Towards Zero-Shot Generalization in Offline Reinforcement Learning

We sincerely thank you for your valuable feedback and suggestions. Our responses are as follows.

Q1 could you provide uncertainty estimates?

A1 Thank you for your insightful suggestion. We have included the uncertainty estimates of mean and median returns in Table 2 of our revised manuscript. We also report the Interquartile Means (IQM) with confidence intervals in the revised manuscript to better illustrate the significance of the observed improvements.

Q2 generally, I am surprised that BC performs so well - not only on the expert datasets where it could be expected, but also on the mixed datasets. Do you have a theory about why that is the case?

A2 We would like to emphasize that BC can outperform offline RL methods in certain cases, as its performance is highly dependent on the quality of the behavior policy. Theoretically, as established in [1], which studies the comparison between BC and offline RL in single-task settings, when the behavior policy is optimal, BC can converge to the optimal policy at a rate of $1/N$, where $N$ is the number of trajectories in the offline dataset. This convergence rate is faster than the $1/\sqrt{N}$ rate achieved by most offline RL methods, such as CQL. Consequently, when the offline dataset is finite (as in our case), BC can indeed outperform offline RL methods. However, when the behavior policy is suboptimal, the comparison between BC and offline RL becomes more nuanced and is influenced by factors such as dataset quality and the degree of suboptimality in the behavior policy. The theoretical results in [1] also extend to our methods, as RL with generalization encompasses the single-task RL setting.

It is important to note that our primary goal is not to assert that our methods will always outperform BC, particularly in finite-sample settings. Instead, our aim is to present a theoretically grounded framework that identifies the failure modes of existing offline RL methods in terms of generalization and demonstrates how our proposed approaches address these issues. While BC may outperform offline RL methods in specific scenarios, our contributions lie in providing a deeper understanding of the limitations of existing methods and proposing solutions that offer better generalization under broader conditions.

[1] "When Should We Prefer Offline Reinforcement Learning Over Behavioral Cloning?"

Q3 Figure 2 shows the differences in performance between IQL baseline and the newly proposed approach. Please add that information in the caption.

A3 Thank you for highlighting this issue. We have clarified it in the revised version of the paper. Specifically, Figure 2 illustrates the performance differences between our proposed IQL-4V approach and the original IQL algorithm on a per-game basis, as measured by min-max normalized scores.

Q4 I believe you could show the merits of your method in a much more convincing way of you chose a baseline that would do this - e.g. use a meta learning approach and don't allow it to fine-tune on the target task.

A4 Thank you for your insightful suggestion. We would like to highlight that we do not allow context information during the test phase, therefore it is impossible to incorporate the context information to boost the performance of baseline algorithms such as vanilla IQL. Regarding the suggestion of using a meta-learning approach, we conducted an additional evaluation using the method proposed by Mitchell et al. (2021), without fine-tuning, to provide a direct comparison with our approach on the Miner and Maze Expert datasets. The results are summarized below:

As outlined in Algorithm 1 (MACAW Meta-Training) by Mitchell et al. (2021), the primary distinction between the training process of our IQL-4V method and the meta-training phase of the MACAW algorithm lies in how the critic gradient updates are handled. In MACAW's meta-training, the gradient updates from individual tasks at each training step are consolidated into a single critic network, guided by the "test batch" for each task. Notably, MACAW consistently maintains only one unified critic network throughout the meta-training process. While both our method and meta-learning approaches share the concept of leveraging multiple optimization objectives during training, our method demonstrates superiority. This advantage stems from our approach’s ability to maintain multiple value networks throughout training, which enhances the model’s capacity to effectively capture and utilize diverse contextual information.

Again, we sincerely thank you for your time and constructive feedback. We hope our responses address your concerns, and we welcome any further questions or suggestions.

We sincerely thank you for your valuable feedback and suggestions. Our responses are as follows, which we hope could well address your concerns.

Q1 The empirical findings in Table 2 and Figure 2 do not leave the reader confident that a solution has been found--BC's median performance is better than (or similar to) IQL-4V's on both the expert and mixed datasets. Presumably this can be explained with reference to the sub-optimality gap of PERM reported in Table 1, but the authors do not discuss this.

