__ Summary and Contributions__: This paper addresses the problem where the underlying generative process has a context component but the observation cannot be made for separated context.
Since the observed reward is an aggregation of context-wise rewards across different contexts, the paper proposes two different kernels which have additional modeling capability to explain the contributions of the reward of each context.
SAC assumes independence among context-wise rewards and LCE-A models dependencies between contexts via en embedding.

__ Strengths__: - The paper links a simple tweak of existing kernels and the interesting problem where the function varies depending on contexts, but context-wise function values are not directly observable.
- The characteristic of the ICM kernel using a single spatial kernel is well observed and effectively utilized in aggregated reward CPO.
- By sharing parameters of the kernel for context-wise reward function, this approach has less number of parameters compared to the naive approach. (This is clear for SAC, but the analysis is not performed for LCE-A. Can you also provide this?)
- In the ablation study, various aspects of the method are investigated.

__ Weaknesses__: - Even though it is motivated from the ICM kernel, Assumption 2, sharing a spatial kernel, relies on the quite strong assumption that policy-reward behaviors are quite the same across contexts. On the other hand, in experiment results, it seems that disadvantages from such strong assumption are recovered by the advantages from using data from all contexts to train the shared spatial kernel parameters, which may allow kernel parameters to receive more training signal and to avoid overfitting. Therefore, checking how robust LCE-A is when policy-reward behavior changes quite a lot across contexts would be an interesting ablation study.
- As LCE-A outperforms SAC quite consistently, LCE-A seems to the model of the choice. In contrast to SAC, including parameters of the embedding layer, the number of parameters in LCE-A can be larger than others. However, the complexity of LCE-A is not discussed.

__ Correctness__: - Both SAC kernel and LCE-M kernel are derived simply by computing covariance between functions with certain independence assumptions. All these follows from basic kernel construction and correctly derived.

__ Clarity__: 1. The main idea is simple and clear. The paper delivers the idea and details well enough to make it easy to follow.
2. Typo
Eq(3) : 'k^x(x,x')' -> 'k^x(x_c,x'_c')' ??

__ Relation to Prior Work__: Since the problem considered in this paper (aggregated rewards) has not been actively addressed, the difference made in the paper is quite clear.

__ Reproducibility__: Yes

__ Additional Feedback__:

__ Summary and Contributions__: [updated after rebuttal]
I have read the rebuttal and other reviews. As also pointed out my other reviewers, the technical novelty is somewhat limited. So I'm not increasing my score. However, I think this paper is more of a practical contribution, I'm convinced the experiments are robust and it can be applied in a real industrial setting. Therefore, I still vote for acceptance.
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this paper introduces a new problem, high-dim contexture policy search with unknown context-level rewards, and proposes to solve it using Bayesian optimization with advanced modeling techniques. The target function is a reward function, mapping from policy parameters to reward. Under different context, the optimal policy parameters are different. However, context-level rewards can not be observed. Instead, only aggreated reward can be observed resulting from a distribution of contexts. So we must perform aggregate optimization where the parameters of all contexts must be optimized jointly, hence its dimension num_context by num_parameters is high.
This work proposed two types of kernels, structural additive contextual (SAC) kernel and latent context embedding additive kernel (LCE-A). SAC assumes independence of the contexts and simply add up the kernels for each context weighted by the frequencies of the contexts. LCE-A learns an embedding of each context, then apply a kernel among contexts, and the context kernel and parameter kernel are multiplied and aggregated over all pairs of contexts. LCE-A is able to model the correlations among contexts.
Two types of experiments are conducted. One is on synthetic function Hartmann6, where 5 dimensions are treated as parameters, and 1 dimention is treated as context, discretized uniformly. The experimental results are reasonable, observing context-level reward and optimize the policy independently is much better than only observing aggregate rewards. When we can't observe context-level reward, the proposed methods are better than treating the aggregate reward function as a total black-box.
They also conduct a more "real" experiment optimizing adaptive video playback policy, the proposed methods are compared with a wide range of existing high-dim BO methods and LCE-A demonstrate the best performance.

__ Strengths__: a novel and interesting problem setting that can be applied in practical industrial A/B test problems.

__ Weaknesses__: there is not much technical novelty.

__ Correctness__: appears to be correct

__ Clarity__: the paper is well-written

__ Relation to Prior Work__: I would put this work in the context of a recent research topic known as grey-box BO, and discuss the relationship.

