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Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Yeoreum Lee, Jinwook Jung, Sungyong Baik

Large-scale deep learning models with a pretraining-finetuning paradigm have led to a surge of numerous task-specific models fine-tuned from a common pre-trained model.Recently, several research efforts have been made on merging these large models into a single multi-task model, particularly with simple arithmetic on parameters.Such merging methodology faces a central challenge: interference between model parameters fine-tuned on different tasks.Few recent works have focused on designing a new fine-tuning scheme that can lead to small parameter interference, however at the cost of the performance of each task-specific fine-tuned model and thereby limiting that of a merged model.To improve the performance of a merged model, we note that a fine-tuning scheme should aim for (1) smaller parameter interference and (2) better performance of each fine-tuned model on the corresponding task.In this work, we aim to design a new fine-tuning objective function to work towards these two goals.In the course of this process, we find such objective function to be strikingly similar to sharpness-aware minimization (SAM) objective function, which aims to achieve generalization by finding flat minima.Drawing upon our observation, we propose to fine-tune pre-trained models via sharpness-aware minimization.The experimental and theoretical results showcase the effectiveness and orthogonality of our proposed approach, improving performance upon various merging and fine-tuning methods.Our code is available at https://github.com/baiklab/SAFT-Merge.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Sagi Shaier, Francisco Pereira, Katharina Kann, Lawrence E Hunter, Matt Jones

The evolution of biological neural systems has led to both modularity and sparse coding, which enables energy efficiency and robustness across the diversity of tasks in the lifespan. In contrast, standard neural networks rely on dense, non-specialized architectures, where all model parameters are simultaneously updated to learn multiple tasks, leading to interference. Current sparse neural network approaches aim to alleviate this issue but are hindered by limitations such as 1) trainable gating functions that cause representation collapse, 2) disjoint experts that result in redundant computation and slow learning, and 3) reliance on explicit input or task IDs that limit flexibility and scalability.In this paper we propose Conditionally Overlapping Mixture of ExperTs (COMET), a general deep learning method that addresses these challenges by inducing a modular, sparse architecture with an exponential number of overlapping experts. COMET replaces the trainable gating function used in Sparse Mixture of Experts with a fixed, biologically inspired random projection applied to individual input representations. This design causes the degree of expert overlap to depend on input similarity, so that similar inputs tend to share more parameters. This results in faster learning per update step and improved out-of-sample generalization. We demonstrate the effectiveness of COMET on a range of tasks, including image classification, language modeling, and regression, using several popular deep learning architectures.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Kotaro Yoshida, Yuji Naraki, Takafumi Horie, Ryosuke Yamaki, Ryotaro Shimizu, Yuki Saito, Julian McAuley, Hiroki Naganuma

Model-editing techniques using task arithmetic have rapidly gained attention.Through task arithmetic, simply through arithmetic operations on the weights of pre-trained and fine-tuned models create desired models, such as multi-task models, models in which specific tasks are unsolvable, or domain-transferred models.However, task arithmetic faces challenges, such as poor reproducibility and the high cost associated with adjusting coefficients in the arithmetic operations on model parameters, which have limited its practical success. In this paper, we present three key contributions in the context of task addition and task negation within task arithmetic. First, we propose a new metric called $\tau$Jp which is based on the product of the task vector ($\tau$) and the Jacobian of the pre-trained model with respect to its weights. We show that $\tau$Jp has a causal relationship with the interference that occurs from arithmetic operations. Second, we show that introducing regularization to minimize $\tau$Jp significantly mitigates interference between task inference, which leads to the elimination of coefficient tuning and improved accuracy on each task.Third, in the context of incremental learning, we demonstrate that our $\tau$Jp regularization achieves more robust performance in environments where access to future tasks is unavailable, thus validating the scalability of the approach.Finally, we demonstrate that the $\tau$Jp regularizer further reinforces the performance of task arithmetic by leveraging publicly available fine-tuned models, offering practical benefits for real-world applications.Our code is available at https://github.com/katoro8989/tau-Jp_Task_Arithmetic

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Ruilin Tong, Yuhang Liu, Javen Qinfeng Shi, Dong Gong