Q2 In practice, why does IQL-4V not outperform BC in Section 6? It would be helpful if you could discuss more thoroughly the limitations in translating the theoretical findings to practical application.

A1&A2 We would like to emphasize that BC can outperform offline RL methods in certain cases, as its performance is highly dependent on the quality of the behavior policy. Theoretically, as established in [1], which studies the comparison between BC and offline RL in single-task settings, when the behavior policy is optimal, BC can converge to the optimal policy at a rate of $1/N$, where $N$ is the number of trajectories in the offline dataset. This convergence rate is faster than the $1/\sqrt{N}$ rate achieved by most offline RL methods, such as CQL. Consequently, when the offline dataset is finite (as in our case), BC can indeed outperform offline RL methods. However, when the behavior policy is suboptimal, the comparison between BC and offline RL becomes more nuanced and is influenced by factors such as dataset quality and the degree of suboptimality in the behavior policy. The theoretical results in [1] also extend to our methods, as RL with generalization encompasses the single-task RL setting.

It is important to note that our primary goal is not to assert that our methods will always outperform BC, particularly in finite-sample settings. Instead, our aim is to present a theoretically grounded framework that identifies the failure modes of existing offline RL methods in terms of generalization and demonstrates how our proposed approaches address these issues. While BC may outperform offline RL methods in specific scenarios, our contributions lie in providing a deeper understanding of the limitations of existing methods and proposing solutions that offer better generalization under broader conditions.

[1] "When Should We Prefer Offline Reinforcement Learning Over Behavioral Cloning?"

Q3 The notation is dense and overloaded, which made following the analysis difficult.

A3 We appreciate your feedback and understand that the dense notation and definitions may have made the paper challenging to follow. The definitions of the value function and Q-function in Lines 153-156 follow standard conventions in reinforcement learning studies. However, we acknowledge that presenting these concepts clearly and concisely is crucial to improving readability. Additionally, we have reviewed the language throughout the paper to improve clarity and fluency.

Q4 I'm unsure what the key contribution is. If a practitioner wanted to build algorithms based on the theoretical results it is, in my opinion, not clear where they should begin.

A4 Our main contributions are summarized in the Introduction Section (Lines 52-80). In essence, we prove why previous offline RL algorithms fail to generalize in the zero-shot generalization (ZSG) setting, and we propose two frameworks, PERM and PPPO, that are shown to achieve ZSG both theoretically and empirically.

To provide practical insights, we have implemented our proposed methods and demonstrated their effectiveness in practice. The implementation is based on the key idea of leveraging multiple value networks to capture variations across environments. Detailed descriptions of our experimental setups and results can be found in Section 6, which we hope can guide practitioners in applying our methods.

Q5 Empirically, our frameworks do not find near-optimal policy with ZSG empirically

A5 We have revised the statement in the abstract to clarify and ensure precision.

Q6 At test-time, how do you select which of the policies to use for an arbitrary unseen context?

A6 We respectfully think there may be some misunderstandings. First, in our IQL-nV implementation, we only have 1 policy. Therefore, we do not need to "choose" policy. Second, we keep $n$ value functions, which are only used for training, not for testing. During the testing, we only evaluate our policy but not the value function.

Q7 Minor feedbacks and typos.

A7 Thank you for your valuable suggestions. We have revised our paper accordingly.

Moreover, we have included the link to our code to reproduce the experiments in the revised abstract.

Again, we sincerely thank you for your time and constructive feedback. We hope our responses address your concerns, and we welcome any further questions or suggestions.

We sincerely appreciate your thoughtful feedback and positive remarks about our theoretical contributions and algorithms. Below, we address your concerns and provide clarifications.

Q1 Applying a pessimistic bias to counteract distributional shifts can lead to over-conservative policies that might underperform, particularly in environments where high-risk, high-reward actions are necessary.

