A problem about the relation between 1-oracle and 2-oracle PAC model

This problem is about two-oracle variant of the PAC model. Assume that positive and negative examples are now drawn from two separate distributions $\mathcal{D}_{+}$ and $\mathcal{D}_{-} .$ For an accuracy $(1-\epsilon),$ the learning algorithm must find a hypothesis $h$ such that: $$ \underset{x \sim \mathcal{D}_{+}}{\mathbb{P}}[h(x)=0] \leq \epsilon \text { and } \underset{x \sim \mathcal{D}_{-}}{\mathbb{P}}[h(x)=1] \leq…

Growth function bound related to generalization error

This is an inequality on page 36 of the book Foundations of Machine Learning, but the author only states it without proof. $$ \mathbb{P}\left[\left|R(h)-\widehat{R}_{S}(h)\right|>\epsilon\right] \leq 4 \Pi_{\mathcal{H}}(2 m) \exp \left(-\frac{m \epsilon^{2}}{8}\right) $$ Here The growth function $\Pi_{\mathcal{F}}: \mathbb{N} \rightarrow \mathbb{N}$ for a hypothesis set $\mathcal{H}$ is defined by: $$ \forall m \in \mathbb{N}, \Pi_{\mathcal{F}}(m)=\max _{\left\{x_{1},…

Why Monte – Carlo epsilon soft approach cannot compute Q max (s,a)?

I am new to Reinforcement learning and am currently reading up on the estimation of Q pi(s,a) values using MC soft epsilon soft approach and chanced upon this algorithm. The link to the algorithm is found from this website. https://www.analyticsvidhya.com/blog/2018/11/reinforcement-learning-introduction-monte-carlo-learning-openai-gym/ def monte_carlo_e_soft(env, episodes=100, policy=None, epsilon=0.01): if not policy: policy = create_random_policy(env) # Create an empty…