__ Reproducibility__: Yes

__ Additional Feedback__: the authors claim that the proposed methods work well for a variety of contextual policy optimization use-cases at a large internet firm, would it be possible to describe one or two examples in some details without breaking anonymity and confidentiality (if any)? E.g. what's the problem setting, what performance is achieved compared to what baseline, etc.
What are the embedding sizes for the LCE-A kernel? One thing I'm worried about is how did you learn a good embedding with only a few data points? The authors mentioned unsupervised pretraining in future work, which means there is no pre-train in this work.
How do you explain the abnormally large variance of two data points (C0 and C4) in Figure 6 (right).
one typo:
L285: "10 %" -> "10%"

__ Summary and Contributions__: This paper presents a couple of kernels to deal with contextual BO with an application of adaptive bitrate policy for video playback.

__ Strengths__: The empirical evaluation is strong. Although the numerical example is limited to a single function, and therefore, biased, the analysis is thoroughtly performed. The methods are also evaluated on a real problem, albeit simulated. The evaluation includes a comparison of many alternatives in the literature.

__ Weaknesses__: The theoretical contribution is minimal. LCE-M kernel is also a special case of a SoS kernel, with known embeddings. In fact, in can be seen as a reformulation of the Kcc kernel of ICM. The SAC kernel seem to be a variant of the integrated response methods, that has been previously applied in BO. See reference below.

__ Correctness__: The empirical evaluation is correct and the claims are reasonable.

__ Clarity__: The paper is well written and easy to follow

__ Relation to Prior Work__: Overall, the review of the state of art and related work is very thorough. However, I found the approach in section 3 very similar to the integrated responce methods in the EGO community. See for example and references therein: Tesch M, Schneider J, Choset H. Adapting control policies for expensive systems to changing environments. In2011 IEEE/RSJ International Conference on Intelligent Robots and Systems 2011 Sep 25 (pp. 357-364). IEEE.

__ Reproducibility__: Yes

__ Additional Feedback__: Update post-rebuttal:
As commented before, the operation research community has studied this problem before. I now understand the differences with Tesch et al. but the aggregated/averaged/integrated response has also been addressed before. For example in the references [20, 21] in Tesch et al. assume that you cannot observe the environment and that it is randomly selected. You can also find interesting the thesis of Brian J. Williams.
While the strategy presented here, specially for the LCE kernels, seems different, previous work should be addressed for a strong contribution.
For the presented application/motivation, I recommend the authors also to clarify why this strategy is better than a two step process, where you first measure the environment (network quality) and then, you solve for that context. As far as I know as an outsider, the latter is closer to current methods for ABR.
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The proposed method only affects the surrogate model via the kernel function. However, previous approaches on contextual/integrated approached had to also modify the acquisition function. For example, in Tesch et al, they found that the system focused on policies that performed well in "easy" contexts, but suboptimal in "difficult" context. Have this appeared in the experiments? Are context different enough to have easy/difficult contexts?
Are the embeddings E() known in advance for the experiments? Can they be learned or adapted? Would that be similar to learning the whole B matrix as in [6]?

__ Summary and Contributions__:
In this work authors study contextual policy optimization where the context rewards are not known. Gaussian process is used to model the reward. In contextual setting each context is treated as task. So multi-task GP is used to model reward in multiple contextual settings. The modeling of the covariance of the MTGP is done with context-parameter separable kernels . The authors explains their method with elaborate experiments.

__ Strengths__: 1.The paper introduces the contextual policy optimization with unknown context reward.
2. The paper focuses on real -world problem (adaptive bit rate) in contextual policy optimization setting.
3. The paper exploits reward -context separability to improve over the existing model.

__ Weaknesses__: Please see the comments.

__ Correctness__: The paper looks correct.

__ Clarity__: The paper is mostly well written. A section with problem statement would be helpful.

__ Relation to Prior Work__: The paper clearly states the relevant prior work in Bayesian optimization, Multi-task case and Contextual case.

__ Reproducibility__: Yes

__ Additional Feedback__: 1. The paper needs a problem statement section clearly explaining the problem and goal.
2. The concise description of the section 2 and 3 would be better.
3. In Section 2.1 for ICM , the paper states that matrix B is learned. What is the learning method and how well can it learned?
4. In section 2.2 for LCM, the dimension of the problem increases. As stated earlier that BO struggles with high dimension (>15). Then why LCM is used ?
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The authors have performed detailed experiments but I have found the theoretical contribution to be limited. This is not my area of work. So I am unsure of the impact of this work in this field. I am keeping my score the same.