remains solvable when the equilibrium is represented by weighted samples drawn from a generative model, even though the data were actually generated by a different (pure-strategy) game model. Concretely, the paper trains a CVAE as the nominal strategy $q_{i,\phi}$ for each agent, then optimizes a neural-network cost $l_\theta$ so that the mixed-strategy Nash equilibrium of Eq. (11), solved by BRNE, assigns high likelihood to demonstrated future trajectories; Eq. (23) approximates that likelihood by a weighted squared error. In the benchmark, the learned parameter $\theta$ yields robot runtime cost and minimum-distance-to-others distributions that overlap with the ground-truth and oracle baselines, with collision rates near or below the oracle's, across noise-free and noisy observation settings. The authors interpret this as evidence that generative trajectory models can absorb model mismatch and measurement noise while still recovering behavior that other agents expect.

Load-bearing premise

The load-bearing premise is that the weighted squared error in Eq. (23) is a faithful surrogate for the log-likelihood of the equilibrium mixed strategy; the paper does not derive or bound this approximation, and a non-monotone surrogate would bias the learned cost function.

Editorial extensions

If this is right

  • A robot can plan by treating other agents as drawing from learned distributions, so it does not need to know their exact cost weights or solver.
  • Because the forward solve is differentiable and trained on fewer than 100 demonstrations (about 20 minutes of training), the pipeline is practical for small-scale interaction scenarios.
  • Adding Gaussian measurement noise with standard deviations of 0.05 and 0.1 to observations leaves performance comparable to the noise-free variant, so the method tolerates sensing error.
  • In the simulation, the inferred strategy yields lower collision rates than the CVAE-only and Blind baselines (1.0% versus 8.0% and 17.0%), while running at 0.08 seconds per time step compared with 0.20 seconds for the forward game solver.

Reading between the lines

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

  • Editorial inference: nothing in the method depends on the CVAE specifically; replacing it with diffusion-based trajectory models should work as long as the nominal strategy can be sampled and the forward solver stays differentiable, which would broaden the approach to higher-dimensional or longer-horizon maneuvers.
  • Editorial inference: the Eq. (23) approximation is the most likely failure point in real data; if instead the equilibrium density were evaluated by kernel density estimation, the inverse game might require far fewer trajectory samples per agent, but the paper does not test this.
  • Editorial inference: the benchmark's fixed, homogeneous agent set and known simulation model may make the nominal CVAE's coverage artificially good; a test with heterogeneous agents or human trajectories would reveal whether the learned cost generalizes beyond the training distribution.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 7 minor

Summary. The paper proposes an inverse mixed-strategy game method in which each agent's nominal trajectory distribution is a conditional variational autoencoder (CVAE) and the inter-agent cost is a neural network. The forward game is the KL-regularized mixed-strategy game of [30], solved by the differentiable BRNE weight-update algorithm. The inverse problem is posed as maximum likelihood estimation over the equilibrium distribution (Eq. 20), and Algorithm 2 optimizes a weighted squared-error surrogate (Eq. 23) by backpropagation through the sample-based forward solver. The method is evaluated in a simulated five-agent navigation benchmark where data are generated by iLQGames, with comparisons to a ground-truth baseline, an oracle inverse-game baseline, a CVAE-only baseline, and a blind baseline, under two levels of measurement noise.

Significance. The paper addresses an important practical gap—inferring game-theoretic objectives from noisy, multi-modal demonstrations—and connects it to modern generative trajectory models. Its concrete strengths are unusual: the implementation is made available, training times and hyperparameters are reported, and the benchmark includes an oracle baseline that uses the privileged game solver, making the empirical comparison transparent. I do not see a circularity problem: the learned cost is evaluated on test trials against external ground truth and oracle baselines, not fitted to the test data. The main empirical claim—comparable to the ground-truth model and oracle, better than CVAE-only and blind baselines—is plausible if the learning objective is accepted. However, the formal foundation is incomplete: the central step from the MLE objective (20) to the surrogate loss (23) is asserted without derivation or error bound, and the evaluation rests on a single simulated scenario. If the surrogate gap is resolved, this would be a solid practical contribution to inverse game theory and robot navigation.

