Recent advances have shown that sequential fine-tuning (SeqFT) of pre-trained vision transformers (ViTs), followed by classifier refinement using approximate distributions of class features, can be an effective strategy for class-incremental learning (CIL). However, this approach is susceptible to distribution drift, caused by the sequential optimization of shared backbone parameters. This results in a mismatch between the distributions of the previously learned classes and that of the updated model, ultimately degrading the effectiveness of classifier performance over time. To address this issue, we introduce a latent space transition operator and propose Sequential Learning with Drift Compensation (SLDC). SLDC aims to align feature distributions across tasks to mitigate the impact of drift. First, we present a linear variant of SLDC, which learns a linear operator by solving a regularized least-squares problem that maps features before and after fine-tuning. Next, we extend this with a weakly nonlinear SLDC variant, which assumes that the ideal transition operator lies between purely linear and fully nonlinear transformations. This is implemented using learnable, weakly nonlinear mappings that balance flexibility and generalization. To further reduce representation drift, we apply knowledge distillation (KD) in both algorithmic variants. Extensive experiments on standard CIL benchmarks demonstrate that SLDC significantly improves the performance of SeqFT. Notably, by combining KD to address representation drift with SLDC to compensate distribution drift, SeqFT achieves performance comparable to joint training across all evaluated datasets.

In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the prediction performance of models. Some existing estimators and regularizers attempt to achieve unbiased estimation to improve the predictive performance. However, variances and generalization bound of these methods are generally unbounded when the propensity scores tend to zero, compromising their stability and robustness. In this paper, we first theoretically reveal that limitations of regularization techniques. Besides, we further illustrate that, for more general estimators, unbiasedness will inevitably lead to unbounded variance. These general laws inspire us that the estimator designs is not merely about eliminating bias, reducing variance, or simply achieve a bias-variance trade-off. Instead, it involves a quantitative joint optimization of bias and variance. Then, we develop a systematic fine-grained dynamic learning framework to jointly optimize bias and variance, which adaptively selects an appropriate estimator for each user-item pair according to the predefined objective function. With this operation, the generalization bounds and variances of models are reduced and bounded with theoretical guarantees. Extensive experiments are conducted to verify the theoretical results and the effectiveness of the proposed dynamic learning framework.

Cross-Domain Sequential Recommendation (CDSR) methods aim to tackle the data sparsity and cold-start problems present in Single-Domain Sequential Recommendation (SDSR). Existing CDSR works design their elaborate structures relying on overlapping users to propagate the cross-domain information. However, current CDSR methods make closed-world assumptions, assuming fully overlapping users across multiple domains and that the data distribution remains unchanged from the training environment to the test environment. As a result, these methods typically result in lower performance on online real-world platforms due to the data distribution shifts. To address these challenges under open-world assumptions, we design an Adaptive Multi-Interest Debiasing framework for cross-domain sequential recommendation (AMID), which consists of a multi-interest information module (MIM) and a doubly robust estimator (DRE). Our framework is adaptive for open-world environments and can improve the model of most off-the-shelf single-domain sequential backbone models for CDSR. Our MIM establishes interest groups that consider both overlapping and non-overlapping users, allowing us to effectively explore user intent and explicit interest. To alleviate biases across multiple domains, we developed the DRE for the CDSR methods. We also provide a theoretical analysis that demonstrates the superiority of our proposed estimator in terms of bias and tail bound, compared to the IPS estimator used in previous work. To promote related research in the community under open-world assumptions, we collected an industry financial CDSR dataset from Alipay, called "MYbank-CDR". Extensive offline experiments on four industry CDSR scenarios including the Amazon and MYbank-CDR datasets demonstrate the remarkable performance of our proposed approach. Additionally, we conducted a standard A/B test on Alipay, a large-scale financial platform with over one billion users, to validate the effectiveness of our model under open-world assumptions. Code and dataset are available at https://github.com/WujiangXu/AMID.

Inspired by the successive relaxation method, a novel discounted iterative adaptive dynamic programming framework is developed, in which the iterative value function sequence possesses an adjustable convergence rate. The different convergence properties of the value function sequence and the stability of the closed-loop systems under the new discounted value iteration (VI) are investigated. Based on the properties of the given VI scheme, an accelerated learning algorithm with convergence guarantee is presented. Moreover, the implementations of the new VI scheme and its accelerated learning design are elaborated, which involve value function approximation and policy improvement. A nonlinear fourth-order ball-and-beam balancing plant is used to verify the performance of the developed approaches. Compared with the traditional VI, the present discounted iterative adaptive critic designs greatly accelerate the convergence rate of the value function and reduce the computational cost simultaneously.

