A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper a generalized linear tensor bandits algorithm designed to tackle these challenges by incorporating low-dimensional tensor structures, and further derive a unified analytical framework of the proposed algorithm. Specifically, our framework introduces a convex optimization approach with the weakly decomposable regularizers, enabling it to not only achieve better results based on the tensor low-rankness structure assumption but also extend to cases involving other low-dimensional structures such as slice sparsity and low-rankness. The theoretical analysis shows that, compared to existing low-rankness tensor result, our framework not only provides better bounds but also has a broader applicability. Notably, in the special case of degenerating to low-rank matrices, our bounds still offer advantages in certain scenarios.

The Power of Adaptation: Boosting In-Context Learning through Adaptive Prompting

Large Language Models (LLMs) have demonstrated exceptional abilities across a broad range of language-related tasks, including generating solutions to complex reasoning problems. An effective technique to enhance LLM performance is in-context learning, which encourages a step-by-step reasoning process by including explanatory examples to guide the model's responses. However, selecting appropriate exemplars for the model poses a challenge, as each dataset demands a distinct set of exemplars to enable the LLM to learn effectively and perform well on the test set. Current studies often rely on uncertainty- or diversity-based selection strategies to select exemplars for annotation and to improve model learning. However, these studies typically employ a non-adaptive approach, selecting a set of exemplars all at once. We argue that this non-adaptive strategy may result in a set of exemplars with high redundancy in terms of the knowledge covered, ultimately reducing their overall informativeness. To address this limitation, we propose \textsc{Adaptive-Prompt}, a novel method that adaptively selects exemplars by leveraging model feedback from previously chosen exemplars. Experimental results show that \textsc{Adaptive-Prompt} significantly enhances LLM performance across a variety of reasoning tasks.

Why Go Full? Elevating Federated Learning Through Partial Network Updates

Federated learning is a distributed machine learning paradigm designed to protect user data privacy, which has been successfully implemented across various scenarios. In traditional federated learning, the entire parameter set of local models is updated and averaged in each training round. Although this full network update method maximizes knowledge acquisition and sharing for each model layer, it prevents the layers of the global model from cooperating effectively to complete the tasks of each client, a challenge we refer to as layer mismatch. This mismatch problem recurs after every parameter averaging, consequently slowing down model convergence and degrading overall performance. To address the layer mismatch issue, we introduce the FedPart method, which restricts model updates to either a single layer or a few layers during each communication round. Furthermore, to maintain the efficiency of knowledge acquisition and sharing, we develop several strategies to select trainable layers in each round, including sequential updating and multi-round cycle training. Through both theoretical analysis and experiments, our findings demonstrate that the FedPart method significantly surpasses conventional full network update strategies in terms of convergence speed and accuracy, while also reducing communication and computational overheads.

Learning Submodular Sequencing from Samples

This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility function, we assume that we are given only a set of samples. Each sample includes a random sequence of items and its associated utility. We present an algorithm that, given polynomially many samples drawn from a two-stage uniform distribution, achieves an approximation ratio dependent on the curvature of individual submodular functions. Our results apply in a wide variety of real-world scenarios, such as ranking products in online retail platforms, where complete knowledge of the utility function is often impossible to obtain. Our algorithm gives an empirically useful solution in such contexts, thus proving that limited data can be of great use in sequencing tasks. From a technical perspective, our results extend prior work on ``optimization from samples'' by generalizing from optimizing a set function to a sequence-dependent function.

The Power of Second Chance: Personalized Submodular Maximization with Two Candidates

Most of existing studies on submodular maximization focus on selecting a subset of items that maximizes a \emph{single} submodular function. However, in many real-world scenarios, we might have multiple user-specific functions, each of which models the utility of a particular type of user. In these settings, our goal would be to choose a set of items that performs well across all the user-specific functions. One way to tackle this problem is to select a single subset that maximizes the sum of all of the user-specific functions. Although this aggregate approach is efficient in the sense that it avoids computation of sets for individual functions, it really misses the power of personalization - for it does not allow to choose different sets for different functions. In this paper, we introduce the problem of personalized submodular maximization with two candidate solutions. For any two candidate solutions, the utility of each user-specific function is defined as the better of these two candidates. Our objective is, therefore, to select the best set of two candidates that maximize the sum of utilities of all the user-specific functions. We have designed effective algorithms for this problem. We also discuss how our approach generalizes to multiple candidate solutions, increasing flexibility and personalization in our solution.

DualFed: Enjoying both Generalization and Personalization in Federated Learning via Hierachical Representations

In personalized federated learning (PFL), it is widely recognized that achieving both high model generalization and effective personalization poses a significant challenge due to their conflicting nature. As a result, existing PFL methods can only manage a trade-off between these two objectives. This raises an interesting question: Is it feasible to develop a model capable of achieving both objectives simultaneously? Our paper presents an affirmative answer, and the key lies in the observation that deep models inherently exhibit hierarchical architectures, which produce representations with various levels of generalization and personalization at different stages. A straightforward approach stemming from this observation is to select multiple representations from these layers and combine them to concurrently achieve generalization and personalization. However, the number of candidate representations is commonly huge, which makes this method infeasible due to high computational costs.To address this problem, we propose DualFed, a new method that can directly yield dual representations correspond to generalization and personalization respectively, thereby simplifying the optimization task. Specifically, DualFed inserts a personalized projection network between the encoder and classifier. The pre-projection representations are able to capture generalized information shareable across clients, and the post-projection representations are effective to capture task-specific information on local clients. This design minimizes the mutual interference between generalization and personalization, thereby achieving a win-win situation. Extensive experiments show that DualFed can outperform other FL methods. Code is available at https://github.com/GuogangZhu/DualFed.