major comments (3)
  1. [Sec. III-C, Eq. (23)] The approximation log p*_{i,d,θ}(\bar s) ≈ −Σ_k w^k ||\bar s − s^k||^2 is load-bearing and unjustified. The forward game returns a weighted empirical measure {(s^k, w^k)}, so the log-likelihood of a continuous demonstration \bar s is not even defined without smoothing; the surrogate is, up to constants, the negative expected squared distance under the equilibrium distribution, a second moment, not a log-density. Because θ enters through the forward game (21), optimizing the surrogate can in principle drive the equilibrium distribution toward the correct conditional mean while leaving low likelihood at the demonstrations. No monotonicity or error-bound argument connects the two objectives. The authors should either derive the surrogate from a proper density estimate (e.g., a kernel density estimator and its bandwidth/error analysis), or explicitly reframe the contribution as minimizing a squared-error risk rather than solving the MLE problem (20).
  2. [Sec. III-A, Eqs. (13)–(14) and Algorithm 1] The inverse learning inherits the sample-based approximation of the forward game from [30] without proof, and it relies on gradients through that approximation being faithful to the exact Nash equilibrium of (11). If the weight update (13) has degeneracy or bias for finite K, the learned θ minimizes a loss against an approximate forward solver that may not correspond to any equilibrium of the exact game. The paper should state the approximation assumptions (number of samples K, convergence criterion, weight degeneracy) and provide at least a sensitivity study on K to establish that the learned cost is not an artifact of the finite-sample solver.
  3. [Sec. IV, Evaluation] The empirical evaluation is limited to a single simulated scenario—five homogeneous agents initialized on a circle with opposing goals—and the headline comparison is based on median/quartile box plots with no report of the number of test trials or any statistical significance testing. The claim in Sec. IV-D that the method 'significantly outperforms' CVAE and Blind baselines is not supported by inference statistics. At minimum, the number of test trials and per-trial variance should be reported, and ideally the method should be tested on a second scenario or on perturbations of the environment geometry to demonstrate that the learned cost generalizes beyond one task configuration.
minor comments (7)
  1. [Sec. IV-B] The reported learning rate '1e94' is presumably '1e-4'; the typo should be corrected.
  2. [Sec. III-B, Eqs. (15)–(16) and Sec. III-C, Eq. (20)] The notation 'T9τ1' appears in Eqs. (15) and (16) while 'T − τ1' appears in Eq. (20); these should be made consistent, presumably as 'T − τ1'.
  3. [Abstract and Sec. I] The abstract claims the method can 'leverage both offline and online data,' but the evaluation subjects the method only to offline training with noisy observations; the online adaptation mechanism (reconditioning the CVAE on new observations) is described but not separately ablated or measured.
  4. [Sec. IV-A, data collection] It is unclear whether the Gaussian noise added to x and y positions is applied to all agents' observations at both training and test time, and whether the robot's own state is also noisy; this should be stated explicitly.
  5. [Sec. IV-C, metrics] The 'robot runtime cost' metric is defined as the iLQGames cost assumed by the four agents for the robot; the paper should explain why this proxy appropriately measures alignment with the other agents' expectations and how it relates to the safety metric.
  6. [Sec. IV-B, implementation details] Only the learning rate is reported for the MLP and CVAE training; providing the optimizer name and any learning-rate schedule would improve reproducibility.
  7. [Fig. 2] The figure caption does not state which cost parameter or dataset trial is used to produce the 'before' and 'after' panels; adding this information would clarify what the visualization shows.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: held-out evaluation supports the inverse-game claim; the self-cited forward solver [30] is a component, not a fitted prediction.