A1 We have some discussions in Remark 8 about why pessimism could help generalization in our ZSG setting. In our framework, pessimism can indeed facilitate generalization, rather than hinder it. Specifically, we employ pessimism to construct reliable Q functions for each environment individually. This approach supports broader generalization by maintaining multiple Q-networks separately. By doing so, we ensure that each Q function is robust within its specific environment, while the collective set of Q functions enables the system to generalize across different environments. Furthermore, our theoretical results demonstrate that the proposed pessimistic approach balances caution and generalization effectively, making it well-suited for ZSG.

Q2 This paper’s methods also assume that each environment's context information and datasets are either directly available or accurately inferable, which limits the use cases from random sampled or mixed quality datasets.

A2 We respectfully believe there may be a misunderstanding regarding our assumptions. In our setting, context information is required only during training on the offline dataset and is not available during evaluation, nor is it assumed to be perfectly inferable. Furthermore, the offline dataset does not need to include exact context variables—only labels that distinguish trajectories collected from different environments ($1, 2, \dots, n$). These labels enable differentiation across environments without requiring explicit context values or high-quality datasets, thereby broadening the applicability of our approach.

Q3 The suboptimality bounds in the paper rely on having a large number of sufficiently varied environments, and may be loose in situations with fewer or more similar environments, and the policy may perform poorly in unseen contexts.

A3 We agree that the suboptimality bounds depend on the number of environments (n). Specifically, the $I_1$ terms in our bounds scale with $\sqrt{1/n}$, where $n$ is the number of different contextual MDPs with the context drawn from the same distribution $C$. Note that dependency is statistically unavoidable and aligns with standard generalization bounds in supervised learning, where generalization performance improves with more diverse training samples. Intuitively, if the number of samples is too small, we can not expect good generalization results.

Q4 Both PERM and PPPO involve parameters that adjust the degree of pessimism applied, where the sensitivity of them are not fully discussed.

A4 Thank you for this valuable suggestion. The degree of pessimism in our approach is controlled by the uncertainty quantifier $\Gamma$, as defined in Definition 5. A larger $\Gamma$ corresponds to a greater degree of pessimism. Ideally, $\Gamma$ should be chosen as the smallest value that satisfies the inequality in Line 266.

The impact of $\Gamma$ is reflected in the $I_2$ terms in Theorems 9 and 14, where the suboptimality gap scales with $\Gamma$. This indicates that an overly pessimistic uncertainty quantifier may degrade performance by unnecessarily increasing the suboptimality gap. Conversely, an appropriately tuned $\Gamma$ balances caution and generalization, ensuring reliable policy evaluation and improved performance.

Q5 PERM requires maintaining separate models or critic functions for each environment in the training set, which can quickly become computationally expensive as the number of environments grows. PPPO, while model-free, still requires multiple policies for different environments, which limits scalability when working with diverse and high-dimensional data.

A5 Thank you for highlighting these concerns. In our paper, we address the practical challenges of the theoretical algorithms with specific mitigations. Practically, we propose merging multiple data splits into a shared context, which leads to the development of the IQL-nV algorithm for our empirical evaluations (see Line 477 and subsequent discussion). Theoretically, we establish rigorous bounds for both PERM and PPPO after merging the datasets, as detailed in Remark 12, Remark 15, and Appendix C of the paper. These measures ensure that our approach remains both computationally feasible and scalable.

Q6 The selection of the baseline methods are not justified, why not compare the proposed methods with SOTA methods?

A6 We choose IQL since it is a well-known method with Markovian policy. In Mediratta et al. (2023), the SOTA methods for comparison are identified as BC, which we have indeed included in our experiments. Our results demonstrate that the variants of IQL proposed in our paper significantly enhance its performance, bringing it close to the level achieved by BC. The primary focus of our work is to explore the mechanisms for improving offline RL performance in a generalization setting. We chose IQL as a representative method because of its suitability for this investigation.

Again, thank you very much for reviewing our work and your positive comments. We are happy to provide further clarifications if needed.

Q5 How meaningful is the proposed objective of comparing to the best Markovian policy, and could a worst-case bound over contexts or an alternative setting involving history-dependent policies provide a more appropriate benchmark?

