Sen Lin

Sen Lin, Peizhong Ju, Yingbin Liang et al.

Continual learning (CL), which aims to learn a sequence of tasks, has attracted significant recent attention. However, most work has focused on the experimental performance of CL, and theoretical studies of CL are still limited. In particular, there is a lack of understanding on what factors are important and how they affect "catastrophic forgetting" and generalization performance. To fill this gap, our theoretical analysis, under overparameterized linear models, provides the first-known explicit form of the expected forgetting and generalization error. Further analysis of such a key result yields a number of theoretical explanations about how overparameterization, task similarity, and task ordering affect both forgetting and generalization error of CL. More interestingly, by conducting experiments on real datasets using deep neural networks (DNNs), we show that some of these insights even go beyond the linear models and can be carried over to practical setups. In particular, we use concrete examples to show that our results not only explain some interesting empirical observations in recent studies, but also motivate better practical algorithm designs of CL.

Sen Lin, Daouda Sow, Kaiyi Ji et al.

Bilevel optimization has become a powerful tool in a wide variety of machine learning problems. However, the current nonconvex bilevel optimization considers an offline dataset and static functions, which may not work well in emerging online applications with streaming data and time-varying functions. In this work, we study online bilevel optimization (OBO) where the functions can be time-varying and the agent continuously updates the decisions with online streaming data. To deal with the function variations and the unavailability of the true hypergradients in OBO, we propose a single-loop online bilevel optimizer with window averaging (SOBOW), which updates the outer-level decision based on a window average of the most recent hypergradient estimations stored in the memory. Compared to existing algorithms, SOBOW is computationally efficient and does not need to know previous functions. To handle the unique technical difficulties rooted in single-loop update and function variations for OBO, we develop a novel analytical technique that disentangles the complex couplings between decision variables, and carefully controls the hypergradient estimation error. We show that SOBOW can achieve a sublinear bilevel local regret under mild conditions. Extensive experiments across multiple domains corroborate the effectiveness of SOBOW.

Peizhong Ju, Sen Lin, Mark S. Squillante et al.

Transfer learning is a useful technique for achieving improved performance and reducing training costs by leveraging the knowledge gained from source tasks and applying it to target tasks. Assessing the effectiveness of transfer learning relies on understanding the similarity between the ground truth of the source and target tasks. In real-world applications, tasks often exhibit partial similarity, where certain aspects are similar while others are different or irrelevant. To investigate the impact of partial similarity on transfer learning performance, we focus on a linear regression model with two distinct sets of features: a common part shared across tasks and a task-specific part. Our study explores various types of transfer learning, encompassing two options for parameter transfer. By establishing a theoretical characterization on the error of the learned model, we compare these transfer learning options, particularly examining how generalization performance changes with the number of features/parameters in both underparameterized and overparameterized regimes. Furthermore, we provide practical guidelines for determining the number of features in the common and task-specific parts for improved generalization performance. For example, when the total number of features in the source task's learning model is fixed, we show that it is more advantageous to allocate a greater number of redundant features to the task-specific part rather than the common part. Moreover, in specific scenarios, particularly those characterized by high noise levels and small true parameters, sacrificing certain true features in the common part in favor of employing more redundant features in the task-specific part can yield notable benefits.

Sen Lin, Li Yang, Deliang Fan et al.

By learning a sequence of tasks continually, an agent in continual learning (CL) can improve the learning performance of both a new task and `old' tasks by leveraging the forward knowledge transfer and the backward knowledge transfer, respectively. However, most existing CL methods focus on addressing catastrophic forgetting in neural networks by minimizing the modification of the learnt model for old tasks. This inevitably limits the backward knowledge transfer from the new task to the old tasks, because judicious model updates could possibly improve the learning performance of the old tasks as well. To tackle this problem, we first theoretically analyze the conditions under which updating the learnt model of old tasks could be beneficial for CL and also lead to backward knowledge transfer, based on the gradient projection onto the input subspaces of old tasks. Building on the theoretical analysis, we next develop a ContinUal learning method with Backward knowlEdge tRansfer (CUBER), for a fixed capacity neural network without data replay. In particular, CUBER first characterizes the task correlation to identify the positively correlated old tasks in a layer-wise manner, and then selectively modifies the learnt model of the old tasks when learning the new task. Experimental studies show that CUBER can even achieve positive backward knowledge transfer on several existing CL benchmarks for the first time without data replay, where the related baselines still suffer from catastrophic forgetting (negative backward knowledge transfer). The superior performance of CUBER on the backward knowledge transfer also leads to higher accuracy accordingly.

