__ Summary and Contributions__: Motivated by the sensitivity of existing meta-RL methods to shifting task distributions, this paper introduces Model-Based Adversarial Meta RL (adMRL) which attempts to minimize the worst-case "sub-optimality gap" defined as the difference between the optimal return possible within the policy class and the return achieved after adaptation. The worst-case part is implemented using an optimization scheme that alternates between learning a dynamics model on a task and finding a task that is maximally suboptimal for the current model. The algorithm is applicable in a setting where all tasks share the same transition dynamics and different tasks have different reward functions with a known parametrization that is provided to the agent.

__ Strengths__: I think explicitly optimizing for the worst-case sub-optimality gap is an interesting idea. I have checked the derivation of the estimator for the gradient of the sub-optimality gap w.r.t. the task parameter which I believe is correct.

__ Weaknesses__: I think the paper is potentially misleading in its setting and choice of baselines. As I understand it, the method requires access to a task (or reward) parametrization, even at test time. I think this is an interesting and relevant setting but it is a very different setting from the regular meta-RL and I believe the comparisons to PEARL and MAML, which do not use this additional information, are not relevant. Furthermore the paper only acknowledges this in a footnote which could easily be missed on a cursory read. I think there should be a more prominent discussion of the setting and the applicability of the baselines.
In addition, as the authors note, even the zero-shot test performance is very good and further adaptation leads to almost no improvement on the tasks considered in this paper. This suggests to me that a multi-task policy with access to the task parameter would perhaps perform similarly zero shot. If that is the case then I think the chosen tasks are simple not informative in this setting. In any case, the multi-task policy seems like a substantially better baseline to me than PEARL or MAML.

__ Correctness__: I believe the derivation is correct. I think the empirical methodology is flawed (see above).

__ Clarity__: I think the paper would benefit from a clearer discussion of the specific setting that is assumed early in the paper. In general the paper is clearly written.

__ Relation to Prior Work__: As stated above I think the paper is not very explicit about how it differs from the standard meta-RL setting. I also would have liked to see more discussion about related work in non-meta RL (e.g. adversarial curricula, minimax formulations in multi-task RL, adversarial approaches to robust RL).

__ Reproducibility__: Yes

__ Additional Feedback__: Suggestions for improvement:
- Add multi-task baseline
- Consider alternative tasks (if zero-shot performance is almost perfect then this setting does not require adaptation)
- Consider alternative baselines that use the same information as AdMRL
- Improve discussion of the setting relative to meta-RL.
Minor comments and typos:
section 4.1:
- perhaps this section would be a little easier to follow if \hat{\theta} were replaced by \theta^{adapted} or \theta^{model}
- "unique maximizer under model dynamics": this assumption is likely invalid in most deep RL settings and it might be worth a short discussion.
page 3: line 109/110: tasks /policies are parameterized by parameters in subsets of R^k and R^p, respectively, not by the subsets themselves.
algorithm 1, line 12: I don't think the projection to the task parameter space is defined anywhere and in any case I think it could be omitted here in the interest of brevity
appendix B: line 464 "compute" -> "computing"
Meta review:
Having read the author feedback and other reviews, I am raising my score to marginally below acceptance threshold. The authors did address some of my concerns about baselines. However this was a substantial omission in the original paper since the other baselines (MAML, PEARL) receive less information and I am a little surprised that the MT baselines do not do better. I would prefer a full review of details and associated code to ensure that the MT baselines are well tuned.

__ Summary and Contributions__: The paper introduces a Model-based Meta-RL approach which minimizes the worst-case difference between the optimal return and the return achieved by the algorithm after adaptation at meta-test time. The approach formalizes a minimax objective which alternates between learning a dynamics model on a task and finding an adversarial task for the current model. In order to find an adversarial task for the given model, the approach assumes a parameterized task setup, which then allows in computing the gradient of suboptimality with respect to the task parameters. Finally, the paper demonstrates that this approach is able to adapt substantially faster than other model-free and model-based meta-learning baselines.
-------- Post-rebuttal --------
I have read the other reviews and the authors' rebuttal. The rebuttal does clarify the questions that I had raised in my review.
Looking at the new baseline (MT) added by the authors in the rebuttal, it seems to contradict the intuitions that I have. I would have expected this baseline to match AdMRL, but it seems to be producing a poorer empirical performance -- this raises a few more questions which needs to be discussed.
So, my score remains unchanged.

__ Strengths__: The authors have motivated the problem and have empirically evaluated the approach on standard MuJoCo benchmarks. Furthermore, they have compared against existing meta-learning baselines. The idea of formalizing the meta-learning problem as a minimax objective is unique, which is key for adapting to adversarial task distributions at meta-test time. As far as I can tell, the results are significant and would be appealing to the wider RL community.

__ Weaknesses__: The idea of using the minimax objective to drive the model-learning and meta-learning is intuitive. In its current form, the approach requires access to the optimal performance that can be achieved by a policy in the given task. However, the other baselines such as PEARL and MAML do not have access to such an oracle, which I think makes their empirical results in Section 5.1 unfair. Furthermore, assuming access to such an oracle may not be possible in many RL domains. It would be useful and would strengthen the paperif the authors could add some discussion about these points.

