Restricted Boltzmann Machine-driven Interactive Estimation of Distribution Algorithm for personalized search

Abstract

Effective and efficient personalized search is one of the most pursued objectives in the era of big data. The challenge of this problem lies in its complex quantifying evaluations and dynamic user preferences. A user-involved interactive evolutionary algorithm is a good choice if it has reliable preference surrogate and powerful evolutionary strategies. A Restricted Boltzmann Machine (RBM) assisted Interactive Estimation of Distribution Algorithm (IEDA) is presented to enhance the IEDA in solving the personalized search. Specifically, a dual-RBM module is developed to simultaneously provide a preference surrogate and a probability model for conducting the individual selection and generation of the IEDA. Firstly, the positive and negative preferences of the currently involved user in IEDA are distinguished and combined to achieve a dual-RBM, and then the weighted energy functions of the RBM model together with social group information from users with similar preferences are designed as the preference surrogate. The probability of the trained positive RBM on the visible units is fetched as the reproduction model of EDA since it reflects the attribute distributions of more preferred items. Some benchmarks from the Movielens and Amazon datasets are applied to experimentally demonstrate the superiority of the proposed algorithm in improving the efficiency and effectiveness of the interactive evolutionary computations served personalized search.

Introduction

The task of personalized search is to find items that meet a user’s specific (can be changeable) preferences or requirements, therefore, its nature is an optimization problem. Evolutionary algorithms (EAs) will be effective on solving this problem supposing the user’s preferences or intentions can be explicitly expressed with accurate mathematical models. Unfortunately, such an assumption is hard to be satisfied even if the user’s preference is very certain and clear, not to mention the changeable scenarios.

The optimized objective of personalized search is based on users’ qualitative evaluation, comparison and decisions with their experiential knowledge and preferences, i.e., it is subjective, variable and fuzzy compared with traditional mathematically defined objectives. Accordingly, traditional optimization methods as well as various successful nature-inspired EAs for explicitly defined mathematical functions are no longer applicable. It is of practical significance to develop suitable EAs to effectively solve personalized search problems.

In the family of EAs, interactive evolutionary computations (IECs) are powerful for optimizing problems with qualitative objectives and expected to be effective for the personalized search [1], [2], [3]. In the past decades, fruitful studies on IECs have been devoted to alleviate users’ evaluation burdens in the evolutionary process, especially for complicated optimization tasks. The corresponding work can be classified into three groups: (1) Designing friendly interfaces, e.g., changing continuous evaluation mode to a discrete or fuzzy number ones [2], [4]; (2) enhancing evolutionary operators to accelerate the evolution process, e.g., Chen et al. [5] presented a Bayesian model based IEC to effectively reduce initial decision space according to the historical search; (3) developing surrogate or learning assisted IECs to quantitatively approximate the preference or evaluation of a given user on a candidate, i.e., in such IECs, the fitness function of the qualitative objective is estimated to drive the evolutionary operations as traditional ones [4], [5], [6]. We here try to effectively solve the personalized search with surrogate-assisted IECs since they have been successfully applied to some complex design and multi-objective decision problems.

Surrogate assisted IECs are similar to that of EAs. A user is required to first evaluate some individuals along with the evolutionary search, and these individuals together with the evaluated scores are used to train or build a model to approximate the user’s preferences. Then, the model is applied as a fitness surrogate in the subsequent evolution process, and the user only needs to revise few wrongly evaluated estimations by the surrogate. The model will be managed or updated when the user finds that the estimation is far from his/her preferences. Clearly, the surrogate building, including data collection, model selection and training, is critical for developing a reliable surrogate assisted IEC [7], [8], [9]. Model selection and training have been greatly attracted in various applications. Sun et al. [1] presented a semi-supervised learning based surrogate when the training data of interactive genetic algorithms are difficult to be sufficiently collected in handling complicated design problems. Pan et al. [8] proposed a classification-based surrogate to improve interactive decisions when using many-objective EA for numerically defined expensive optimization problems. Integrating parallel computing with surrogate-based EAs, Akinsolu et al. [10] proposed a parallel surrogate assisted algorithm to enhance the mutation operators of differential evolution for electromagnetic design. We also used probabilistic conditional preference network as a surrogate for personalized book search [11]. As for collecting the training data, only few studies have been developed. Chen et al. [5] presented a Bayesian induced interactive Estimation of Distribution Algorithm (IEDA) for personalized laptop search, in which users’ interactive time is used to construct an RBF-based surrogate model. Tian et al. [12] articulated granularity into a surrogate building to effectively collect the training data with relatively smaller computation cost when solving high-dimensional expensive optimization problems.

