We derive a concentration bound of the type `for all $n \geq n_0$ for some $n_0$' for TD(0) with linear function approximation. We work with online TD learning with samples from a single sample path of the underlying Markov chain. This makes our analysis significantly different from offline TD learning or TD learning with access to independent samples from the stationary distribution of the Markov chain. We treat TD(0) as a contractive stochastic approximation algorithm, with both martingale and Markov noises. Markov noise is handled using the Poisson equation and the lack of almost sure guarantees on boundedness of iterates is handled using the concept of relaxed concentration inequalities.

翻译：我们针对带有线性函数近似的TD(0)算法推导了形如"对所有$n \geq n_0$（其中$n_0$由某个条件确定）"的浓度界。我们研究的是在线TD学习，其样本来自底层马尔可夫链的单一样本路径。这使得我们的分析与离线TD学习或基于马尔可夫链平稳分布独立样本的TD学习存在显著差异。我们将TD(0)视为一种具有鞅噪声和马尔可夫噪声的收缩随机逼近算法。其中，马尔可夫噪声通过泊松方程处理，而迭代有界性缺乏几乎必然保证的问题则借助松弛浓度不等式概念加以解决。