__ Correctness__: The claims, method and the empirical methodology are correct.

__ Clarity__: The paper is clear and well-written.

__ Relation to Prior Work__: The authors do a good work of consolidating and discussing the prior work in the domain of model-based RL and in meta-learning.

__ Reproducibility__: Yes

__ Additional Feedback__: Overall, the paper is clear and is well-motivated. The approach is intuitive and simple to understand. It is also fairly novel in meta-RL.
I have a few questions regarding the current version of the paper.
1. Would AdMRL outperform by a huge margin if the other baselines (PEARL and MAML) were modified to utilize the optimal return that can be achieved by a policy in the given MDP?
2. Could AdMRL provide faster adaptation at test-time if some other proxy metrics are used in the minimax objective as opposed to the optimal return for a given task? Have the authors considered other candidates for this, and if so, would it be possible to discuss some of them?
3. Would the code for AdMRL be open-sourced? The algorithm for computing gradients with respect to the task parameters is interesting and would be helpful for future research.
4. How much further away are the dynamics models learned by AdMRL, MB-Unif and MB-Gauss against the true environment dynamics? This would be a useful metric to report in addition to the visualizations provided in Figure 4.

__ Summary and Contributions__: This paper proposed Model-based Adversarial Meta-Reinforcement Learning (AdMRL). AdMRL takes the non-distributional approach and can address the distribution shift issue of meta-RL. AdMRL formulates a minimax problem, minimizing the sub-optimality gap over the parameterized dynamics and maximizing it over the parameterized tasks.
Experiments show superior performance compared to MAML and PEARL.
The proposed approach can be practically very useful with broad impacts. However, the strong assumption of differentiable reward functions limits the scope of its applications.

__ Strengths__: * Novel framework AdMRL. Integrating multiple practical alternatives into a complex theoretical framework is nontrivial.
* Consistent good performance with less tasks and samples than the SOTA baselines.

__ Weaknesses__: The strong assumption on differentiable reward functions.
It would be better to show the effects of each design choice although they are quite intertwined.

__ Correctness__: Yes

__ Clarity__: It's well written. The notation might be improved, sometimes confusing.

__ Relation to Prior Work__: Yes, very clearly positioned among related work.

__ Reproducibility__: Yes

__ Additional Feedback__:

__ Summary and Contributions__: The paper proposes a model-based meta learning algorithm that aims for learning a model that can robustly adapt to new rewards not seen during training. The key idea in this paper is to optimize a dynamics model such that the worst-case suboptimality gap (difference between policy from the model and policy from the actual dynamics) is minimized. The authors demonstrate that by learning a model that optimizes the worst-case suboptimality gap, it can achieve more robust behavior when testing on the training rewards, and is reported to generalize better to unseen reward functions.
The main contributions of the paper are the novel algorithm of optimizing the worst-case suboptimality gap for better generalization, as well as the derivation of the reward parameter gradient for optimizing the objective over the reward functions.

__ Strengths__: The proposed idea of optimizing the worst-case suboptimality gap with a model-based approach seems novel and solid. The experiments in general support the effectiveness and correctness of the method. I think the work can potentially inspire future research on devising generalizable meta-rl algorithms and the proposed way of computing the reward parameter gradient using implicit function theorem can be potentially useful in different situations.

__ Weaknesses__: The paper currently has limited results on the generalization ability of the method. More analysis on this could be helpful. Also, the current proposed method assumes a fixed dynamics, which may limit its applicability to more general transfer learning problems.

__ Correctness__: The claims, method, and the empirical methodology seem correct to me.

__ Clarity__: The paper is well written.

__ Relation to Prior Work__: Yes.

__ Reproducibility__: Yes

__ Additional Feedback__: After reading the other reviews and the authors' rebuttal, I have increased my score to 7. The additional experiments are greatly appreciated, but I think more details should be provided for them: e.g. what algorithms were used to train the MT-joint baseline? I feel that if the policy has all the necessary information and is trained with a model-free approach, it should be able to obtain comparable or better result than a model-based approach (with much worse sample complexity, of course). That being said, the comparison between model-based and model-free methods is not the focus of the work and the experiments with model-based baselines do show good results.
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I think the paper presents an interesting idea for improving the robustness of model-based rl method to different reward functions. I have a few questions regarding the details of the algorithm, as listed below.
1. The Advantage function used in Eq. 4 in my understanding is the advantage for the original dynamics, however according to Alg 1, what’s available would be the advantage for the learned dynamics. Since it’s for the zero-shot policy, wouldn’t that incur error in the advantage function?
2. In the comparison with the model-based methods, how are the experiments done? Is it equivalent to Algorithm 1 without the task parameter optimization?
3. Since the reward function is assumed to be parameterized, it would potentially be easier to train a policy using model-free methods with the reward function parameters as part of the input instead of using meta-learning algorithms like MAML. It would be interesting to see some comparisons with this strategy.