In recent years, the application of function approximators, such as neural networks and polynomials, has ushered in a new stage of development in solving optimal control problems. However, considering the existence of approximation errors, the stability of the controlled system cannot be guaranteed. Therefore, in view of the prevalence of approximation errors, we investigate optimal tracking control problems for discrete-time systems. First, a novel value function is introduced into the intelligent critic framework. Second, an implicit method is utilized to demonstrate the boundedness of the iterative value functions with approximation errors. An explicit method is applied to prove the stability of the system with approximation errors. Furthermore, an evolving policy is designed to iteratively tackle the optimal tracking control problem and demonstrate the stability of the system. Finally, the effectiveness of the developed method is verified through numerical as well as practical examples.

In recent years, semi-supervised graph learning with data augmentation (DA) has been the most commonly used and best-performing method to improve model robustness in sparse scenarios with few labeled samples. However, most existing DA methods are based on the homogeneous graph, but none are specific for the heterogeneous graph. Differing from the homogeneous graph, DA in the heterogeneous graph faces greater challenges: heterogeneity of information requires DA strategies to effectively handle heterogeneous relations, which considers the information contribution of different types of neighbors and edges to the target nodes. Furthermore, over-squashing of information is caused by the negative curvature formed by the non-uniformity distribution and the strong clustering in a complex graph. To address these challenges, this article presents a novel method named HG-MDA (Semi-Supervised Heterogeneous Graph Learning with Multi-Level Data Augmentation). For the problem of heterogeneity of information in DA, node and topology augmentation strategies are proposed for the characteristics of the heterogeneous graph. Additionally, meta-relation-based attention is applied as one of the indexes for selecting augmented nodes and edges. For the problem of over-squashing of information, triangle-based edge adding and removing are designed to alleviate the negative curvature and bring the gain of topology. Finally, the loss function consists of the cross-entropy loss for labeled data and the consistency regularization for unlabeled data. To effectively fuse the prediction results of various DA strategies, sharpening is used. Existing experiments on public datasets (i.e., ACM, DBLP, and OGB) and the industry dataset MB show that HG-MDA outperforms current SOTA models. Additionally, HG-MDA is applied to user identification in internet finance scenarios, helping the business to add 30% key users, and increase loans and balances by 3.6%, 11.1%, and 9.8%.

Multi-task learning (MTL) is widely used in the online recommendation and financial services for multi-step conversion estimation, but current works often overlook the sequential dependence among tasks. In particular, sequential dependence multi-task learning (SDMTL) faces challenges in dealing with complex task correlations and extracting valuable information in real-world scenarios, leading to negative transfer and a deterioration in the performance. Herein, a systematic learning paradigm of the SDMTL problem is established for the first time, which applies to more general multi-step conversion scenarios with longer conversion paths or various task dependence relationships. Meanwhile, an SDMTL architecture, named Task-Aware Feature Extraction (TAFE), is designed to enable the dynamic task representation learning from a sample-wise view. TAFE selectively reconstructs the implicit shared information corresponding to each sample case and performs the explicit task-specific extraction under dependence constraints, which can avoid the negative transfer, resulting in more effective information sharing and joint representation learning. Extensive experiment results demonstrate the effectiveness and applicability of the proposed theoretical and implementation frameworks. Furthermore, the online evaluations at MYbank showed that TAFE had an average increase of 9.22% and 3.76% in various scenarios on the post-view click-through & conversion rate (CTCVR) estimation task. Currently, TAFE is deployed in an online platform to provide various traffic services.

In this article, to solve the optimal tracking control problem (OTCP) for discrete-time (DT) nonlinear systems, general value iteration (GVI) scheme and online value iteration (VI) algorithms with novel value function are discussed. First, the disadvantage of the traditional value function for the OTCP is presented and the novel value function is introduced. Second, we analyze the monotonicity and convergence of GVI and establish the admissibility condition of GVI to evaluate the admissibility of the current iterative control. Note that a novel approach is introduced to analyze the admissibility. Third, based on the attraction domain, improved control policies with online VI can be obtained by judging the location of the current tracking error and reference point. Finally, the stability of the online VI-based control system is guaranteed. Besides, we provide two simulation examples to show the performance of the proposed methods.

