mlsanityData to 14 Oct 2026

Analysis of Off-Policy n-Step TD-Learning with Linear Function Approximation

arXiv 2502.08941 ↗First posted 13 Feb 2025cs.LG cs.AIcited by 0

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

This paper analyzes multi-step temporal difference (TD)-learning algorithms within the ``deadly triad'' scenario, characterized by linear function approximation, off-policy learning, and bootstrapping. In particular, we prove that n-step TD-learning algorithms converge to a solution as the sampling horizon n increases sufficiently. The paper is divided into two parts. In the first part, we comprehensively examine the fundamental properties of their model-based deterministic counterparts, including projected value iteration, gradient descent algorithms, which can be viewed as prototype deterministic algorithms whose analysis plays a pivotal role in understanding and developing their model-free reinforcement learning counterparts. In particular, we prove that these algorithms converge to meaningful solutions when n is sufficiently large. Based on these findings, in the second part, two n-step TD-learning algorithms are proposed and analyzed, which can be seen as the model-free reinforcement learning counterparts of the model-based deterministic algorithms.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 24 of its 39 references that are in the map. First posted on arXiv 13 Feb 2025.

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24 of 39 references.

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  1. 2024The ODE Method for Stochastic Approximation and Reinforcement Learning with Markovian Noise15 Jan

Other references · 23

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2015Continuous control with deep reinforcement learningcited by 3,407
  3. 2015Trust Region Policy Optimizationcited by 2,580
  4. 2015High-Dimensional Continuous Control Using Generalized Advantage Estimationcited by 2,026
  5. 2015Deep Reinforcement Learning with Double Q-learningcited by 1,745
  6. 2017Rainbow: Combining Improvements in Deep Reinforcement Learningcited by 786
  7. 2017A Distributional Perspective on Reinforcement Learningcited by 765
  8. 2018Deep Reinforcement Learning and the Deadly Triadcited by 174
  9. 2015Memory-based control with recurrent neural networkscited by 78
  10. 2021Breaking the Deadly Triad with a Target Networkcited by 47
  11. 2017Multi-step Reinforcement Learning: A Unifying Algorithmcited by 42
  12. 2020Gradient Temporal-Difference Learning with Regularized Correctionscited by 38
11 more
  1. 2019Understanding Multi-Step Deep Reinforcement Learning: A Systematic Study of the DQN Targetcited by 31
  2. 2022Target Network and Truncation Overcome The Deadly Triad in Q-Learningcited by 31
  3. 2017Multi-step Off-policy Learning Without Importance Sampling Ratioscited by 19
  4. 2015Generalized Emphatic Temporal Difference Learning: Bias-Variance Analysiscited by 17
  5. 2021Finite-Sample Analysis of Off-Policy TD-Learning via Generalized Bellman Operatorscited by 17
  6. 2016Effective Multi-step Temporal-Difference Learning for Non-Linear Function Approximationcited by 7
  7. 2021New Versions of Gradient Temporal Difference Learningcited by 6
  8. 2019A Convergent Off-Policy Temporal Difference Algorithmcited by 5
  9. 2023Multi-Bellman operator for convergence of Q-learning with linear function approximationcited by 3
  10. 2023Backstepping Temporal Difference Learningcited by 2
  11. 2023n-Step Temporal Difference Learning with Optimal ncited by 2

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  1. 2024Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation
  2. 2026Towards Parameter-Free Temporal Difference Learning
  3. 2025Stabilizing Temporal Difference Learning via Implicit Stochastic Recursion
  4. 2025A Unifying View of Linear Function Approximation in Off-Policy RL Through Matrix Splitting and Preconditioning
  5. 2024Multi-State TD Target for Model-Free Reinforcement Learning
  6. 2025Accelerating Multi-Task Temporal Difference Learning under Low-Rank Representation
  7. 2025Deterministic Policy Gradient for Reinforcement Learning with Continuous Time and State
  8. 2026Almost Sure Convergence of Differential Temporal Difference Learning for Average Reward Markov Decision Processes