full rationale

The paper's central claim—that the learned inverse mixed-strategy game produces Nash-optimal robot actions comparable to the ground-truth iLQGames model and an oracle inverse baseline—is evaluated on held-out navigation trials against external baselines (Section IV-D), so the predictions are not fitted to the test data. The inverse objective (20) is an MLE over demonstrations; Algorithm 2 optimizes a weighted sample surrogate (23). This surrogate is an approximation without a derivation or error bound, but it is not a definitional identity and no equation reduces to its own input by construction. The only significant self-citation is [30], which supplies the forward mixed-strategy game model (10)-(11) and the BRNE solver. That citation is a published, separate forward-game result used as a component; the inverse learning over θ and ϕ is this paper's contribution and is tested on data generated by a different algorithm (iLQGames). Thus the self-citation is not load-bearing in a circular sense. Training the CVAE and the cost MLP on the same offline dataset is standard practice and does not by itself make the held-out evaluation circular. Score 1 reflects the presence of the self-cited forward solver, not any reduction of the central claim.

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

The central claim rests on a small number of assumptions: the observed data are generated by a mixed-strategy Nash equilibrium, the forward game solver from prior work converges, the CVAE sample set covers the relevant behavior space, and the surrogate loss in Eq. (23) preserves the MLE optimum. The cost network and CVAE parameters are fitted to data; the latent dimension and sample counts are hand-chosen. No new physical entities are introduced.

free parameters (4)
  • Inter-agent cost network parameters θ = Learned via backpropagation (MLP with 3 hidden layers of 256 units)
    The neural network lθ is the free function optimized in the inverse game; its weights are the primary fitted quantities.
  • CVAE parameters ϕ = Trained by ELBO maximization on the offline dataset (50 epochs)
    The encoder/decoder weights of the conditional variational autoencoder define the nominal mixed strategy and are fitted to the same offline data.
  • Latent dimension (4) = 4
    A 4-dimensional latent space is a hand-chosen architectural choice that constrains the expressivity of the nominal strategy.
  • Sample count K (100 training, 200 inference) = 100 / 200
    The number of trajectory samples per agent determines the fidelity of the sample-based approximation of the mixed strategy; too few samples could bias the equilibrium.
assumptions (4)
  • domain assumption Assumption 2: observed behaviors are governed by a mixed strategy Nash equilibrium (Eq. 8)
    The paper assumes observed joint trajectories are samples from a mixed strategy Nash equilibrium, which justifies the MLE objective. This is not verified for real data and is violated in the authors' own simulation (data come from a pure-strategy iLQGames solver).
  • domain assumption BRNE convergence and sample-based approximation of the forward game are accurate (from [30])
    The inverse learning relies on the Bayesian recursive Nash equilibrium algorithm and its asymptotic sample approximation, but the convergence guarantees are cited from prior work by the same authors rather than proved here.
  • ad hoc to paper CVAE sample support covers the true equilibrium behavior space
    The forward game can only reweight the CVAE-generated trajectory samples; if the samples do not include collision-avoiding alternatives, the learned cost cannot recover the true equilibrium. No coverage guarantee is provided.
  • ad hoc to paper Surrogate log-likelihood approximation (Eq. 23) preserves the MLE optimum
    The weighted squared-error loss is used in place of the true log-likelihood without theoretical justification. The validity of this surrogate is central to the inverse learning.

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Pith. "Pith review of Inverse Mixed Strategy Games with Generative Trajectory Models." pith.science (2026). https://pith.science/paper/P2K3BRBL

@misc{pith2026250203356,
  author       = {Pith},
  title        = {Pith review of: Inverse Mixed Strategy Games with Generative Trajectory Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P2K3BRBL}},
  note         = {Machine review of arXiv:2502.03356}
}
read the original abstract

Game-theoretic models are effective tools for modeling multi-agent interactions, especially when robots need to coordinate with humans. However, applying these models requires inferring their specifications from observed behaviors -- a challenging task known as the inverse game problem. Existing inverse game approaches often struggle to account for behavioral uncertainty and measurement noise, and leverage both offline and online data. To address these limitations, we propose an inverse game method that integrates a generative trajectory model into a differentiable mixed-strategy game framework. By representing the mixed strategy with a conditional variational autoencoder (CVAE), our method can infer high-dimensional, multi-modal behavior distributions from noisy measurements while adapting in real-time to new observations. We extensively evaluate our method in a simulated navigation benchmark, where the observations are generated by an unknown game model. Despite the model mismatch, our method can infer Nash-optimal actions comparable to those of the ground-truth model and the oracle inverse game baseline, even in the presence of uncertain agent objectives and noisy measurements.