Yung-Fu Chen, Sen Lin, Anish Arora

We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that efficiently and scalably learn routing policies that are local, i.e., they only consider node states and the states of neighboring nodes. Remarkably, one of these DNNs we train learns a policy that exactly matches the performance of greedy forwarding; another generally outperforms greedy forwarding. Our algorithm design exploits network domain knowledge in several ways: First, in the selection of input features and, second, in the selection of a ``seed graph'' and subsamples from its shortest paths. The leverage of domain knowledge provides theoretical explainability of why the seed graph and node subsampling suffice for learning that is efficient, scalable, and generalizable. Simulation-based results on uniform random graphs with diverse sizes and densities empirically corroborate that using samples generated from a few routing paths in a modest-sized seed graph quickly learns a model that is generalizable across (almost) all random graphs in the wireless network model.

Sheng Yue, Guanbo Wang, Wei Shao et al.

This work aims to tackle a major challenge in offline Inverse Reinforcement Learning (IRL), namely the reward extrapolation error, where the learned reward function may fail to explain the task correctly and misguide the agent in unseen environments due to the intrinsic covariate shift. Leveraging both expert data and lower-quality diverse data, we devise a principled algorithm (namely CLARE) that solves offline IRL efficiently via integrating "conservatism" into a learned reward function and utilizing an estimated dynamics model. Our theoretical analysis provides an upper bound on the return gap between the learned policy and the expert policy, based on which we characterize the impact of covariate shift by examining subtle two-tier tradeoffs between the exploitation (on both expert and diverse data) and exploration (on the estimated dynamics model). We show that CLARE can provably alleviate the reward extrapolation error by striking the right exploitation-exploration balance therein. Extensive experiments corroborate the significant performance gains of CLARE over existing state-of-the-art algorithms on MuJoCo continuous control tasks (especially with a small offline dataset), and the learned reward is highly instructive for further learning.

Li Yang, Sen Lin, Fan Zhang et al.

Inspired by the success of Self-supervised learning (SSL) in learning visual representations from unlabeled data, a few recent works have studied SSL in the context of continual learning (CL), where multiple tasks are learned sequentially, giving rise to a new paradigm, namely self-supervised continual learning (SSCL). It has been shown that the SSCL outperforms supervised continual learning (SCL) as the learned representations are more informative and robust to catastrophic forgetting. However, if not designed intelligently, the training complexity of SSCL may be prohibitively high due to the inherent training cost of SSL. In this work, by investigating the task correlations in SSCL setup first, we discover an interesting phenomenon that, with the SSL-learned background model, the intermediate features are highly correlated between tasks. Based on this new finding, we propose a new SSCL method with layer-wise freezing which progressively freezes partial layers with the highest correlation ratios for each task to improve training computation efficiency and memory efficiency. Extensive experiments across multiple datasets are performed, where our proposed method shows superior performance against the SoTA SSCL methods under various SSL frameworks. For example, compared to LUMP, our method achieves 12\%/14\%/12\% GPU training time reduction, 23\%/26\%/24\% memory reduction, 35\%/34\%/33\% backward FLOPs reduction, and 1.31\%/1.98\%/1.21\% forgetting reduction without accuracy degradation on three datasets, respectively.

Mahdi Kazemi, Aftab Hussain, Md Rafiqul Islam Rabin et al.

