Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper studies posted-price auctions for ROI-constrained value
maximizing bidders, who seek to maximize their total value subject to
the condition that the return-on-investment (ROI) on their spend is at
least some prespecified ratio. This is in contrast to
utility-maximizing bidders who seek to maximize their total utility
(value - spend). Past results have shown that in the
utility-maximizing case, using an anonymous posted price mechanism can
achieve a (1/2) approximation of the welfare (or revenue). The current
paper shows that if personalized prices are allowed, the same (1/2)
approximation continues to hold. However, the paper presents instances
where the no anonymous posted price mechanism can achieve an
approximation ratio on welfare greater than 0.483. Furthermore, the
authors show that the using the optimal anonymous posted price
mechanism for the utility-maximizing case obtains a (1/2) (1- 1/e)
approximation of the optimal welfare. The authors also relate their
results to prior-independent dynamic auctions and combinatorial
auctions.

strengths_and_weaknesses: The paper extends the results for utility-maximizing bidders to
value-maximizing bidders with ROI constraints, an approach common in
online advertizing. The results are obtained by directly reducing the
analysis to that in the utility-maximizing case using personalized
prices.

The authors construct explicit instances where anonymous posted-prices
achieve strictly less than (1/2) approximation to welfare, though a
tight characterization for this setting is missing.

The authors also provide a tight characterization in the
value-maximizing setting for the usual anonymous posted price
mechanism used in the utility-maximizing setting.

questions:  For the combinatorial auctions setting, the proof of Proposition~7
uses the factthat the welfare is at least as large as the max of
revenue and buyers' utility. For the welfare to be at least as large
as the revenue, the implicit assumption that the ROI is equal to 1 is
required. Does the same (1/4) guarantee hold for general ROI, or does
the guarantee deteriorate?

limitations: None
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper studies the price of anarchy / efficiency in auctions for ROI-constrained value-maximizing bidders. More specifically it studies posted-price types of auctions. First, it states that an approximation ratio of $\frac{1}{2}$ when non-anonymized posted-prices are possible as it can be reduced to finding posted-prices for utility-maximizing buyers, which is a solve problem. Then, it shows that when using an anonymized posted-price, the approximation ratio is upper-bounded by 0.479. After, it shows that an approximation ratio of $\frac{1}{2}(1-1/e)$ can be obtained with the same allocation as for utility-maximizing buyers. Finally, it provides a $\frac{1}{4}$ approx ratio guarantee when valuations are non-additive.
strengths_and_weaknesses: 1. I find Prop. 1 (or 4) is strait-forward: one can write the lagrangian version of the buyer optimization problem between lines 147-148 and observe that choosing $q = \frac{p \lambda^*}{1+\lambda^*}$ where $\lambda^*$ is the optimal lagrange multiplier leads to the optimization problem of a utility-maximizing buyers faced with price $q$. It does not feel like a hugely novel result.

2. I'm not a big fan of Sec. 5. The mechanism has a prior-dependent / non-measurable parameter $p^*$ and the section shows it can be tracked using an adapted sequence of parameters $p_t$ by discretizing its support and running a multi-armed bandit. In my mind, the real challenge about removing prior-dependence is to do so without introducing incentives for the buyers to lie. It's not clear to me that buyers wouldn't be incentivized to lie here, as accepting a price at time $t$ influences the price they get in the future (see [1,2] or [3] for a survey).

3. My main concern about the paper is the strength of the claims. The main results are Th. 3 and 4 in my opinion, but the gap between the upper and the lower bound is large.

[1] Repeated contextual auctions with strategic buyers, Amin et al 2014
[2] Characterizing Truthful Multi-armed Ban- dit Mechanisms, Babaioff et al 2014
[3] Learning in repeated auctions, Nedelec et al 2022
questions: I know the paper I'm going to refer to has been published right before NeurIPS submission deadline, so I only put this as a question. Recent results showed that approximation ratios better than $\frac{1}{2}$ can be attained with randomized VCG [4]. Do you think similar ideas could help improve the efficiency of posted-price auctions ?

[4] Auction Design in an Auto-bidding Setting: Randomization Improves Efficiency Beyond VCG. Mehta 2022.
limitations: I don't have many suggestions on the form of the paper as I find it particularly well-written and easy to read. 

I'd say if authors want to "thicken" the content, they can look towards randomized posted-prices as it seems to be the promising direction for such problems.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper studies the posted price auctions for ROI constrianed value maximizers. Personalized posted prices are shown to be equivalent to posted price auctions for utility maximizers. For anonymous posted prices, a mechanism is provided, proving to be $\frac12(1-1/e)$ approximation. The mechanism is further a to applied prior-independent mechanism with constant approximation, and extended to combinatorial auctions with submodular / XOS agents.
strengths_and_weaknesses: Strengths:
1. The studied problem, auction designs for value maximizers, is important and attracts much attention in the field of auctions recently. The paper is probably one of the first few papers on posted price auctions for value maximizers. 
2. Concrete theoretical results are provided. Most proofs, as far as I checked, are corrected. 
3. The paper is clearly written and well organized.

Weaknesses:
One proof is not fully justified. See questions.
questions: In the proof of Proposition 4 (Line 193), why the construction satisfy the condition $p\geq \mathbb{E}_{v\sim D}[v]$?
limitations: Not applicable.
review_title: null

Meta-review: metareview: This paper got uniformly positive reviews. That said, reading into the actual text of the reviews, it is evident that the results are not as strong as one might like. The biggest limitation is that the result rely heavily on personalized pricing for reducing the problem to one of utility maximization for utility maximizers; posted prices are often not a very attractive approach in practice.
confidence: Less certain
Decision: Accept