A5 First, we address this concern in Remark 1 (Lines 168–175), where we compare our setting with POMDPs and history-dependent policies. Our choice to focus on Markovian policies is motivated by their simplicity and practicality. The goal of this work is to provide a generalizable framework that extends existing offline RL methods, which primarily focus on Markovian policies (e.g., IQL), to address generalization across contexts. While history-dependent policies are an interesting and potentially powerful direction, they fall outside the scope of this work.

Second, regarding worst-case bounds, we clarify in Remark 2 (Lines 176–183) that such bounds are not achievable in the zero-shot generalization (ZSG) setting. This assertion is supported by prior work (Ye et al., 2023), which establishes lower bounds for the online RL setting. Since the offline RL setting is inherently more challenging, these lower bounds hold for our scenario as well. Consequently, our approach focuses on achievable objectives within the ZSG framework.

Finally, we are indeed studying the setting suggested in your comment, where context information is not accessible during evaluation and may not be explicitly included in the offline data. The only assumption we make is that the context distribution remains the same between training and evaluation. History-dependent policy could be more powerful, but it is beyond the scope of our current work and could be an exciting direction for future research.

Q6 The presence of an oracle for each individual dataset seems like a strong assumption. Could you elaborate on how one could implement the oracle and what kind of estimates would be feasiable for $\Gamma(s,a)$

A6 First, the assumption of an oracle for each individual dataset aligns with prior theoretical work in offline RL, such as Jin et al. (2021).

Second, for linear MDPs, we provide an explicit formula for instantiating the oracle, as detailed in Eq. (29) in Appendix D. This demonstrates how the oracle can be practically implemented in specific cases.

Finally, for general non-linear MDPs, we discuss feasible implementations in Remark 7 (Lines 281-284). A practical approach is to use bootstrapping techniques to estimate uncertainty, as in the Bootstrapped DQN method (Osband et al., 2016). We note that when the bootstrapping method is straightforward to implement, the assumption of having access to an uncertainty quantifier is reasonable.

Q7 For the counterexample CMDP in section 4, it seems unreasonable to expect the agent to do well on actions that are never observed. There would be no observed rewards for those actions so the agent has no information.

A7 We apologize for the confusion. First, we would like to clarify that the two MDP graphs in Figure 1 indeed share the same state-action space (i.e., they are components ${u,v}$ of the same cMDP). As a result, the data distribution $\mu$ effectively covers all the actions in the underlying MDP. Second, we emphasize that the data distributions $\mu_u$ and $\mu_v$ are derived from the near-optimal policy within each context. These distributions are almost entirely skewed toward the actions with maximum rewards in their respective contexts, which satisfies our assumptions and provides the agent with sufficient information about the maximum reward policies.

Q8 Why does Table 2 report the deterministic policy result for Miner instead of the stochastic policy variant, and would this not more fairly reflect the impact of stochastic versus deterministic policies relative to the additional value networks?

A8 We did not specifically optimize hyperparameters, including whether to use a stochastic or deterministic policy, for each individual game in Procgen due to the computational cost. Instead, we used a consistent set of hyperparameters across all games. While a stochastic policy performs better for the Miner dataset, it yields suboptimal performance when considering the entire collection of games. This is why, for the expert dataset, we adopt the stochastic policy to maximize overall performance, as detailed in Table 4, which outlines our hyperparameter selection process.

Regarding the difference between stochastic and deterministic policies, we emphasize that the choice is case-dependent. For instance, we use a deterministic policy for the mixed dataset, as shown in Table 4. Additionally, with respect to the number of value networks, Table 2 demonstrates that IQL-4V outperforms IQL with a deterministic policy for the mixed dataset, highlighting the utility of increasing the number of value networks.

Q9 Is the stochastic policy suggested in this work or is it a variant from previous works?

A9 The use of a stochastic policy has indeed been considered by Mediratta et al. (2023) as an important hyperparameter configuration. However, their application of the stochastic policy was limited to BC evaluation and was not utilized for IQL evaluation. In contrast, our work specifically suggests employing a stochastic policy for IQL with multiple value networks. This recommendation is based on our observation that it significantly enhances overall performance on expert datasets.

