Submitted by Assigned_Reviewer_1
Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The paper presents a new algorithm for global optimization that avoids deltacover sampling and that achieves exponential regret, generalizing this way the work of Freitas el al., 2012 that relies on an impractical sampling procedure.
The paper is well written and is easy to follow and the role of the new algorithm within the current literature of boundedbased search methods is well explained. In this sense, I think that this work deserves some attention from the community.
I vote 5, however, a not a better score because I think that the experimental section is below the standard of what one expect to see in a BO paper. My main critics to this section are:
 The authors do no compare the methods for multiple initial evaluations of *f* as it is the standard in BO methods. Therefore no meaningful statical comparison of the methods can be obtained.
 Although they propose a boundedbased search method, the authors should compare they results with state of the art of BO approaches. Information theoretic approaches, such as, Entropy Search, are not used in the experiments.
 All the experiments are carried out in synthetic functions (whose maximum dimension is 6). No real wetlab of parameter tuning experiment is used to illustrate the performance of the method in real scenarios.
Q2: Please summarize your review in 12 sentences
The paper presents a new global optimization algorithm that avoids deltacover sampling and that achieves exponential regret. The paper is nice, with some interesting theoretical results but in my opinion the experimental section is below the standards of NIPS paper.
Submitted by Assigned_Reviewer_2
Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The paper presents a variant of Bayesian Global Optimization where future samples are generated through a space/interval partitioning algorithm.
Using UCB, this avoids the (internal) global optimization problem of how to choose the next sample.
Theoretical analysis shows that the approach yields theoretical improvements (exponential regret), thereby improving over previous work.
The algorithm is clearly described and explained/illustrated with an example.
The paper makes a novel contribution and is overall clearly presented.
I have one reservation with this paper.
The experimental results seem to be only for 1D test functions (not explicitly stated).
I suspect that the interval partitioning approach does not scale well to higher dimensions (hyperrectangles) because the "resolution" would be required to grow exponentially.
The approach is related to the wellknown DIRECT algorithm, which is known to suffer badly when the dimensionality of the problem increases.
I think something at least needs to be said about this in the paper.
It does not change the theoretical contribution but is clearly significant for any practical purposes.
Minor comments:
p.2, UCB is considered "for brevity".
Does this mean you could do something with expected improvement, for example?
I got the feeling it had to be UCB.
p.3 "...we simultaneously conduct global and local searches based on all the candidates of the bounds."
I couldn't understand this statement.
p.4 "At n=16, the far right...but no function evaluation occurs."
Can you say why for clarity?
Q2: Please summarize your review in 12 sentences
The paper presents a variant of Bayesian Global Optimization where future samples are generated through a space/interval partitioning algorithm, which yields theoretical improvements (exponential regret).
The work appears sound and novel but seems to be only evaluated on 1D test problems.
Submitted by Assigned_Reviewer_3
Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
The paper describes a method of Bayesian global optimization which does not require dcover sampling or auxiliary optimization.
The paper is organized such that the main contributions of the paper are well described in the main section.
The authors provide a good illustrative example of the algorithm in section 3.2, which gives the reader a nice high level understanding.
Section 3.3 also clearly communicates the workings of the algorithm programmatically for future implementation/replication.
Experimental results as well prove to be quite exciting.
Additionally, the authors note that the paper brings together ideas from the Bayesian global optimization literature that do and do not use continuity estimation.
Q2: Please summarize your review in 12 sentences
The paper describes InfiniteMetric GP Optimization (IMGPO), an algorithm for Bayesian optimization without the need for auxiliary optimization or dcover sampling.
The paper is not only clearly written, but provides a strong contribution to the NIPS community.
Submitted by Assigned_Reviewer_4
Q1: Comments to author(s). First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. (For detailed reviewing guidelines, see http://nips.cc/PaperInformation/ReviewerInstructions)
(light review) Abstract formulation is redondant l49 the function l72 misplaced parenthesis
Q2: Please summarize your review in 12 sentences
Being unfamiliar with GP and global optimization, the reviewer's evaluation is an educated guess.
The paper is well written and rather didactic, making good use of graphs to explain the procedures. Both theoretical and experimental results seem to conclusively demonstrate the advantage of the authors' approach.
Q1:Author
rebuttal: Please respond to any concerns raised in the reviews. There are
no constraints on how you want to argue your case, except for the fact
that your text should be limited to a maximum of 5000 characters. Note
however, that reviewers and area chairs are busy and may not read long
vague rebuttals. It is in your own interest to be concise and to the
point.
== Reviewer 1 == Thank you for the comments.
Please note that we did compare our algorithm with the most closely
related stateoftheart algorithms (SOO and BaMSOO). Also, we used
standard benchmark test functions taken from the global optimization
literature.
Thank you for pointing out that many other experimental
results in Bayesian optimization are reported with random initial
evaluations. Based on that suggestion, we reran our experiments and found
that, under those conditions, our algorithm actually performs better
compared to the stateoftheart methods.
For evaluation on a
nonsynthetic function, we are now successfully using our algorithm to
optimize the parameters of a filtering algorithm (based on RKHS embedding
of probability densities). We would be able to report these results in a
final version of the paper.
== Reviewer 2 == Thank you for
the comments. Please note that we evaluated our algorithm with 1D  6D
test functions (not just 1D test functions). Because the dimensionality of
each test function was indicated only in the figure title, it could have
been confusing, so we have now added that information in the text as
well.
For the concern regarding the input dimensionality, please
see the last section of this feedback, titled ``== Input Dimensionality
==''.
== Reviewer 4 == Thank you for the comments. We have
revised the results by showing the average performance as suggested. The
relative performances across the algorithms stayed the same. Indeed, it
produced more preferable results for our algorithm. We agree with the
comment on the log regret in Figure 2. Ideally, we should show the results
in both scales, but we followed the convention that has been used in
previous work.
For the concern regarding the input dimensionality,
please see the last section of this feedback, titled ``== Input
Dimensionality ==''.
For the real parameter tuning, we are now
successfully using our algorithm to optimize the parameters of a filtering
algorithm (based on RKHS embedding of probability).
== Reviewer
5 == Thank you for the comments.
== Reviewer 6 == Thank
you for the comments. We revised the paper accordingly.
==
Input Dimensionality == As reviewer 2 suggests (and reviewers 1 and 3
imply), scaling up to high dimensions is a key issue in Bayesian
optimization in general. However, unlike DIRECT type algorithms, our
algorithm is as good (bad) as GPUCB in terms of scaling up to higher
dimensions. While the required ``resolution'' of the partitioning may
suffer badly from the curse of dimensionality, the required number of the
function evaluations grows similarly to GPUCB. This is because while
refining the ``resolution'' of the partitioning, the function evaluations
are avoided due to the UCB computed by GP. Notice that a typical BO
algorithm has more serious problems in terms of the resolution required
without the function evaluations in auxiliary optimization.
The
dimensionality of the test functions used in this paper does not directly
reflect limitations of our approach. We simply tested our algorithm with
convenient standard benchmark functions in the related global optimization
literature. It would be interesting to see how it works with moderate
dimensionality. For higher dimensions, if we can assume ``effective
dimensionality'', our approach could be applied by simply using random
projection (Wang et al., 2013: Bayesian Optimization in High Dimensions
via Random Embeddings) or learn it with Bayesian inference. A more
ambitious approach would be to use a partitioning strategy that suffers
much less from the curse of dimensionality.
We would add a refined
version of the above discussion regarding input dimensionality to a final
paper version, subject to overall space
constraints.