This work investigates the application of Machine Unlearning (MU) for mitigating the impact of trojans embedded in conventional large language models of natural language (Text-LLMs) and large language models of code (Code-LLMs) We propose a novel unlearning approach, LYA, that leverages both gradient ascent and elastic weight consolidation, a Fisher Information Matrix (FIM) based regularization technique, to unlearn trojans from poisoned models. We compare the effectiveness of LYA against conventional techniques like fine-tuning, retraining, and vanilla gradient ascent. The subject models we investigate are BERT and CodeBERT, for sentiment analysis and code defect detection tasks, respectively. Our findings demonstrate that the combination of gradient ascent and FIM-based regularization, as done in LYA, outperforms existing methods in removing the trojan's influence from the poisoned model, while preserving its original functionality. To the best of our knowledge, this is the first work that compares and contrasts MU of trojans in LLMs, in the NL and Coding domain.

Hang Wang, Sen Lin, Junshan Zhang

Warm-Start reinforcement learning (RL), aided by a prior policy obtained from offline training, is emerging as a promising RL approach for practical applications. Recent empirical studies have demonstrated that the performance of Warm-Start RL can be improved \textit{quickly} in some cases but become \textit{stagnant} in other cases, especially when the function approximation is used. To this end, the primary objective of this work is to build a fundamental understanding on ``\textit{whether and when online learning can be significantly accelerated by a warm-start policy from offline RL?}''. Specifically, we consider the widely used Actor-Critic (A-C) method with a prior policy. We first quantify the approximation errors in the Actor update and the Critic update, respectively. Next, we cast the Warm-Start A-C algorithm as Newton's method with perturbation, and study the impact of the approximation errors on the finite-time learning performance with inaccurate Actor/Critic updates. Under some general technical conditions, we derive the upper bounds, which shed light on achieving the desired finite-learning performance in the Warm-Start A-C algorithm. In particular, our findings reveal that it is essential to reduce the algorithm bias in online learning. We also obtain lower bounds on the sub-optimality gap of the Warm-Start A-C algorithm to quantify the impact of the bias and error propagation.

Daouda Sow, Sen Lin, Zhangyang Wang et al.

Assigning importance weights to adversarial data has achieved great success in training adversarially robust networks under limited model capacity. However, existing instance-reweighted adversarial training (AT) methods heavily depend on heuristics and/or geometric interpretations to determine those importance weights, making these algorithms lack rigorous theoretical justification/guarantee. Moreover, recent research has shown that adversarial training suffers from a severe non-uniform robust performance across the training distribution, e.g., data points belonging to some classes can be much more vulnerable to adversarial attacks than others. To address both issues, in this paper, we propose a novel doubly-robust instance reweighted AT framework, which allows to obtain the importance weights via exploring distributionally robust optimization (DRO) techniques, and at the same time boosts the robustness on the most vulnerable examples. In particular, our importance weights are obtained by optimizing the KL-divergence regularized loss function, which allows us to devise new algorithms with a theoretical convergence guarantee. Experiments on standard classification datasets demonstrate that our proposed approach outperforms related state-of-the-art baseline methods in terms of average robust performance, and at the same time improves the robustness against attacks on the weakest data points. Codes will be available soon.

Daouda Sow, Sen Lin, Yingbin Liang et al.

Online meta-learning has recently emerged as a marriage between batch meta-learning and online learning, for achieving the capability of quick adaptation on new tasks in a lifelong manner. However, most existing approaches focus on the restrictive setting where the distribution of the online tasks remains fixed with known task boundaries. In this work, we relax these assumptions and propose a novel algorithm for task-agnostic online meta-learning in non-stationary environments. More specifically, we first propose two simple but effective detection mechanisms of task switches and distribution shift based on empirical observations, which serve as a key building block for more elegant online model updates in our algorithm: the task switch detection mechanism allows reusing of the best model available for the current task at hand, and the distribution shift detection mechanism differentiates the meta model update in order to preserve the knowledge for in-distribution tasks and quickly learn the new knowledge for out-of-distribution tasks. In particular, our online meta model updates are based only on the current data, which eliminates the need of storing previous data as required in most existing methods. We further show that a sublinear task-averaged regret can be achieved for our algorithm under mild conditions. Empirical studies on three different benchmarks clearly demonstrate the significant advantage of our algorithm over related baseline approaches.

Hongbo Li, Qinhang Wu, Sen Lin et al.