Figures

Figures reproduced from arXiv: 2502.03356 by the authors.

Figure 1
Figure 1. The pure strategy inverse game formula (left) often [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Snapshots from a test with our method (blue: robot). [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Quantitative results of the navigation benchmark. We show the median, quartiles, and distribution of the results. Our [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

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Works this paper leans on

36 extracted references · 27 canonical work pages

  1. [30]

    Mixed strategy Nash equilibrium for crowd navigation,

    M. Muchen Sun, F. Baldini, K. Hughes, P. Trautman, and T. Murphey, “Mixed strategy Nash equilibrium for crowd navigation,” The International Journal of Robotics Research , p. 02783649241302342, Nov. 2024, publisher: SAGE Publications Ltd STM. [Online]. Available: https://doi.org/10.1177/02783649241302342

    work page doi:10.1177/02783649241302342 2024

  2. [1]

    Robot navigation in dense human crowds: the case for cooperation,

    P. Trautman, J. Ma, R. M. Murray, and A. Krause, “Robot navigation in dense human crowds: the case for cooperation,” in 2013 IEEE International Conference on Robotics and Automation , May 2013, pp. 2153–2160, iSSN: 1050-4729. [Online]. Available: https://ieeexplore.ieee.org/document/6630866

    work page arXiv 2013

  3. [2]

    Core Challenges of Social Robot Navigation: A Survey,

    C. Mavrogiannis, F. Baldini, A. Wang, D. Zhao, P. Trautman, A. Steinfeld, and J. Oh, “Core Challenges of Social Robot Navigation: A Survey,” ACM Transactions on Human-Robot Interaction, vol. 12, no. 3, pp. 36:1–36:39, Apr. 2023. [Online]. Available: https://dl.acm.org/doi/10.1145/3583741

    doi:10.1145/3583741 2023

  4. [3]

    Planning and Decision-Making for Autonomous Vehicles,

    W. Schwarting, J. Alonso-Mora, and D. Rus, “Planning and Decision-Making for Autonomous Vehicles,” Annual Review of Control, Robotics, and Autonomous Systems , vol. 1, no. V olume 1, 2018, pp. 187–210, May 2018, publisher: Annual Reviews. [Online]. Available: https://www.annualreviews.org/content/journals/ 10.1146/annurev-control-060117-105157

    doi:10.1146/annurev-control-060117-105157 2018

  5. [4]

    Social behavior for autonomous vehicles,

    W. Schwarting, A. Pierson, J. Alonso-Mora, S. Karaman, and D. Rus, “Social behavior for autonomous vehicles,” Proceedings of the National Academy of Sciences , vol. 116, no. 50, pp. 24 972–24 978, Dec. 2019, publisher: Proceedings of the National Academy of Sciences. [Online]. Available: https://www.pnas.org/doi/10.1073/pnas. 1820676116

    doi:10.1073/pnas 2019

  6. [5]

    Non-Cooperative Games,

    J. Nash, “Non-Cooperative Games,” Annals of Mathematics , vol. 54, no. 2, pp. 286–295, 1951, publisher: Annals of Mathematics. [Online]. Available: https://www.jstor.org/stable/1969529

    arXiv 1951

  7. [6]

    Learning Structured Output Represen- tation using Deep Conditional Generative Models,

