TD-learning is a foundation reinforcement learning (RL) algorithm for value
prediction. Critical to the accuracy of value predictions is the quality of
state representations. In this work, we consider the question: how does
end-to-end TD-learning impact the representation over time? Complementary to
prior work, we provide a set of analysis that sheds further light on the
representation dynamics under TD-learning. We first show that when the
environments are reversible, end-to-end TD-learning strictly decreases the
value approximation error over time. Under further assumptions on the
environments, we can connect the representation dynamics with spectral
decomposition over the transition matrix. This latter finding establishes
fitting multiple value functions from randomly generated rewards as a useful
auxiliary task for representation learning, as we empirically validate on both
tabular and Atari game suites.

探讨了 TD-learning 对时间序列中状态表示的影响，特别是在环境可逆的情况下，TD-learning 可以严格减少价值近似误差，同时将其与转移矩阵的谱分解相联系，并用随机生成的奖励拟合多个值函数来辅助表征学习。

TD-learning 下表示动态的更好理解

Towards a Better Understanding of Representation Dynamics under  TD-learning

Off-policy learning ability is an important feature of reinforcement learning
(RL) for practical applications. However, even one of the most elementary RL
algorithms, temporal-difference (TD) learning, is known to suffer form
divergence issue when the off-policy scheme is used together with linear
function approximation. To overcome the divergent behavior, several off-policy
TD-learning algorithms, including gradient-TD learning (GTD), and TD-learning
with correction (TDC), have been developed until now. In this work, we provide
a unified view of such algorithms from a purely control-theoretic perspective,
and propose a new convergent algorithm. Our method relies on the backstepping
technique, which is widely used in nonlinear control theory. Finally,
convergence of the proposed algorithm is experimentally verified in
environments where the standard TD-learning is known to be unstable.

本文从纯控制理论的角度提供了对各种纠正离策略误差 TD 学习算法（包括 GTD 和 TDC）的统一视角，并提出了一种基于后掠技术的新的收敛算法，最终在标准 TD-learning 不稳定的环境中实验证实了该算法的收敛性。

反步时间差分学习

Backstepping Temporal Difference Learning

Most practical recommender systems focus on estimating immediate user
engagement without considering the long-term effects of recommendations on user
behavior. Reinforcement learning (RL) methods offer the potential to optimize
recommendations for long-term user engagement. However, since users are often
presented with slates of multiple items - which may have interacting effects on
user choice - methods are required to deal with the combinatorics of the RL
action space. In this work, we address the challenge of making slate-based
recommendations to optimize long-term value using RL. Our contributions are
three-fold. (i) We develop SLATEQ, a decomposition of value-based
temporal-difference and Q-learning that renders RL tractable with slates. Under
mild assumptions on user choice behavior, we show that the long-term value
(LTV) of a slate can be decomposed into a tractable function of its component
item-wise LTVs. (ii) We outline a methodology that leverages existing myopic
learning-based recommenders to quickly develop a recommender that handles LTV.
(iii) We demonstrate our methods in simulation, and validate the scalability of
decomposed TD-learning using SLATEQ in live experiments on YouTube.

该研究提供了使用深度强化学习技术解决个性化推荐系统中长期用户参与度问题的方法，通过分解价值函数，考虑了物品组合效应，并实验证明了该方法的可行性和扩展性。