Tackling Feature-Classifier Mismatch in Federated Learning via Prompt-Driven Feature Transformation

In traditional Federated Learning approaches like FedAvg, the global model underperforms when faced with data heterogeneity. Personalized Federated Learning (PFL) enables clients to train personalized models to fit their local data distribution better. However, we surprisingly find that the feature extractor in FedAvg is superior to those in most PFL methods. More interestingly, by applying a linear transformation on local features extracted by the feature extractor to align with the classifier, FedAvg can surpass the majority of PFL methods. This suggests that the primary cause of FedAvg's inadequate performance stems from the mismatch between the locally extracted features and the classifier. While current PFL methods mitigate this issue to some extent, their designs compromise the quality of the feature extractor, thus limiting the full potential of PFL. In this paper, we propose a new PFL framework called FedPFT to address the mismatch problem while enhancing the quality of the feature extractor. FedPFT integrates a feature transformation module, driven by personalized prompts, between the global feature extractor and classifier. In each round, clients first train prompts to transform local features to match the global classifier, followed by training model parameters. This approach can also align the training objectives of clients, reducing the impact of data heterogeneity on model collaboration. Moreover, FedPFT's feature transformation module is highly scalable, allowing for the use of different prompts to tailor local features to various tasks. Leveraging this, we introduce a collaborative contrastive learning task to further refine feature extractor quality. Our experiments demonstrate that FedPFT outperforms state-of-the-art methods by up to 7.08%.

The Diversity Bonus: Learning from Dissimilar Distributed Clients in Personalized Federated Learning

Personalized Federated Learning (PFL) is a commonly used framework that allows clients to collaboratively train their personalized models. PFL is particularly useful for handling situations where data from different clients are not independent and identically distributed (non-IID). Previous research in PFL implicitly assumes that clients can gain more benefits from those with similar data distributions. Correspondingly, methods such as personalized weight aggregation are developed to assign higher weights to similar clients during training. We pose a question: can a client benefit from other clients with dissimilar data distributions and if so, how? This question is particularly relevant in scenarios with a high degree of non-IID, where clients have widely different data distributions, and learning from only similar clients will lose knowledge from many other clients. We note that when dealing with clients with similar data distributions, methods such as personalized weight aggregation tend to enforce their models to be close in the parameter space. It is reasonable to conjecture that a client can benefit from dissimilar clients if we allow their models to depart from each other. Based on this idea, we propose DiversiFed which allows each client to learn from clients with diversified data distribution in personalized federated learning. DiversiFed pushes personalized models of clients with dissimilar data distributions apart in the parameter space while pulling together those with similar distributions. In addition, to achieve the above effect without using prior knowledge of data distribution, we design a loss function that leverages the model similarity to determine the degree of attraction and repulsion between any two models. Experiments on several datasets show that DiversiFed can benefit from dissimilar clients and thus outperform the state-of-the-art methods.

Decoupling General and Personalized Knowledge in Federated Learning via Additive and Low-Rank Decomposition

To address data heterogeneity, the key strategy of Personalized Federated Learning (PFL) is to decouple general knowledge (shared among clients) and client-specific knowledge, as the latter can have a negative impact on collaboration if not removed. Existing PFL methods primarily adopt a parameter partitioning approach, where the parameters of a model are designated as one of two types: parameters shared with other clients to extract general knowledge and parameters retained locally to learn client-specific knowledge. However, as these two types of parameters are put together like a jigsaw puzzle into a single model during the training process, each parameter may simultaneously absorb both general and client-specific knowledge, thus struggling to separate the two types of knowledge effectively. In this paper, we introduce FedDecomp, a simple but effective PFL paradigm that employs parameter additive decomposition to address this issue. Instead of assigning each parameter of a model as either a shared or personalized one, FedDecomp decomposes each parameter into the sum of two parameters: a shared one and a personalized one, thus achieving a more thorough decoupling of shared and personalized knowledge compared to the parameter partitioning method. In addition, as we find that retaining local knowledge of specific clients requires much lower model capacity compared with general knowledge across all clients, we let the matrix containing personalized parameters be low rank during the training process. Moreover, a new alternating training strategy is proposed to further improve the performance. Experimental results across multiple datasets and varying degrees of data heterogeneity demonstrate that FedDecomp outperforms state-of-the-art methods up to 4.9\%.

Submodular Participatory Budgeting

Participatory budgeting refers to the practice of allocating public resources by collecting and aggregating individual preferences. Most existing studies in this field often assume an additive utility function, where each individual holds a private utility for each candidate project, and the total utility of a set of funded projects is simply the sum of the utilities of all projects. We argue that this assumption does not always hold in reality. For example, building two playgrounds in the same neighborhood does not necessarily lead to twice the utility of building a single playground. To address this, we extend the existing study by proposing a submodular participatory budgeting problem, assuming that the utility function of each individual is a monotone and submodular function over funded projects. We propose and examine three preference elicitation methods, including \emph{ranking-by-marginal-values}, \emph{ranking-by-values} and \emph{threshold approval votes}, and analyze their performances in terms of distortion. Notably, if the utility function is addicative, our aggregation rule designed for threshold approval votes achieves a better distortion than the state-of-the-art approach.