The next-basket recommendations are a well-studied problem in the academic field. As a rule, we want to predict top-K goods that might be added to the last known basket of the user based on the previous purchase history. However, the existing studies do not take into account that each user can be limited by the amount of money. Therefore, clients of online websites might be interested in the opportunity to receive personal recommendations with a given fixed cost. For example, we can take the average spending over the history of customer's purchases as an upper bound. In this article, we consider addressing the problem of making next-basket recommendations with set total cost restrictions.
(M. Ananyeva)
1234-5678-9012 (M. Ananyeva)
= { ,1 , … , ,| | }.
It is implied, that any recommender model can be used to obtain these scores, which is beyond our scope. Also, we obtain a list of items prices = { 1, … , | | }. For each user, we have a true basket with some purchased items in the last transaction ,
= { ,1 , … , ,| | } where || is a number of goods in the last purchased basket. The aim is to predict items in , ̂ , = { ,̂1 , … , ,̂
with a -length recommendations }. is a total cost for a user . We generate the list based on the restrictions for each user: of the used total cost in recommended baskets. The second histogram presents the distribution of the number of recommended items. The line graph presents Recall@k w.r.t. diferent k values both for the classical NBR problem and the proposed next-basket with constraints task.
=1
=1
∑ , →
∑ , <
(
However, a few remarks are required here. Usually, we have no information on how many items || a customer will add to the next cart. To overcome this problem, we can generate the lists ̂
, for diferent values and select
those that maximize the equation (
Also, the parameter can be varied by the user in real-time. The user can change the thresholds of the total cost and select the best option with personal recommendations.
We use a genetic algorithm in order to find the optimal ,̂ . The generated populations of multi-hot vectors with size from the most relevant items ,
= { ,1 , … , , }
for each user. The -th component of a generated
vector (gene of a chromosome) is supposed to be equal to
1 and the corresponding -th element of the
recommendations list will be included to the final predictions. If
the condition (
otherwise. Therefore, the
genetic algorithm will maximize (
[1, 2] Ta-Feng dataset1, which is extensively used in recommender systems.
It includes purchase history of goods with given pricing. Users in the Ta-Feng dataset can purchase diferent quantities of the same goods. Nonetheless, we will consider proposing a product based on the dataset’s average price. Furthermore, we assume that the recommendations cannot contain duplicates, which means that each item can only be suggested once and in a single occurrence. We employ the same data preparation strategy as in TIFU-KNN [1] to evaluate our approach, and we use a leave-one-basket [3] scenario.
Experiment Settings.
value can be chosen by the researchers. For instance, we could predict the total cost of the last known basket for each user or vary the values of
across some range on a dataset.
In particular, it is possible to calculate the average basket cost from the training set for each user and take this aggregated statistic as a constraint. In our case, equals the true cost of the last basket ∑ , customer. It approximates the case when the customer
of each knows exactly how much he is can aford or is willing to spend.
We adopt the genetic algorithm, using the implementation from the open-source framework geneticalgorithm22. For solving this task on the Ta-Feng dataset, we use only the 20 most relevant items and population 1https://www.kaggle.com/datasets/chiranjivdas09/ta-feng-grocerysize of 40 vectors. PersonTopFreq approach is applied reward, and the conditions for buying the entire bundle as a recommender model that returns the most popular or only certain items from it are open. In addition, the items from the baskets of all users, demonstrating the diferent cases which allow a user to add or delete an high performance in TIFU-KNN [1]. Also, we use nega- item allow the platforms to make a user-friendly intertive ranks of items as , because negativity is needed for face with updates in recommendations in real time. In maximizing the of items included in the final predic- particular, after each customer’s action with the basket, tions. Application of other recommendation approaches the recommended bundle of items can be recalculated for the next basket task is left for future work. entirely or iteratively, by replacing each added or deleted
Performance Comparison. Figure 1 (a) shows the item with a new item of the same price in order not average rate of the used total cost, which is quite close to exceed the total price. Finally, we could use bundle to the cost of the basket from the testing sample. In this recommendations in the ofline experiments as baseline graph, all predicted baskets with a higher total cost are solutions or adapt them to this formalized task. neglected. The costs of most collected baskets are close Approaches. Instead of genetic algorithms, we could to and satisfy the user’s needs. also try to adopt a graph-based A* algorithm, integer pro
Figure 1 (b) demonstrates the number of goods that gramming, or knapsack problem with dynamic programwere included in the baskets, which is close to the Gaus- ming techniques to address the problem of generating sian distribution. next-basket recommendations with a total cost constraint.
Figure 1 (c) compares the values of Recall@k w.r.t. the Still, some open issues should be discussed. For instance, diferent values for two cases. The results when we should the sum of relevance scores be equal to the total recommend only top-k relevant items are in green. The relevance score and be constrained by the lower bound Recall@k values with top-k items with the total cost re- of relevance or not? What are the reasonable restrictions strictions from the 20 most relevant items are in blue. for relevance scores considering their diferent ranges There is no extreme diference between the two meth- of values, negative and positive scores from the recomods observed, but our recommendations fit additional mender algorithms? These are only a few examples of restrictions in the TCANBR scenario. open questions.
Total Cost values. In this paper, we suggested a way to set a total cost value. However, we could think of 4. Discussion predicting the total cost for each user, for example, using linear regression or other machine learning models. In During the discussion panel of this brainstorming ides, user cases, when the customer updates the maximum that took place at the 5th Workshop on Online Recom- afordable cost, we can take this value in real-time and use mender Systems and User Modeling (Seattle, WA, USA, it on the inference step. Otherwise, we could also think of 2022)3, we can summarize the open issues and several using the segments of customers instead of personalized future directions for future work. values of the total cost. For example, the customers with
Additional constraints. Taking into account the for- low, medium, and high income and three diferent values malization problem mentioned above, we could think of for this constraint correspondingly. additional restrictions that can be applied to bring the so- Item quantity. One of the problems, which we nelution closer to real conditions. Firstly, we could extend glect for the simplicity, is the challenge to take into acto the lower and upper bounds of the price for recom- count the diferent quantities for each item in the lists of mended items. It can either be set as hyperparameters recommendations. In case we want to add this additional or as extra constraints in our task. It would help to solve restriction to the task, we should think carefully about a problem of making the list of recommendations only how to include this constraint and optimize the function. with cheap or expensive items. Secondly, we could extend We also should think about whether we allow duplicated the task to introducing the profit margins, which both items. For example, the milk, but of diferent brands and customers and enterprises pursue considering business prices. In addition, some items could be bought always metrics. in single pieces, but some others are taken in multiple
Bundle recommendations. Considering the fact that pieces or are the goods sold by weight. In our case, we we want to generate a list of recommended items, we implied no duplicates and only 1 allowed piece of each might think about it as bundle recommendations. In par- item for simplicity. ticular, it could enhance the diversity or complementarity The list of problems mentioned above is not exhaustive of predicted items. Thus, the approaches for bundle rec- and can be continued and developed into comprehensive ommendations could also bee used to solve the task of versions of formalization task and be addressed by diferconstrained recommendations with total cost. However, ent approaches. the questions on how to evaluate the bundle, attribute the
In this article, we briefly introduced a formalization problem of the next-basket constrained recommendations problem. The tested approach simulates a case when a customer of an online marketplace can spend a particular upper bound of the amount of money. Alternatively, some online services can fit the recommendations into a suggested budget for each user. This problem task suggests generating item recommendations that do not exceed the specified maximum total cost.