    K. Sohn, H. Lee, and X. Yan, “Learning Structured Output Represen- tation using Deep Conditional Generative Models,” in Advances in Neural Information Processing Systems , vol. 28. Curran Associates, Inc., 2015. [Online]. Available: https://papers.nips.cc/paper files/ paper/2015/hash/8d55a249e6baa5c06772297520da2051-Abstract.html

    work page 2015

  8. [7]

    Planning for Autonomous Cars that Leverage Effects on Human Actions,

    D. Sadigh, S. Sastry, S. A. Seshia, and A. D. Dragan, “Planning for Autonomous Cars that Leverage Effects on Human Actions,” vol. 12, Jun. 2016. [Online]. Available: https://www.roboticsproceedings.org/ rss12/p29.html

    work page 2016

Show all 36 references
  1. [8]

    Best Response Model Predictive Control for Agile Interactions Between Autonomous Ground Vehicles,

    G. Williams, B. Goldfain, P. Drews, J. M. Rehg, and E. A. Theodorou, “Best Response Model Predictive Control for Agile Interactions Between Autonomous Ground Vehicles,” in 2018 IEEE International Conference on Robotics and Automation (ICRA) , May 2018, pp. 2403–2410, iSSN: 257...

    2018

  2. [9]

    Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Games,

    D. Fridovich-Keil, E. Ratner, L. Peters, A. D. Dragan, and C. J. Tomlin, “Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Games,” in 2020 IEEE International Conference on Robotics and Automation (ICRA) , May 2020, pp. 147...

    2020

  3. [10]

    ALGAMES: a fast augmented Lagrangian solver for constrained dynamic games,

    S. Le Cleac’h, M. Schwager, and Z. Manchester, “ALGAMES: a fast augmented Lagrangian solver for constrained dynamic games,” Autonomous Robots, vol. 46, no. 1, pp. 201–215, Jan. 2022. [Online]. Available: https://doi.org/10.1007/s10514-021-10024-7

    2022 doi

  4. [11]

    Game-Theoretic Planning for Risk-Aware Interactive Agents,

    M. Wang, N. Mehr, A. Gaidon, and M. Schwager, “Game-Theoretic Planning for Risk-Aware Interactive Agents,” in 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , Oct. 2020, pp. 6998–7005, iSSN: 2153-0866. [Online]. Available: https://ieeexplore.ie...

    2020

  5. [12]

    Stochastic Dynamic Games in Belief Space,

    W. Schwarting, A. Pierson, S. Karaman, and D. Rus, “Stochastic Dynamic Games in Belief Space,” IEEE Transactions on Robotics , vol. 37, no. 6, pp. 2157–2172, Dec. 2021. [Online]. Available: https://ieeexplore.ieee.org/document/9439814

    2021

  6. [13]

    Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions,

    N. Mehr, M. Wang, M. Bhatt, and M. Schwager, “Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions,” IEEE Transactions on Robotics , pp. 1–15, 2023

    2023

  7. [14]

    MPOGames: Efficient Multimodal Partially Observable Dynamic Games,

    O. So, P. Drews, T. Balch, V . Dimitrov, G. Rosman, and E. A. Theodorou, “MPOGames: Efficient Multimodal Partially Observable Dynamic Games,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) , May 2023, pp. 3189–3196. [Online]. Available: https://ieeexpl...

    2023

  8. [15]

    Soft-Bellman Equilibrium in Affine Markov Games: Forward Solutions and Inverse Learning,

    S. Chen, Y . Yu, D. Fridovich-Keil, and U. Topcu, “Soft-Bellman Equilibrium in Affine Markov Games: Forward Solutions and Inverse Learning,” in 2023 62nd IEEE Conference on Decision and Control (CDC), Dec. 2023, pp. 2202–2207, iSSN: 2576-2370. [Online]. Available: https://ieee...