Mixture-of-Experts (MoE) models improve transformer efficiency but lack a unified theoretical explanation, especially when both feed-forward and attention layers are allowed to specialize. To this end, we study the Mixture-of-Transformers (MoT), a tractable theoretical framework in which each transformer block acts as an expert governed by a continuously trained gating network. This design allows us to isolate and study the core learning dynamics of expert specialization and attention alignment. In particular, we develop a three-stage training algorithm with continuous training of the gating network, and show that each transformer expert specializes in a distinct class of tasks and that the gating network accurately routes data samples to the correct expert. Our analysis shows how expert specialization reduces gradient conflicts and makes each subtask strongly convex. We prove that the training drives the expected prediction loss to near zero in $O(\log(ε^{-1}))$ iteration steps, significantly improving over the $O(ε^{-1})$ rate for a single transformer. We further validate our theoretical findings through extensive real-data experiments, demonstrating the practical effectiveness of MoT. Together, these results offer the first unified theoretical account of transformer-level specialization and learning dynamics, providing practical guidance for designing efficient large-scale models.

Keru Chen, Honghao Wei, Zhigang Deng et al.

The high costs and risks involved in extensive environment interactions hinder the practical application of current online safe reinforcement learning (RL) methods. While offline safe RL addresses this by learning policies from static datasets, the performance therein is usually limited due to reliance on data quality and challenges with out-of-distribution (OOD) actions. Inspired by recent successes in offline-to-online (O2O) RL, it is crucial to explore whether offline safe RL can be leveraged to facilitate faster and safer online policy learning, a direction that has yet to be fully investigated. To fill this gap, we first demonstrate that naively applying existing O2O algorithms from standard RL would not work well in the safe RL setting due to two unique challenges: \emph{erroneous Q-estimations}, resulted from offline-online objective mismatch and offline cost sparsity, and \emph{Lagrangian mismatch}, resulted from difficulties in aligning Lagrange multipliers between offline and online policies. To address these challenges, we introduce \textbf{Marvel}, a novel framework for O2O safe RL, comprising two key components that work in concert: \emph{Value Pre-Alignment} to align the Q-functions with the underlying truth before online learning, and \emph{Adaptive PID Control} to effectively adjust the Lagrange multipliers during online finetuning. Extensive experiments demonstrate that Marvel significantly outperforms existing baselines in both reward maximization and safety constraint satisfaction. By introducing the first policy-finetuning based framework for O2O safe RL, which is compatible with many offline and online safe RL methods, our work has the great potential to advance the field towards more efficient and practical safe RL solutions.

Yung-Fu Chen, Sen Lin, Anish Arora

We propose a simple algorithm that needs only a few data samples from a single graph for learning local routing policies that generalize across a rich class of geometric random graphs in Euclidean metric spaces. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that let each graph node efficiently and scalably route (i.e., forward) packets by considering only the node's state and the state of the neighboring nodes. Our algorithm design exploits network domain knowledge in the selection of input features and design of the policy function for learning an approximately optimal policy. Domain knowledge also provides theoretical assurance that the choice of a ``seed graph'' and its node data sampling suffices for generalizable learning. Remarkably, one of these DNNs we train -- using distance-to-destination as the only input feature -- learns a policy that exactly matches the well-known Greedy Forwarding policy, which forwards packets to the neighbor with the shortest distance to the destination. We also learn a new policy, which we call GreedyTensile routing -- using both distance-to-destination and node stretch as the input features -- that almost always outperforms greedy forwarding. We demonstrate the explainability and ultra-low latency run-time operation of Greedy Tensile routing by symbolically interpreting its DNN in low-complexity terms of two linear actions.

Junze Deng, Qinhang Wu, Peizhong Ju et al.

