Response to Reviewer y9BV
**Q1.** DIAR is different from simply adding value function learning to LDCQ. Our goal was to make Q-function learning more precise, so we introduced a value function to ensure balanced training of the Q-function. By incorporating constraints from the value function during training, we can predict Q-values with greater accuracy. Additionally, the diffusion model, as a generative model, can produce a wide variety of meaningful latent vectors. We aimed to leverage this capability to enhance both Q-function and value-function learning. In the Bellman equation for Q-function learning in LDCQ, $Q(s_t,z) ← (r_{t:t+H}+\gamma^H Q(s_{t+H}, argmax(Q(s_{t+H},z_i)))$, the reward term $r_{t:{t+H}}$ is undefined if $z$ is not sampled from the offline dataset. However, by introducing the value function, we can indirectly evaluate the value of latent vectors generated by the diffusion model. As a result, DIAR uses not only the offline dataset but also latent vectors sampled from the diffusion model in the training process for both Q-functions and value functions. This approach led to significant performance improvements on datasets such as Maze2D, AntMaze, and Kitchen.
**Q2.** Our goal was to address offline reinforcement learning problems using a diffusion model. To this end, we compared DIAR with algorithms like Diffuser and DD, as well as skill-based algorithms. While the tasks in our experiments focused on goal based tasks, we did not explicitly involve providing the goal as input or solving tasks where the objective is to directly reach a specified destination. However, since DIAR can also function as a goal-conditioned RL algorithm, it would be possible to include the goal as part of the input and conduct additional experiments for comparison under goal-conditioned settings. Evaluating the ability to find an optimal path from the current state to a specified goal is as important as the experiments we have conducted so far and could offer further insights into DIAR’s capabilities.
**Q3.** The value function is used to evaluate whether the current decision is appropriate, and if it is not, a new decision is generated. However, it is challenging to train the value function perfectly. If the value function fails to accurately assess the value of the current state, the new decision generated may not be more optimal. Additionally, since we do not have access to unlimited data, this limitation can pose challenges for the DIAR model. Currently, AR is designed based on a few assumptions, but we plan to refine it into a more general algorithm in the future, making it applicable to a wider range of tasks and domains.
**Q4.** The purpose of introducing AR was to address the possibility of finding a more optimal choice when selecting a long action sequence all at once. Therefore, if there is a method to evaluate the current decision, AR can be applied even without relying on the value function. Additionally, AR can be used in environments with dense rewards. However, to enable more general applicability, the algorithm needs to be further expanded and refined.
**Q5.** As the reviewer mentioned, a tighter bound for the value is indeed $\gamma^{-H}V(s_t)$. In Section 4.3, the bound is calculated using $\gamma^{-H}V(s_t)$. However, when applying AR, we did not explicitly use $\gamma$. Instead, we evaluated the latent vectors' values based on the value function $V(s_t)$. To account for the possibility of a noisy value function, we incorporated a slight margin, allowing AR to operate effectively when there is a significant difference in value. When the value differences are small, the algorithm tends to follow the original decision more closely, maintaining a balance between exploration and adhering to the initial choice.