In decision-making under uncertainty, multi-armed bandit (MAB) [4] problems are a key paradigm with applications in recommendation systems and online advertising. These problems entail balancing exploration-exploitation trade-offs, as an agent draws from a set of K arms with unknown reward distributions to maximize cumulative rewards or minimize regret over time. Two notable variations of MAB include the dueling-bandit problem and the cooperative multiplayer MAB problem. In the dueling-bandit scenario [36], feedback comes from pairwise comparisons between K arms, useful in situations like human-feedback driven tasks, including ranker evaluation [25] and preference-based recommendation systems [10]. Meanwhile, the cooperative multiplayer MAB focuses on a group of M players collaboratively solving challenges in a distributed decisionmaking environment, enhancing learning through shared information. This approach finds applications in fields like multi-robot systems [19] and distributed recommender systems [27]. The M-player K-arm cooperative dueling bandit problem, combining aspects of the two previously studied variations, introduces a new dimension to cooperative decision-making with preference-based feedback, yet remains unexplored to the best of our knowledge.

In mobile and IoT systems, Federated Learning (FL) is increasingly important for effectively using data while maintaining user privacy. One key challenge in FL is managing statistical heterogeneity, such as non-i.i.d. data, arising from numerous clients and diverse data sources. This requires strategic cooperation, often with clients having similar characteristics. However, we are interested in a fundamental question: does achieving optimal cooperation necessarily entail cooperating with the most similar clients? Typically, significant model performance improvements are often realized not by partnering with the most similar models, but through leveraging complementary data. Our theoretical and empirical analyses suggest that optimal cooperation is achieved by enhancing complementarity in feature distribution while restricting the disparity in the correlation between features and targets. Accordingly, we introduce a novel framework, \texttt{FedSaC}, which balances similarity and complementarity in FL cooperation. Our framework aims to approximate an optimal cooperation network for each client by optimizing a weighted sum of model similarity and feature complementarity. The strength of \texttt{FedSaC} lies in its adaptability to various levels of data heterogeneity and multimodal scenarios. Our comprehensive unimodal and multimodal experiments demonstrate that \texttt{FedSaC} markedly surpasses other state-of-the-art FL methods.

In this paper, we investigate an offline reinforcement learning (RL) problem where datasets are collected from two domains. In this scenario, having datasets with domain labels facilitates efficient policy training. However, in practice, the task of assigning domain labels can be resource-intensive or infeasible at a large scale, leading to a prevalence of domain-unlabeled data. To formalize this challenge, we introduce a novel offline RL problem setting named Positive-Unlabeled Offline RL (PUORL), which incorporates domain-unlabeled data. To address PUORL, we develop an offline RL algorithm utilizing positive-unlabeled learning to predict the domain labels of domain-unlabeled data, enabling the integration of this data into policy training. Our experiments show the effectiveness of our method in accurately identifying domains and learning policies that outperform baselines in the PUORL setting, highlighting its capability to leverage domain-unlabeled data effectively.

The current thesis aims to explore the reinforcement learning field and build on existing methods to produce improved ones to tackle the problem of learning in high-dimensional and complex environments. It addresses such goals by decomposing learning tasks in a hierarchical fashion known as Hierarchical Reinforcement Learning. We start in the first chapter by getting familiar with the Markov Decision Process framework and presenting some of its recent techniques that the following chapters use. We then proceed to build our Hierarchical Policy learning as an answer to the limitations of a single primitive policy. The hierarchy is composed of a manager agent at the top and employee agents at the lower level. In the last chapter, which is the core of this thesis, we attempt to learn lower-level elements of the hierarchy independently of the manager level in what is known as the "Eigenoption". Based on the graph structure of the environment, Eigenoptions allow us to build agents that are aware of the geometric and dynamic properties of the environment. Their decision-making has a special property: it is invariant to symmetric transformations of the environment, allowing as a consequence to greatly reduce the complexity of the learning task.

Foundation models are usually pre-trained on large-scale datasets and then adapted to downstream tasks through tuning. However, the large-scale pre-training datasets, often inaccessible or too expensive to handle, can contain label noise that may adversely affect the generalization of the model and pose unexpected risks. This paper stands out as the first work to comprehensively understand and analyze the nature of noise in pre-training datasets and then effectively mitigate its impacts on downstream tasks. Specifically, through extensive experiments of fully-supervised and image-text contrastive pre-training on synthetic noisy ImageNet-1K, YFCC15M, and CC12M datasets, we demonstrate that, while slight noise in pre-training can benefit in-domain (ID) performance, where the training and testing data share a similar distribution, it always deteriorates out-of-domain (OOD) performance, where training and testing distributions are significantly different. These observations are agnostic to scales of pre-training datasets, pre-training noise types, model architectures, pre-training objectives, downstream tuning methods, and downstream applications. We empirically ascertain that the reason behind this is that the pre-training noise shapes the feature space differently. We then propose a tuning method (NMTune) to affine the feature space to mitigate the malignant effect of noise and improve generalization, which is applicable in both parameter-efficient and black-box tuning manners. We additionally conduct extensive experiments on popular vision and language models, including APIs, which are supervised and self-supervised pre-trained on realistic noisy data for evaluation. Our analysis and results demonstrate the importance of this novel and fundamental research direction, which we term as Noisy Model Learning.