Rehearsal-based methods have shown superior performance in addressing catastrophic forgetting in continual learning (CL) by storing and training on a subset of past data alongside new data in current task. While such a concurrent rehearsal strategy is widely used, it remains unclear if this approach is always optimal. Inspired by human learning, where sequentially revisiting tasks helps mitigate forgetting, we explore whether sequential rehearsal can offer greater benefits for CL compared to standard concurrent rehearsal. To address this question, we conduct a theoretical analysis of rehearsal-based CL in overparameterized linear models, comparing two strategies: 1) Concurrent Rehearsal, where past and new data are trained together, and 2) Sequential Rehearsal, where new data is trained first, followed by revisiting past data sequentially. By explicitly characterizing forgetting and generalization error, we show that sequential rehearsal performs better when tasks are less similar. These insights further motivate a novel Hybrid Rehearsal method, which trains similar tasks concurrently and revisits dissimilar tasks sequentially. We characterize its forgetting and generalization performance, and our experiments with deep neural networks further confirm that the hybrid approach outperforms standard concurrent rehearsal. This work provides the first comprehensive theoretical analysis of rehearsal-based CL.

Zheng Wang, Wanhao Yu, Li Yang et al.

Continual Learning (CL) seeks to build an agent that can continuously learn a sequence of tasks, where a key challenge, namely Catastrophic Forgetting, persists due to the potential knowledge interference among different tasks. On the other hand, deep neural networks (DNNs) are shown to converge to a terminal state termed Neural Collapse during training, where all class prototypes geometrically form a static simplex equiangular tight frame (ETF). These maximally and equally separated class prototypes make the ETF an ideal target for model learning in CL to mitigate knowledge interference. Thus inspired, several studies have emerged very recently to leverage a fixed global ETF in CL, which however suffers from key drawbacks, such as impracticability and limited performance.To address these challenges and fully unlock the potential of ETF in CL, we propose Progressive Neural Collapse (ProNC), a novel framework that completely removes the need of a fixed global ETF in CL. Specifically, ProNC progressively expands the ETF target in a principled way by adding new class prototypes as vertices for new tasks, ensuring maximal separability across all encountered classes with minimal shifts from the previous ETF. We next develop a new CL framework by plugging ProNC into commonly used CL algorithm designs, where distillation is further leveraged to balance between target shifting for old classes and target aligning for new classes. Extensive experiments show that our approach significantly outperforms related baselines while maintaining superior flexibility, simplicity, and efficiency.

Hongbo Li, Sen Lin, Lingjie Duan et al.

Continual learning (CL) has garnered significant attention because of its ability to adapt to new tasks that arrive over time. Catastrophic forgetting (of old tasks) has been identified as a major issue in CL, as the model adapts to new tasks. The Mixture-of-Experts (MoE) model has recently been shown to effectively mitigate catastrophic forgetting in CL, by employing a gating network to sparsify and distribute diverse tasks among multiple experts. However, there is a lack of theoretical analysis of MoE and its impact on the learning performance in CL. This paper provides the first theoretical results to characterize the impact of MoE in CL via the lens of overparameterized linear regression tasks. We establish the benefit of MoE over a single expert by proving that the MoE model can diversify its experts to specialize in different tasks, while its router learns to select the right expert for each task and balance the loads across all experts. Our study further suggests an intriguing fact that the MoE in CL needs to terminate the update of the gating network after sufficient training rounds to attain system convergence, which is not needed in the existing MoE studies that do not consider the continual task arrival. Furthermore, we provide explicit expressions for the expected forgetting and overall generalization error to characterize the benefit of MoE in the learning performance in CL. Interestingly, adding more experts requires additional rounds before convergence, which may not enhance the learning performance. Finally, we conduct experiments on both synthetic and real datasets to extend these insights from linear models to deep neural networks (DNNs), which also shed light on the practical algorithm design for MoE in CL.

Sen Lin, Li Yang, Deliang Fan et al.

Catastrophic forgetting is one of the major challenges in continual learning. To address this issue, some existing methods put restrictive constraints on the optimization space of the new task for minimizing the interference to old tasks. However, this may lead to unsatisfactory performance for the new task, especially when the new task is strongly correlated with old tasks. To tackle this challenge, we propose Trust Region Gradient Projection (TRGP) for continual learning to facilitate the forward knowledge transfer based on an efficient characterization of task correlation. Particularly, we introduce a notion of `trust region' to select the most related old tasks for the new task in a layer-wise and single-shot manner, using the norm of gradient projection onto the subspace spanned by task inputs. Then, a scaled weight projection is proposed to cleverly reuse the frozen weights of the selected old tasks in the trust region through a layer-wise scaling matrix. By jointly optimizing the scaling matrices and the model, where the model is updated along the directions orthogonal to the subspaces of old tasks, TRGP can effectively prompt knowledge transfer without forgetting. Extensive experiments show that our approach achieves significant improvement over related state-of-the-art methods.

