mlsanityData to 14 Oct 2026

Multi-Task Imitation Learning for Linear Dynamical Systems

arXiv 2212.00186 ↗First posted 1 Dec 2022cs.LG cs.SY eess.SYcited by 23

On the map: Offline RL and imitation learning from data → Imitation learning methods

Abstract (arXiv)

We study representation learning for efficient imitation learning over linear systems. In particular, we consider a setting where learning is split into two phases: (a) a pre-training step where a shared k-dimensional representation is learned from H source policies, and (b) a target policy fine-tuning step where the learned representation is used to parameterize the policy class. We find that the imitation gap over trajectories generated by the learned target policy is bounded by tildeOleft( frack nxHNshared + frack nuNtargetright), where nx > k is the state dimension, nu is the input dimension, Nshared denotes the total amount of data collected for each policy during representation learning, and Ntarget is the amount of target task data. This result formalizes the intuition that aggregating data across related tasks to learn a representation can significantly improve the sample efficiency of learning a target task. The trends suggested by this bound are corroborated in simulation.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data. Builds on 33 of its 52 references that are in the map. First posted on arXiv 1 Dec 2022.

Builds on

33 of 52 references.

Closest ancestors · 2

Same direction, newest first

  1. 2022TaSIL: Taylor Series Imitation Learning30 May
  2. 2020Provable Representation Learning for Imitation Learning via Bi-level Optimization24 Feb

Other references · 31

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,897
  3. 2018IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architecturescited by 883
  4. 2016RL2: Fast Reinforcement Learning via Slow Reinforcement Learningcited by 503
  5. 2017End-to-end Driving via Conditional Imitation Learningcited by 485
  6. 2019Efficient Off-Policy Meta-Reinforcement Learning via Probabilistic Context Variablescited by 389
  7. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 250
  8. 2017Distral: Robust Multitask Reinforcement Learningcited by 233
  9. 2020Few-Shot Learning via Learning the Representation, Provablycited by 214
  10. 2015The Benefit of Multitask Representation Learningcited by 195
  11. 2020On the Theory of Transfer Learning: The Importance of Task Diversitycited by 186
  12. 2020Provable Meta-Learning of Linear Representationscited by 161
19 more
  1. 2018Multi-task Deep Reinforcement Learning with PopArtcited by 141
  2. 2021Representation Matters: Offline Pretraining for Sequential Decision Makingcited by 91
  3. 2021Conservative Data Sharing for Multi-Task Offline Reinforcement Learningcited by 64
  4. 2021How Fine-Tuning Allows for Effective Meta-Learningcited by 41
  5. 2021Adaptive-Control-Oriented Meta-Learning for Nonlinear Systemscited by 39
  6. 2015Learning with Square Loss: Localization through Offset Rademacher Complexitycited by 38
  7. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 38
  8. 2021On the Power of Multitask Representation Learning in Linear MDPcited by 30
  9. 2022Provable Benefit of Multitask Representation Learning in Reinforcement Learningcited by 29
  10. 2020Knowledge Transfer in Multi-Task Deep Reinforcement Learning for Continuous Controlcited by 28
  11. 2020Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimatorcited by 26
  12. 2019Learning Internal Representations (COLT 1995)cited by 25
  13. 2021Meta-Adaptive Nonlinear Control: Theory and Algorithmscited by 23
  14. 2020Scalable Multi-Task Imitation Learning with Autonomous Improvementcited by 21
  15. 2022Control-oriented meta-learningcited by 17
  16. 2021Joint Learning of Linear Time-Invariant Dynamical Systemscited by 16
  17. 2022Provable General Function Class Representation Learning in Multitask Bandits and MDPscited by 12
  18. 2022Meta-Learning Online Control for Linear Dynamical Systemscited by 5
  19. 2022Data-based Transfer Stabilization in Linear Systemscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 8; 2024: 10; 2025: 4; 2026: 1.

23 papers.

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  1. 2023Transformers as Algorithms: Generalization and Stability in In-context Learningcited by 222
  2. 2023Inverse Dynamics Pretraining Learns Good Representations for Multitask Imitationcited by 31
  3. 2024Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQRcited by 17
  4. 2023Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Datacited by 13
  5. 2023Learning Personalized Models with Clustered System Identificationcited by 11
  6. 2023Robot Fleet Learning via Policy Mergingcited by 11
  7. 2023Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecificationcited by 6
  8. 2024Computational Teaching for Driving via Multi-Task Imitation Learningcited by 6
  9. 2025Coreset-Based Task Selection for Sample-Efficient Meta-Reinforcement Learningcited by 6
  10. 2024Asynchronous Heterogeneous Linear Quadratic Regulator Designcited by 4
  11. 2024Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Controlcited by 4
  12. 2024Combining Federated Learning and Control: A Surveycited by 3
11 more
  1. 2024DIDA: Denoised Imitation Learning based on Domain Adaptationcited by 2
  2. 2024Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samplescited by 2
  3. 2025Redefining Clustered Federated Learning for System Identification: The Path of ClusterCraftcited by 2
  4. 2023A Statistical Guarantee for Representation Transfer in Multitask Imitation Learningcited by 1
  5. 2023Joint Problems in Learning Multiple Dynamical Systemscited by 1
  6. 2024Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systemscited by 1
  7. 2025Harnessing Data from Clustered LQR Systems: Personalized and Collaborative Policy Optimizationcited by 1
  8. 2024Shared-unique Features and Task-aware Prioritized Sampling on Multi-task Reinforcement Learningcited by 0
  9. 2024Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problemcited by 0
  10. 2025A State Alignment-Centric Approach to Federated System Identification: The FedAlign Frameworkcited by 0
  11. 2026How to Mitigate the Distribution Shift Problem in Robotics Control: A Robust and Adaptive Approach Based on Offline to Online Imitation Learningcited by 0

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  1. 2021Provable Representation Learning for Imitation with Contrastive Fourier Features
  2. 2020Learning to Generalize Across Long-Horizon Tasks from Human Demonstrations
  3. 2025The Pitfalls of Imitation Learning when Actions are Continuous
  4. 2024Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview
  5. 2022Learning and Retrieval from Prior Data for Skill-based Imitation Learning
  6. 2025Offline Imitation Learning upon Arbitrary Demonstrations by Pre-Training Dynamics Representations
  7. 2025Robust Offline Imitation Learning Through State-level Trajectory Stitching
  8. 2021Smooth Imitation Learning via Smooth Costs and Smooth Policies