In this article, the generalized N -step value gradient learning (GNSVGL) algorithm, which takes a long-term prediction parameter λ into account, is developed for infinite horizon discounted near-optimal control of discrete-time nonlinear systems. The proposed GNSVGL algorithm can accelerate the learning process of adaptive dynamic programming (ADP) and has a better performance by learning from more than one future reward. Compared with the traditional N -step value gradient learning (NSVGL) algorithm with zero initial functions, the proposed GNSVGL algorithm is initialized with positive definite functions. Considering different initial cost functions, the convergence analysis of the value-iteration-based algorithm is provided. The stability condition for the iterative control policy is established to determine the value of the iteration index, under which the control law can make the system asymptotically stable. Under such a condition, if the system is asymptotically stable at the current iteration, then the iterative control laws after this step are guaranteed to be stabilizing. Two critic neural networks and one action network are constructed to approximate the one-return costate function, the λ -return costate function, and the control law, respectively. It is emphasized that one-return and λ -return critic networks are combined to train the action neural network. Finally, via conducting simulation studies and comparisons, the superiority of the developed algorithm is confirmed.

This article puts emphasis on the deterministic value-iteration-based$Q$-learning (VIQL) algorithm with adjustable convergence speed, followed by the application verification on trajectory tracking for completely unknown nonaffine systems. It is worth emphasizing that, under the effect of learning rates, the convergence speed can be adjusted and the new convergence criterion of the VIQL framework is investigated. The merit of the adjustable VIQL scheme is that it can quicken the learning speed and decrease the number of iterations, thereby reducing the computation burden. To carry out the model-free VIQL algorithm, the offline data of system states and reference trajectories are collected to provide the reference control, the tracking error, and the tracking control, which promotes the parameter updating of the adjustable VIQL algorithm via the off-policy learning scheme. By this updating operation, the convergent optimal tracking policy can guarantee that arbitrary initial state tracks the desired trajectory and can completely obviate the terminal tracking error. Finally, numerical simulations are conducted to indicate the validity of the designed tracking control algorithm.

Multi-Target Cross Domain Recommendation(CDR) has attracted a surge of interest recently, which intends to improve the recommendation performance in multiple domains (or systems) simultaneously. Most existing multi-target CDR frameworks primarily rely on the existence of the majority of overlapped users across domains. However, general practical CDR scenarios cannot meet the strictly overlapping requirements and only share a small margin of common users across domains. Additionally, the majority of users have quite a few historical behaviors in such small-overlapping CDR scenarios. To tackle the aforementioned issues, we propose a simple-yet-effective neural node matching based framework for more general CDR settings, i.e., only (few) partially overlapped users exist across domains and most overlapped as well as non-overlapped users do have sparse interactions. The present framework mainly contains two modules: (i) intra-to-inter node matching module, and (ii) intra node complementing module. Concretely, the first module conducts intra-knowledge fusion within each domain and subsequent inter-knowledge fusion across domains by fully connected user-user homogeneous graph information aggregating. By doing this, the knowledge of all users, especially the non-overlapping users, could be well extracted and transferred without relying heavily on overlapping users. The second module introduces user-item matching to complement the potential missing interactions for each user and correct his/her under-represented representations, especially for the users with observed sparse interactions. Essentially, companion objectives are also inserted into each module to guide the knowledge transferring procedures, which leads to positive effects on multiple domains simultaneously. Extensive experiments on four multi-target CDR tasks from both public and real-world large-scale financial industry datasets demonstrate the remarkable performance of our proposed approach. Our code is publicly available at the link: https://github.com/WujiangXu/NMCDRR.

In online recommendation, financial service, etc., the most common application of multi-task learning (MTL) is the multi-step conversion estimations. A core property of the multi-step conversion is the sequential dependence among tasks. However, most existing works focus far more on the specific post-view click-through rate (CTR) and post-click conversion rate (CVR) estimations, which neglect the generalization of sequential dependence multi-task learning (SDMTL). Additionally, the performance of the SDMTL framework is also deteriorated by the interference derived from implicitly conflict information passing between adjacent tasks. In this paper, a systematic learning paradigm of the SDMTL problem is established for the first time, which can transform the SDMTL problem into a general MTL problem with constraints and be applicable to more general multi-step conversion scenarios with stronger task dependence. Also, the distribution dependence relationship between adjacent task spaces is illustrated from a theoretical point of view. On the other hand, an SDMTL architecture, named Task Aware Feature Extraction (TAFE), is developed to enable dynamic task representation learning from a sample-wise view. TAFE selectively reconstructs the implicit shared information corresponding to each sample case and performs explicit task-specific extraction under dependence constraints. Extensive experiments on offline public and real-world industrial datasets, and online A/B implementations demonstrate the effectiveness and applicability of proposed theoretical and implementation frameworks.