Social networks are often associated with rich side information, such as texts and images. While numerous methods have been developed to identify communities from pairwise interactions, they usually ignore such side information. In this work, we study an extension of the Stochastic Block Model (SBM), a widely used statistical framework for community detection, that integrates vectorial edges covariates: the Vectorial Edges Covariates Stochastic Block Model (VEC-SBM). We propose a novel algorithm based on iterative refinement techniques and show that it optimally recovers the latent communities under the VEC-SBM. Furthermore, we rigorously assess the added value of leveraging edge's side information in the community detection process. We complement our theoretical results with numerical experiments on synthetic and semi-synthetic data.

To improve the ability of the large language model (LLMs) to handle complex reasoning problems, chain-of-thoughts (CoT) methods were proposed to guide LLMs to reason step-by-step, facilitating problem solving from simple to complex tasks. State-of-the-art approaches for generating such a chain involve interactive collaboration, where the learner generates candidate intermediate thoughts, evaluated by the LLM, guiding the generation of subsequent thoughts. However, a widespread yet understudied problem is that the evaluation from the LLM is typically noisy and unreliable, potentially misleading the generation process in selecting promising intermediate thoughts. In this paper, motivated by Vapnik's principle, we propose a novel comparison-based CoT generation algorithm that directly identifies the most promising thoughts with the noisy feedback from the LLM. In each round, we randomly pair intermediate thoughts and directly prompt the LLM to select the more promising one from each pair, allowing us to identify the most promising thoughts through an iterative process. To further model the noise in the comparison, we resort to the techniques of ensemble and dueling bandits and propose two variants of the proposed algorithm. Experiments on three real-world mathematical and reasoning tasks demonstrate the effectiveness of our proposed algorithm and verify the rationale of the direct pairwise comparison.

In reinforcement Learning (RL), an instant reward signal is generated for each action of the agent, such that the agent learns to maximize the cumulative reward to obtain the optimal policy. However, in many real-world applications, the instant reward signals are not obtainable by the agent. Instead, the learner only obtains rewards at the ends of bags, where a bag is defined as a partial sequence of a complete trajectory. In this situation, the learner has to face the significant difficulty of exploring the unknown instant rewards in the bags, which could not be addressed by existing approaches, including those trajectory-based approaches that consider only complete trajectories and ignore the inner reward distributions. To formally study this situation, we introduce a novel RL setting termed Reinforcement Learning from Bagged Rewards (RLBR), where only the bagged rewards of sequences can be obtained. We provide the theoretical study to establish the connection between RLBR and standard RL in Markov Decision Processes (MDPs). To effectively explore the reward distributions within the bagged rewards, we propose a Transformer-based reward model, the Reward Bag Transformer (RBT), which uses the self-attention mechanism for interpreting the contextual nuances and temporal dependencies within each bag. Extensive experimental analyses demonstrate the superiority of our method, particularly in its ability to mimic the original MDP's reward distribution, highlighting its proficiency in contextual understanding and adaptability to environmental dynamics.

Weakly supervised learning generally faces challenges in applicability to various scenarios with diverse weak supervision and in scalability due to the complexity of existing algorithms, thereby hindering the practical deployment. This paper introduces a general framework for learning from weak supervision (GLWS) with a novel algorithm. Central to GLWS is an Expectation-Maximization (EM) formulation, adeptly accommodating various weak supervision sources, including instance partial labels, aggregate statistics, pairwise observations, and unlabeled data. We further present an advanced algorithm that significantly simplifies the EM computational demands using a Non-deterministic Finite Automaton (NFA) along with a forward-backward algorithm, which effectively reduces time complexity from quadratic or factorial often required in existing solutions to linear scale. The problem of learning from arbitrary weak supervision is therefore converted to the NFA modeling of them. GLWS not only enhances the scalability of machine learning models but also demonstrates superior performance and versatility across 11 weak supervision scenarios. We hope our work paves the way for further advancements and practical deployment in this field.

Knowledge Distillation (KD) aims to learn a compact student network using knowledge from a large pre-trained teacher network, where both networks are trained on data from the same distribution. However, in practical applications, the student network may be required to perform in a new scenario (i.e., the target domain), which usually exhibits significant differences from the known scenario of the teacher network (i.e., the source domain). The traditional domain adaptation techniques can be integrated with KD in a two-stage process to bridge the domain gap, but the ultimate reliability of two-stage approaches tends to be limited due to the high computational consumption and the additional errors accumulated from both stages. To solve this problem, we propose a new one-stage method dubbed ``Direct Distillation between Different Domains" (4Ds). We first design a learnable adapter based on the Fourier transform to separate the domain-invariant knowledge from the domain-specific knowledge. Then, we build a fusion-activation mechanism to transfer the valuable domain-invariant knowledge to the student network, while simultaneously encouraging the adapter within the teacher network to learn the domain-specific knowledge of the target data. As a result, the teacher network can effectively transfer categorical knowledge that aligns with the target domain of the student network. Intensive experiments on various benchmark datasets demonstrate that our proposed 4Ds method successfully produces reliable student networks and outperforms state-of-the-art approaches.