    2023

  9. [16]

    Blending Data-Driven Priors in Dynamic Games,

    J. Lidard, H. Hu, A. Hancock, Z. Zhang, A. G. Contreras, V . Modi, J. DeCastro, D. Gopinath, G. Rosman, N. E. Leonard, M. Santos, and J. F. Fisac, “Blending Data-Driven Priors in Dynamic Games,” Jul. 2024. [Online]. Available: http://arxiv.org/abs/2402.14174

    2024 arXiv

  10. [17]

    Learning to Play Trajectory Games Against Opponents With Unknown Objectives,

    X. Liu, L. Peters, and J. Alonso-Mora, “Learning to Play Trajectory Games Against Opponents With Unknown Objectives,” IEEE Robotics and Automation Letters , vol. 8, no. 7, pp. 4139–4146, Jul. 2023. [Online]. Available: https://ieeexplore.ieee.org/abstract/ document/10137879

    2023

  11. [18]

    Cost Inference for Feedback Dynamic Games from Noisy Par- tial State Observations and Incomplete Trajectories,

    J. Li, C.-Y . Chiu, L. Peters, S. Sojoudi, C. Tomlin, and D. Fridovich- Keil, “Cost Inference for Feedback Dynamic Games from Noisy Par- tial State Observations and Incomplete Trajectories,” in Proceedings of the 2023 International Conference on Autonomous Agents and Multiagen...

    2023

  12. [19]

    Online and offline learning of player objectives from partial observations in dynamic games,

    L. Peters, V . Rubies-Royo, C. J. Tomlin, L. Ferranti, J. Alonso- Mora, C. Stachniss, and D. Fridovich-Keil, “Online and offline learning of player objectives from partial observations in dynamic games,” The International Journal of Robotics Research , vol. 42, no. 10, pp. 917...

    2023 doi

  13. [20]

    LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planning,

    S. Le Cleac’h, M. Schwager, and Z. Manchester, “LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planning,” IEEE Robotics and Automation Letters , vol. 6, no. 3, pp. 5485–5492, Jul. 2021. [Online]. Available: https://ieeexplore.ieee.org...

    2021

  14. [21]

    Auto-Encoding Bayesian Inverse Games,

    X. Liu, L. Peters, J. Alonso-Mora, U. Topcu, and D. Fridovich- Keil, “Auto-Encoding Bayesian Inverse Games,” in Algorithmic Foundations of Robotics XVI. Chicago IL USA: Springer International Publishing, Feb. 2024, arXiv:2402.08902 [cs, eess]. [Online]. Available: http://arxiv...

    2024 arXiv

  15. [22]

    Inference-Based Strategy Alignment for General-Sum Differential Games,

    L. Peters, D. Fridovich-Keil, C. J. Tomlin, and Z. N. Sunberg, “Inference-Based Strategy Alignment for General-Sum Differential Games,” in Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems, ser. AAMAS ’20. Rich- land, SC: Internationa...

    2020

  16. [23]

    Contingency Games for Multi- Agent Interaction,

    L. Peters, A. Bajcsy, C.-Y . Chiu, D. Fridovich-Keil, F. Laine, L. Ferranti, and J. Alonso-Mora, “Contingency Games for Multi- Agent Interaction,” IEEE Robotics and Automation Letters , vol. 9, no. 3, pp. 2208–2215, Mar. 2024. [Online]. Available: https: //ieeexplore.ieee.org/...

    2024

  17. [24]

    A Game-Theoretic Framework for Joint Forecasting and Planning,

    K. Kedia, P. Dan, and S. Choudhury, “A Game-Theoretic Framework for Joint Forecasting and Planning,” in 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , Oct. 2023, pp. 6773–6778, iSSN: 2153-0866. [Online]. Available: https://ieeexplore.ieee.org...

    2023

  18. [25]

    Learning Mixed Strategies in Trajectory Games,

    L. Peters, D. Fridovich-Keil, L. Ferranti, C. Stachniss, J. Alonso- Mora, and F. Laine, “Learning Mixed Strategies in Trajectory Games,” in Robotics: Science and Systems XVIII . Robotics: Science and Systems Foundation, Jun. 2022. [Online]. Available: http://www.roboticsprocee...