In this article, evolving and incremental value iteration (VI) frameworks are constructed to address the discrete-time zero-sum game problem. First, the evolving scheme means that the closed-loop system is regulated by using the evolving policy pair. During the control stage, we are committed to establishing the stability criterion in order to guarantee the availability of evolving policy pairs. Second, a novel incremental VI algorithm, which takes the historical information of the iterative process into account, is developed to solve the regulation and tracking problems for the nonlinear zero-sum game. Via introducing different incremental factors, it is highlighted that we can adjust the convergence rate of the iterative cost function sequence. Finally, two simulation examples, including linear and nonlinear systems, are conducted to demonstrate the performance and the validity of the proposed evolving and incremental VI schemes.

In this article, a novel value iteration scheme is developed with convergence and stability discussions. A relaxation factor is introduced to adjust the convergence rate of the value function sequence. The convergence conditions with respect to the relaxation factor are given. The stability of the closed-loop system using the control policies generated by the present VI algorithm is investigated. Moreover, an integrated VI approach is developed to accelerate and guarantee the convergence by combining the advantages of the present and traditional value iterations. Also, a relaxation function is designed to adaptively make the developed value iteration scheme possess fast convergence property. Finally, the theoretical results and the effectiveness of the present algorithm are validated by numerical examples.

In this article, a novel neuro-optimal tracking control approach is developed toward discrete-time nonlinear systems. By constructing a new augmented plant, the optimal trajectory tracking design is transformed into an optimal regulation problem. For discrete-time nonlinear dynamics, the steady control input corresponding to the reference trajectory is given. Then, the value-iteration-based tracking control algorithm is provided and the convergence of the value function sequence is established. Therein, the approximation error between the iterative value function and the optimal cost is estimated. The uniformly ultimately bounded stability of the closed-loop system is also discussed in detail. Moreover, the iterative heuristic dynamic programming (HDP) algorithm is implemented by involving the critic and action components, where some new updating rules of the action network are provided. Finally, two examples are used to demonstrate the optimality of the present controller as well as the effectiveness of the proposed method.

For discounted optimal regulation design, the stability of the controlled system is affected by the discount factor. If an inappropriate discount factor is employed, the optimal control policy might be unstabilizing. Therefore, in this article, the effect of the discount factor on the stabilization of control strategies is discussed. We develop the system stability criterion and the selection rules of the discount factor with respect to the linear quadratic regulator problem under the general discounted value iteration algorithm. Based on the monotonicity of the value function sequence, the method to judge the stability of the controlled system is established during the iteration process. In addition, once some stability conditions are satisfied at a certain iteration step, all control policies after this iteration step are stabilizing. Furthermore, combined with the undiscounted optimal control problem, the practical rule of how to select an appropriate discount factor is constructed. Finally, several simulation examples with physical backgrounds are conducted to demonstrate the present theoretical results.

In this article, the general value iteration (GVI) algorithm for discrete-time zero-sum games is investigated. The theoretical analysis focuses on stability properties of the systems and also the admissibility properties of the iterative policy pair. A new criterion is established to determine the admissibility of the current policy pair. Besides, based on the admissibility criterion, the improved GVI algorithm toward zero-sum games is developed to guarantee that all iterative policy pairs are admissible if the current policy pair satisfies the criterion. On the basis of the attraction domain, we demonstrate that the state trajectory will stay in the region using the fixed or the evolving policy pair if the initial state belongs to the domain. It is emphasized that the evolving policy pair can stabilize the controlled system. These theoretical results are applied to linear and nonlinear systems via offline and online critic control design.

This article is concerned with the stability of the closed-loop system using various control policies generated by value iteration. Some stability properties involving admissibility criteria, the attraction domain, and so forth, are investigated. An offline integrated value iteration (VI) scheme with a stability guarantee is developed by combining the advantages of VI and policy iteration, which is convenient to obtain admissible control policies. Also, based on the concept of attraction domain, an online adaptive dynamic programming algorithm using immature control policies is developed. Remarkably, it is ensured that the state trajectory under the online algorithm converges to the origin. Particularly, for linear systems, the online ADP algorithm with a general scheme possesses more enhanced stability property. The theoretical results reveal that the stability of the linear system can be guaranteed even if the control policy sequence includes finite unstable elements. The numerical results verify the effectiveness of the present algorithms.

In this paper, through event-triggered approach, the constrained near-optimal control problem for a class of nonlinear discrete-time systems is investigated and solved by heuristic dynamic programming (HDP) technique. The proposed method can reduce the amount of computation remarkably without deteriorating the system stability. In order to overcome the control constraints and reduce the computational burden, a nonquadratic performance index is introduced. Then, stability analysis of the event-triggered system with control constraints and an event-triggered constrained controller design algorithm are given. Three neural networks are used in the HDP scheme, which are designed to identify the unknown nonlinear system, approximate value function, and control law, respectively. In the model neural network, an effective method is developed to initialize its weights. Finally, two examples are included to demonstrate the present method.