Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation
<|reference_start|>Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation: This paper analyzes multi-step 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, and the control theoretic approach, 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, two n-step TD-learning algorithms are proposed and analyzed, which can be seen as the model-free reinforcement learning counterparts of the gradient and control theoretic algorithms.<|reference_end|>
@article{lee2024analysis,
    title={Analysis of Off-Policy Multi-Step TD-Learning with Linear Function
  Approximation},
    author={Donghwan Lee},
    journal={arXiv preprint arXiv:2402.15781},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.15781},
    primaryClass={eess.SY cs.LG cs.SY}
}