Q10 It would be more fair to compare to the 1V version which gets additional parameters to roughly match the ones of nV, n>1.

A10 Thank you for your insightful suggestion. Based on your feedback, we conducted an additional ablation study to explore your proposed scenario, where we implemented IQL-1V with a value network scaled to four times its original size. Namely, we increase the hidden dimension of the fully-connected layers of the value network from 256 to 1024 in the IQL-1V setting, ensuring that the total number of critic parameters matches that of IQL-4V. Below are the results for the Miner Expert dataset:

Interestingly, the results indicate that increasing the model size for the single value network (1V-SP with 4M parameters) actually degrades performance compared to the original IQL-1V setup. We hypothesize that this decline is likely due to overfitting caused by scaling the network without additional structural changes. This observation highlights the practical advantages of our multi-value network approach, which achieves better performance while mitigating overfitting risks.

Q11 Methods making use of ensembles of value networks have indeed been used to combat value overestimation issues in various works, any thoughts on parallels between these lines of work and the current one?

A11 Thank you for bringing up these works. It is worth noting that overestimation bias, as addressed in the cited studies, is a significant challenge in single-task reinforcement learning. While these methods focus on mitigating estimation bias, our use of an ensemble of value networks serves a complementary purpose. Specifically, we leverage the ensemble approach to enhance generalization across tasks, ensuring robust performance in diverse and challenging settings.

Q12 Typos

A12 We have fixed them in revision.

Again, we sincerely thank you for your time and constructive feedback. We hope our responses address your concerns, and we welcome any further questions or suggestions.

We sincerely thank you for your valuable feedback and suggestions. Our responses are as follows, which we hope could well address your concerns.

Q1 The context information is included in the offline dataset. But when the agent is evaluated (run in the environment), is the context information available then?

A1 The context information is only required during training on the offline dataset and is not available during evaluation in the environment. During training, the context information is used solely to group trajectories into different categories or environments. It is neither used as input nor relied upon during inference time.

Importantly, during training, we do not need the exact values of the context variables. Instead, labels indicating which trajectories belong to different environments ($1, 2, \dots, n$) are sufficient. These labels allow us to differentiate between environments without requiring explicit context values. This approach aligns with our goal of achieving generalization without dependence on direct context information.

Q2 Since the MDP can be arbitrarily different between contexts, how would it be possible to generalize to other contexts without any underlying structure?

A2 The contexts in our setting are drawn from the same distribution $C$ for both the offline training data and the testing evaluation. This shared distribution is essential for enabling generalization across contexts.

Our result does not explicitly depend on the size of the context set. Instead, it hinges on the covering number of the function class, as reflected in the $I_1$ term in equation (1) (line 321). This approach aligns with standard supervised learning theory, where generalization bounds depend on the complexity of the hypothesis space (e.g., VC-dimension or covering number) rather than the cardinality of the input space. This ensures that our method generalizes effectively even in cases where the number of contexts is large or infinite.

Q3 If the context variable is included in the dataset and we are only interested in Markovian policies, how is this different from augmenting the state with the context variables and using a standard offline RL algorithm?

A3 The context variables included in the dataset serve primarily as indicators to differentiate which task or environment each trajectory belongs to, rather than containing any semantic information. In our setting, context information is only required during training on the offline dataset and is not available during evaluation. Moreover, the offline dataset does not include explicit context variables but instead provides labels that differentiate trajectories collected from distinct environments. Since these labels do not correspond to explicit context variables, it is not feasible to augment the state with context information and directly apply standard offline RL algorithms.

Q4 Why is $V_{i-1,1}^\pi (x_1)$ not achievable? What does this mean?

A4 By stating that $V_{i-1,1}^\pi (x_1)$ is not achievable, we mean that it cannot be directly computed because the ground-truth transition dynamics of the environment are unknown. As a result, we rely on approximations. Specifically, we use a linear approximation method to iteratively update the value estimation based on the previous iteration's results. This approach aligns with standard techniques used in algorithms like PPO, where similar approximations are employed to estimate value functions in the absence of exact dynamics.