    2022

  19. [26]

    Tra- jectron++: Dynamically-Feasible Trajectory Forecasting with Het- erogeneous Data,

    T. Salzmann, B. Ivanovic, P. Chakravarty, and M. Pavone, “Tra- jectron++: Dynamically-Feasible Trajectory Forecasting with Het- erogeneous Data,” in Computer Vision – ECCV 2020 , A. Vedaldi, H. Bischof, T. Brox, and J.-M. Frahm, Eds. Cham: Springer International Publishing, 20...

    2020

  20. [27]

    Multimodal Deep Generative Models for Trajectory Prediction: A Conditional Variational Autoencoder Approach,

    B. Ivanovic, K. Leung, E. Schmerling, and M. Pavone, “Multimodal Deep Generative Models for Trajectory Prediction: A Conditional Variational Autoencoder Approach,” IEEE Robotics and Automation Letters, vol. 6, no. 2, pp. 295–302, Apr. 2021. [Online]. Available: https://ieeexpl...

    2021

  21. [28]

    Self-Consistent Trajectory Autoencoder: Hierarchical Reinforcement Learning with Trajectory Embeddings,

    J. Co-Reyes, Y . Liu, A. Gupta, B. Eysenbach, P. Abbeel, and S. Levine, “Self-Consistent Trajectory Autoencoder: Hierarchical Reinforcement Learning with Trajectory Embeddings,” in Proceedings of the 35th International Conference on Machine Learning . PMLR, Jul. 2018, pp. 1009...

    2018

  22. [29]

    Task Programming: Learning Data Efficient Behavior Representations,

    J. J. Sun, A. Kennedy, E. Zhan, D. J. Anderson, Y . Yue, and P. Perona, “Task Programming: Learning Data Efficient Behavior Representations,” 2021, pp. 2876–2885. [Online]. Available: https://openaccess.thecvf.com/content/CVPR2021/ html/Sun Task Programming Learning Data Effic...

    2021

  23. [31]

    A Generalized Path Integral Control Approach to Reinforcement Learning,

    E. Theodorou, J. Buchli, and S. Schaal, “A Generalized Path Integral Control Approach to Reinforcement Learning,” Journal of Machine Learning Research, vol. 11, no. 104, pp. 3137–3181, 2010. [Online]. Available: http://jmlr.org/papers/v11/theodorou10a.html

    2010

  24. [32]

    Relative entropy and free energy dualities: Connections to Path Integral and KL control,

    E. A. Theodorou and E. Todorov, “Relative entropy and free energy dualities: Connections to Path Integral and KL control,” in 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) , Dec. 2012, pp. 1466–1473, iSSN: 0743-1546. [Online]. Available: https://ieeexplore.ieee....

    2012

  25. [33]

    Auto-Encoding Variational Bayes,

    D. P. Kingma and M. Welling, “Auto-Encoding Variational Bayes,” 2013, arXiv:1312.6114 [cs, stat]. [Online]. Available: http://arxiv.org/abs/1312.6114

    2013 arXiv

  26. [34]

    JAX: composable transformations of Python+NumPy programs,

    J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman- Milne, and Q. Zhang, “JAX: composable transformations of Python+NumPy programs,” 2018. [Online]. Available: http://github. com/google/jax

    2018

  27. [35]

    Flax: A neural network library and ecosystem for JAX,

    J. Heek, A. Levskaya, A. Oliver, M. Ritter, B. Rondepierre, A. Steiner, and M. v. Zee, “Flax: A neural network library and ecosystem for JAX,” 2024. [Online]. Available: http://github.com/google/flax

    2024

  28. [36]

    Diffusion policy: Visuomotor policy learning via action diffusion,

    C. Chi, Z. Xu, S. Feng, E. Cousineau, Y . Du, B. Burchfiel, R. Tedrake, and S. Song, “Diffusion policy: Visuomotor policy learning via action diffusion,” The International Journal of Robotics Research, p. 02783649241273668, Oct. 2024, publisher: SAGE Publications Ltd STM. [Onl...

    2024

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.