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+This paper introduces a general framework to find a truthful, (approximately)
+revenue-maximizing combinatorial auction mechanism inside a given class of
+mechanisms. A typical situation where this is useful is when considering
+a parametrized class of mechanisms for which the optimal value of the parameter
+depends on the (unknown) distribution of bidders and thus needs to be learned.
+
+The framework is based on the general idea of random sampling, where we learn
+the optimal mechanism on a portion of the population but apply it to another
+portion. The main idea of the framework—which can be thought of as a way to
+make it more robust to variability in the bidders' population—is to first draw
+a set of participatory bidders and then learn on the complement set of bidders
+by repeatedly drawing samples of bidders from the complement set and finding
+a mechanism which maximizes revenue *on average* over the samples. The
+mechanism thus identified is then applied to the set of participatory bidders.
+
+In addition to the introduction of this general framework, the main
+contribution of the papers are:
+
+1. a general bound on the revenue of the mechanisms output by this method,
+   which depends on various parameters quantifying the complexity of the
+   auction class and the variability in the population of bidders.
+
+2. a specific instantiation of the framework to a new class of auctions
+   introduced by the authors, bundling-boosted auctions, for which it is
+   possible to quantify more finely the various parameters described in item 1.
+
+3. an algorithm to efficiently find the mechanism maximizing expected revenue
+   (as required by the framework) for sparse bundling-boosted auctions.
+
+Detailed comments
+=================
+
+The problem considered in this paper is important and the paper brings a nice
+unifying perspective to it by the introduction of a general framework and
+analysis of its performance through learning-theoretic complexity measures.
+Furthermore, the paper is very clear and nicely written (despite the sadly
+restrictive 7 page limit…).
+
+* an important feature of the framework, is that it completely gives up on
+  extracting any revenue from non-participatory bidders. While I understand
+  that this might be a necessary feature given the generality of the scheme,
+  some prior work partially avoid this loss, albeit in much more restrictive
+  settings. Maybe more could be said as a motivation about the trade-off
+  between generality of the scheme and how much revenue we can hope to extract.
+
+* relatedly, I was a bit surprised to see that the bounds on the revenue of the
+  scheme were expressed with respect to the efficient allocation on the entire
+  population. Why use this as a benchmark, as opposed to, for example, the
+  optimal revenue that could be obtained on the entire population? This might
+  be standard in this line of work but adding a sentence of two about this
+  choice might be helpful.
+
+* a drawback of the scheme, which again might be due to its generality is that
+  its guarantees depend of parameters which might be hard to compute or even
+  bound in practice. Although the authors try to explicitate them for specific
+  auction classes, they still remain somewhat opaque. This is particularly true
+  of the partition discrepancy quantity.
+
+* the scheme is reminiscent of the bootstrap method in statistics where
+  multiple samples are drawn with replacement from the same initial sample to
+  account for variability in the population. Maybe this could be mentioned
+  somewhere to connect the paper to the broader statistics/learning literature.