**Summary:**
The paper presents the development of novel value functions and algorithms for reinforcement learning tasks that involve the composition of multiple objectives, specifically the Reach-Always-Avoid (RAA) and Reach-Reach (RR) problems. These problems are inspired by tasks involving goal reaching and hazard avoidance. The paper introduces the Reach-Always-Avoid value function, which is defined as the minimum of the maximum reward and the minimum penalty, and the Reach-Reach value function, which is defined as the minimum of the maximum rewards of two different goals. The authors prove that these value functions can be decomposed into combinations of the existing Reach, Avoid, and Reach-Avoid value functions. They also propose a novel algorithm, DOHJ-PPO, which leverages the decomposed values to learn the optimal policy for these complex tasks. The paper demonstrates the effectiveness of DOHJ-PPO in continuous control tasks, showing that it outperforms several state-of-the-art baselines in terms of performance, safety, and speed.

**Strengths:**

1. **Novelty of Value Functions:** The paper introduces new value functions for composite tasks that have not been addressed in previous literature.
2. **Theoretical Contributions:** The paper provides proofs for the decomposition of the RAA and RR value functions into simpler value functions, which can then be solved using existing reinforcement learning methods.
3. **Practical Algorithm:** The DOHJ-PPO algorithm is designed to solve the RAA and RR value functions, and the paper demonstrates its effectiveness in various continuous control tasks.
4. **Empirical Validation:** The paper includes a comprehensive experimental section that validates the proposed method against a range of baselines, showing superior performance in most cases.

**Weaknesses:**

1. **Complexity of Theoretical Proofs:** The proofs in the paper are mathematically rigorous but may be difficult to follow for readers without a strong background in reinforcement learning theory.
2. **Limited Exploration of Alternative State Augmentations:** The paper focuses on a specific state augmentation scheme, which might not be optimal for all types of problems or environments. Further exploration of alternative state augmentation strategies could provide insights into their impact on performance and generalizability.

**Questions:**

1. **Interpretation of Value Functions:** How do the RAA and RR value functions relate to the underlying reward and penalty functions in real-world applications?
2. **Robustness to State Augmentation Choices:** How sensitive is the performance of DOHJ-PPO to the choice of state augmentation? Are there alternative augmentation schemes that could improve performance in certain scenarios?

**Soundness:**
Soundness: **4** - The paper presents a novel approach to solving complex reinforcement learning tasks involving multiple objectives. The proofs are sound, and the experimental validation is thorough and convincing.

**Presentation:**
Presentation: **4** - The paper is well-organized and clearly structured, with a comprehensive introduction, detailed methodology, and a clear separation of contributions. The experimental results are presented in a manner that is easy to follow.

**Contribution:**
Contribution: **4** - The paper makes significant contributions to the field of reinforcement learning by introducing new value functions for composite tasks and proposing a novel algorithm that effectively learns these functions.

**Rating:**
Rating: **8** - The paper presents a robust and innovative approach to solving complex reinforcement learning tasks, supported by strong theoretical foundations and empirical validation. It is a good paper that could contribute positively to the field with further exploration and application.

**Paper Decision:**
- Decision: **Accept**
- Reasons: The paper demonstrates originality, methodological soundness, significant contribution to the field of reinforcement learning, and clear presentation. It addresses important problems and presents a novel solution, supported by thorough validation against state-of-the-art baselines.