Sen Lin, Jialin Wan, Tengyu Xu et al.

Existing offline reinforcement learning (RL) methods face a few major challenges, particularly the distributional shift between the learned policy and the behavior policy. Offline Meta-RL is emerging as a promising approach to address these challenges, aiming to learn an informative meta-policy from a collection of tasks. Nevertheless, as shown in our empirical studies, offline Meta-RL could be outperformed by offline single-task RL methods on tasks with good quality of datasets, indicating that a right balance has to be delicately calibrated between "exploring" the out-of-distribution state-actions by following the meta-policy and "exploiting" the offline dataset by staying close to the behavior policy. Motivated by such empirical analysis, we explore model-based offline Meta-RL with regularized Policy Optimization (MerPO), which learns a meta-model for efficient task structure inference and an informative meta-policy for safe exploration of out-of-distribution state-actions. In particular, we devise a new meta-Regularized model-based Actor-Critic (RAC) method for within-task policy optimization, as a key building block of MerPO, using conservative policy evaluation and regularized policy improvement; and the intrinsic tradeoff therein is achieved via striking the right balance between two regularizers, one based on the behavior policy and the other on the meta-policy. We theoretically show that the learnt policy offers guaranteed improvement over both the behavior policy and the meta-policy, thus ensuring the performance improvement on new tasks via offline Meta-RL. Experiments corroborate the superior performance of MerPO over existing offline Meta-RL methods.

Liang Liao, Sen Lin, Lun Li et al.

Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order input into a matrix or break it into a series of order-two slices to tackle higher order data such as multispectral images and videos with the SVD. Higher order singular value decomposition (HOSVD) extends the SVD and can approximate higher order data using sums of a few rank-one components. We consider the problem of generalizing HOSVD over a finite dimensional commutative algebra. This algebra, referred to as a t-algebra, generalizes the field of complex numbers. The elements of the algebra, called t-scalars, are fix-sized arrays of complex numbers. One can generalize matrices and tensors over t-scalars and then extend many canonical matrix and tensor algorithms, including HOSVD, to obtain higher-performance versions. The generalization of HOSVD is called THOSVD. Its performance of approximating multi-way data can be further improved by an alternating algorithm. THOSVD also unifies a wide range of principal component analysis algorithms. To exploit the potential of generalized algorithms using t-scalars for approximating images, we use a pixel neighborhood strategy to convert each pixel to "deeper-order" t-scalar. Experiments on publicly available images show that the generalized algorithm over t-scalars, namely THOSVD, compares favorably with its canonical counterparts.

Sen Lin, Li Yang, Zhezhi He et al.

While deep learning has achieved phenomenal successes in many AI applications, its enormous model size and intensive computation requirements pose a formidable challenge to the deployment in resource-limited nodes. There has recently been an increasing interest in computationally-efficient learning methods, e.g., quantization, pruning and channel gating. However, most existing techniques cannot adapt to different tasks quickly. In this work, we advocate a holistic approach to jointly train the backbone network and the channel gating which enables dynamical selection of a subset of filters for more efficient local computation given the data input. Particularly, we develop a federated meta-learning approach to jointly learn good meta-initializations for both backbone networks and gating modules, by making use of the model similarity across learning tasks on different nodes. In this way, the learnt meta-gating module effectively captures the important filters of a good meta-backbone network, based on which a task-specific conditional channel gated network can be quickly adapted, i.e., through one-step gradient descent, from the meta-initializations in a two-stage procedure using new samples of that task. The convergence of the proposed federated meta-learning algorithm is established under mild conditions. Experimental results corroborate the effectiveness of our method in comparison to related work.