Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper studies a multi-product purchase problem. Authors design an optimal ranking policy when the online retailer can precisely model customers’ behaviors. Most of the existing work assume that each customer purchases at most one product and stops browsing immediately. This paper proposes a more realistic setting that customers view the product list sequentially and purchase a product when its utility exceeds a certain threshold with a certain purchase budget. In both non-contextual and contextual settings, they provide UCB-like algorithms and theoretically prove that the algorithms achieve \tilde{O}(\sqrt{T}) regrets in both settings.
strengths_and_weaknesses: Strengths: 
This paper considers a more practical setting where a single customer can make multiple purchases with certain purchase budget and attention span.
Theorem 4.1 provides a nice structure of the optimal ranking policy.
The study of this ranking problem is comprehensive. It studies both the non-contextual and contextual version.
The paper is nicely written.

Weaknesses:

Although the paper considers a more practical problem, it still has some limitations: the paper assumes that V_t follows the geometric distribution with parameter 1-q_t and B_t follows the geometric distribution with parameter 1-s_t. Each item costs one unit of budget.


questions: 1.	According to the purchase probability specified in Eq. (1), the purchase probabilities towards different products are independent of each other. How do you verify this assumption? Please also discuss the corresponding applications.

2.	Could you emphasize the major technical contribution of the online algorithm? For example, how does the analysis differ from the existing work? Which part of the single purchase problem cannot be used in this problem? If it can be emphasized before the main results, it will help to improve the paper.

3.	It is assumed that $V_t$ follows the geometric distribution with parameter 1-q_t and B_t follows the geometric distribution with parameter 1-s_t. I think Theorem 4.1 heavily relies on this assumption. Can the result be generalized to other distributions?

4.	In Section 5, two Theorems specify the regret upper bounds for both non-contextual and contextual problems. Could you also prove that they are both tight?

limitations: The attention span and the purchase budget are both limited to the geometric distribution. It would improve the paper if they can be generalized to other distributions.
review_title: null

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 authors study the problem of product ranking based on a more realistic situation where customers can have multiple purchases and continues viewing products even after buying a product, both being subject to an overall attention span and overall budget. They characterize the optimal ranking policy and design UCB-like algorithms with a provable \tildeO(\sqrt{T}) regret based on both contextual and non-contextual situations. They also show extensive experiments to prove their efficacy on the simulated and real-world datasets.

strengths_and_weaknesses: The paper is very well written (though with minor typos (see below)) and is quite easy to follow. The related work section throws good light into the existing literature on which this work is based. The thorough theoretical section is impressive and the results look good. 

The major comment is on the time complexity of the algorithms in practice. Section 4 shows the time complexity as O(N Log N). Please add a discussion on how Algorithms 1 and 2 can put into practice with similar time complexity and appropriate parallelization for each t. 

Minor typos:
1. Line 53, 314: rankling -> ranking
2. Line 210: management

questions: See above.
limitations: NA
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 problem of product ranking in the following setting (1) customers may purchase more than one product, and (2) customers quit after viewing/purchasing a certain number of products. They first characterize the optimal ranking policy when the customer parameters are known. The paper then investigates the case when customer parameters are unknown. Two UCB-like algorithms with O(\sqrt{T}) regrets are proposed, one for the non-contextual setting (i.e., all customers share the same parameters), and the other for the contextual setting (i.e., customers have personalized parameters). Finally, the effectiveness of the algorithms is tested by simulations. 

strengths_and_weaknesses: Strength:
The paper identifies some limitations of the previous literature and considers a setting that is an “intersection” of several previous setups (mainly Liang et al. (2021), Chen et al. (2021), and Cao and Sun (2019)), which makes their setting more general or realistic compared to each of the previous papers. The paper is complete in the sense that it investigates all the scenarios that have been previously considered (known parameter/non-contextual online setting/contextual online setting) and provides both theoretical analysis and experimental results. I did not check the whole proof, but the theoretical results seem solid and it seems non-trivial to derive the results in this new setting.

Weakness:
For the conceptual contribution, this is an incremental work based on several previous papers. The main concepts and ideas have appeared in previous literature. For the experimental result in the main text, the baselines are some previous methods that are designed under different assumptions. I am not sure how meaningful it is to compare these methods when the synthetic customer data are generated according to a new model. 

Disclaimer:
My evaluation of the theoretical contribution may not be accurate because I was not able to access the full pdf of Liang et al. (2021), which seems to contain quite similar results according to the outline. 
questions: 1. Could you briefly explain the technical challenges and contributions compared to Liang et al. (2021)?
limitations: Yes.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: The paper develops vanilla and contextual bandit approaches to maximize revenue given an unknown parametric customer that purchases multiple products.

strengths_and_weaknesses: One of the major issues with this paper is the extremely light and poor comparison with prior work that diminishes the key contributions. Firstly, multiple purchases have already been modeled in the OR literature that are similar to the MNL (e.g., see "Multi-Purchase Behavior: Modeling and Optimization" by Tulabandhula et al, "Assortment Optimization Under Multiple-Discrete Customer Choices" by Zhang et al, etc). Of course, some of these works focus on the revenue maximization problem in the offline setting. Given this context, the multiple purchase contribution looks like yet another model among this growing collection.

For the online setting, in the non-contextual case,there have been many works that follow the same template (define how the user parametrically interacts with a sequence of lists) such as "Thompson sampling for combinatorial semi-bandits" by Wang et al. and "Dynamic learning of sequential choice bandit problem under marketing fatigue" by Cao et al. Especially the latter work shows almost the same model (sans the budget constraint and multi purchase) with near identical results (characterization of the optimal solution in the offline known behavior case) and deriving regret bounds (albeit sparingly for the contextual case in this particular prior work). Given that this type of proof strategy is well known at this point, it is important to highlight what makes the construction of the algorithm and its analysis difficult. 

These two issues make one believe that the contributions are incremental and the authors should make an effort to highlight differences. 
questions: See above.
limitations: Yes.
review_title: null

Meta-review: metareview: The paper studies the problem of choosing a ranked list of products to show to consumers in a regret minimization model. Consumers are assumed to follow a certain search rule to purchase a subset of presented products, and the goal is to maximize the revenue of the product listing under this search model. The model makes certain assumptions of the previously studied models somewhat more realistic, for example, it allows the consumer to purchase more than one product. The main result is a UCB-like algorithm with the regret of O(sqrt(T)).

On the negative side: Even though the model claims to make the model more realistic than the other models previously studied in the literature, I still find the model quite stylized, and would not call it a practical model for capturing consumer behavior. For example, in the real world, one would expect the consumers to compare their options and take this comparison into account when selecting which item to purchase, whereas in this paper, the consumer makes a probabilistic decision on each item it sees independent of the other items (only conditioning on not having already purchased enough items). 

On the positive side, the paper solves a meaningful and non-trivial, though somewhat stylized problem, and the results are interesting, at least from a theoretical point of view. 

For these reasons, I'm leaning to accept this paper, if it fares well in comparison with other papers on the borderline. 
confidence: Less certain
Decision: Accept