These surrogate-assisted EAs are effective on solving quantitatively or qualitatively defined complex problems. They endeavor to construct/manage the surrogate model with supervised or semi-supervised learning methods with evaluated individuals, and then use the model to approximate the individual fitness to perform evolutionary operators. The following three deficiencies of the exiting algorithms can be concluded. (1) A given user must provide initial interactions for constructing a surrogate, no matter by explicit or implicit ways, which inevitably conflicts with the motivation of alleviating user fatigue. To address this problem, unsupervised learning-based surrogates are more helpful and expectable. (2) The relationship among the evolutionary operators and the surrogate has rarely been considered, i.e., the information implicated in the surrogate construction may be valuable to strengthen the performance of the operators. (3) The intrinsic preference features of a user hidden in his/her historical interactions can greatly benefit to accurately reveal the user’s preferences, however, which has not been concerned even such a technology has been well developed and used in personalized recommendation. Therefore, integrating the achievement of user interest model in personalized recommendation into surrogate-assisted IECs will greatly improve the performance of personalized search.

As for using an unsupervised learning model to construct a surrogate and further capturing the relationship among the evolutionary operators and the surrogate, we presented a Restricted Boltzmann Machine (RBM)-based Estimation of Distribution Algorithm (EDA) for complex numerical problems [13]. In this algorithm, EDA is first performed for some generations on real problems to obtain the training data, and then RBM is trained with those better individuals (without using specific fitness values). Both the probability model of EDA and the fitness function are simultaneously fetched from the trained RBM, i.e., the joint probability of the visible layer in RBM is calculated as the probability model in EDA for population reproduction, and the energy function of the RBM is used to estimate the individual fitness of the optimized complex problem. Experimental results demonstrate its superior in effectively reducing computational complexity and improving the accuracy of fitness estimation. Inspired by these results, we here further study an unsupervised RBM surrogate-assisted IEC for personalized search since it figures out the shortages in existing surrogate-based ECs.

With regard to extract the intrinsic features of a user’s preference, many interest models used in personalized recommendation will provide valuable references [14], [15], e.g., Bayesian model [16], [17], Factorization Machine [18], [19], Multilayer Perceptron [20], [21], RBM [22], [23], Autoencoder model [24], [25], Convolutional Neural Network (CNN) [26], [27]. Rendle et al. [16] presented a Bayesian learning method for personalized ranking by maximizing the posterior estimator. In this method, the training data are grouped into evaluated items and unrated ones as positive and negative information. Cheng et al. [20] proposed a Wide & Deep learning based interest model by jointly training wide linear models and deep neural networks (DNN) to combine the benefits of memorization and generalization for recommendation. Kim et al. [26] presented a novel context-aware recommendation model, called as Convolutional Matrix Factorization (ConvMF), which makes full use of the positive and negative preferences to combine CNN with probabilistic matrix factorization for improving the prediction accuracy. Zhou et al. [28] proposed an attention-based user behavior modeling framework, which effectively integrates all of users’ historical interactive behaviors. However, these models have not been well combined with the IEC process to further effectively improve the personalized evolutionary search.

Motivated by our previous work, we here expand it to interactive personalized search and present a dual-RBM-assisted IEDA by articulating interest model construction with historical interactive behaviors. The RBM-based surrogate in [13] is first enhanced by modifying it into a dual-module one according to the grouped historical information for precisely extracting the user preference features. After the dual-module RBM is trained, the probability model of EDA will be constructed using the critical features of the positive RBM. The surrogate for estimating the fitness of the searched items is ultimately obtained by using the energy functions of the RBMs. The probability and surrogate models will be applied in IEDA to effectively find the satisfied $TopN$ items for the current user. Adequate experiments on typical real-world datasets demonstrate that the proposed algorithm can effectively not only enhance the performance of the personalized search but also alleviate users’ evaluation burdens to improve user experiences in the searching process.

Accordingly, the main contributions of our work are as follows: (1) A dual-RBM module is presented by constructing two related RBM models, i.e., positive and negative ones. These two models are trained with dominant and inferior items evaluated by the current user to accurately track the user preference features. The module is then used to define the probability model and fitness surrogate for EDA; (2) the reproduction probability model of EDA for generating more preferred individuals is defined based on the probability of the visible layer in the positive RBM model by sufficiently using the positive preference features and effectively impairing the impacts of the negative ones; (3) the fitness surrogate is obtained by not only weighting the energy functions of the positive and negative RBM models but also social group knowledge.

The remainder of the paper is organized as follows. Section 2 introduces the notations of our study and the related preliminary work. The proposed dual RBM-driven IEDA is addressed in detail in Section 3. Section 4 presents the comparative experiments and corresponding experimental analysis. The conclusion is finally followed.