Rehearsal-based continual learning (CL) aims to mitigate catastrophic forgetting by maintaining a subset of samples from previous tasks and replaying them. The rehearsal memory can be naturally constructed as a coreset, designed to form a compact subset that enables training with performance comparable to using the full dataset. The coreset selection task can be formulated as bilevel optimization that solves for the subset to minimize the outer objective of the learning task. Existing methods primarily rely on inefficient probabilistic sampling or local gradient-based scoring to approximate sample importance through an iterative process that can be susceptible to ambiguity or noise. Specifically, non-representative samples like ambiguous or noisy samples are difficult to learn and incur high loss values even when training on the full dataset. However, existing methods relying on local gradient tend to highlight these samples in an attempt to minimize the outer loss, leading to a suboptimal coreset. To enhance coreset selection, especially in CL where high-quality samples are essential, we propose a coreset selection method that measures sample importance using reducible loss (ReL) that quantifies the impact of adding a sample to model performance. By leveraging ReL and a process derived from bilevel optimization, we identify and retain samples that yield the highest performance gain. They are shown to be informative and representative. Furthermore, ReL requires only forward computation, making it significantly more efficient than previous methods. To better apply coreset selection in CL, we extend our method to address key challenges such as task interference, streaming data, and knowledge distillation. Experiments on data summarization and continual learning demonstrate the effectiveness and efficiency of our approach.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Leonardo Iurada, Marco Ciccone, Tatiana Tommasi

Task arithmetic has emerged as a promising approach for editing models by representing task-specific knowledge as composable task vectors. However, existing methods rely on network linearization to derive task vectors, leading to computational bottlenecks during training and inference. Moreover, linearization alone does not ensure weight disentanglement, the key property that enables conflict-free composition of task vectors. To address this, we propose TaLoS which allows to build sparse task vectors with minimal interference without requiring explicit linearization and sharing information across tasks. We find that pre-trained models contain a subset of parameters with consistently low gradient sensitivity across tasks, and that sparsely updating only these parameters allows for promoting weight disentanglement during fine-tuning. Our experiments prove that TaLoS improves training and inference efficiency while outperforming current methods in task addition and negation. By enabling modular parameter editing, our approach fosters practical deployment of adaptable foundation models in real-world applications.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Hossein Resani, Behrooz Nasihatkon

In this paper, we introduce a novel framework for memory-efficient and privacy-preserving continual learning in 3D object classification. Unlike conventional memory-based approaches in continual learning that require storing numerous exemplars, our method constructs a compact shape model for each class, retaining only the mean shape along with a few key modes of variation. This strategy not only enables the generation of diverse training samples while drastically reducing memory usage but also enhances privacy by eliminating the need to store original data. To further improve model robustness against input variations—an issue common in 3D domains due to the absence of strong backbones and limited training data—we incorporate Gradient Mode Regularization. This technique enhances model stability and broadens classification margins, resulting in accuracy improvements. We validate our approach through extensive experiments on the ModelNet40, ShapeNet, and ScanNet datasets, where we achieve state-of-the-art performance. Notably, our method consumes only 15% of the memory required by competing methods on the ModelNet40 and ShapeNet, while achieving comparable performance on the challenging ScanNet dataset with just 8.5% of the memory. These results underscore the scalability, effectiveness, and privacy-preserving strengths of our framework for 3D object classification.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Roussel Desmond Nzoyem, David Barton, Tom Deakin

Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This problem becomes more challenging when the changing parameters are unobserved, meaning their value or influence cannot be directly measured when collecting data. To address this issue, we introduce Neural Context Flow (NCF), a robust and interpretable Meta-Learning framework that includes uncertainty estimation. NCF uses Taylor expansion to enable contextual self-modulation, allowing context vectors to influence dynamics from other domains while also modulating themselves. After establishing theoretical guarantees, we empirically test NCF and compare it to related adaptation methods. Our results show that NCF achieves state-of-the-art Out-of-Distribution performance on 5 out of 6 linear and non-linear benchmark problems. Through extensive experiments, we explore the flexible model architecture of NCF and the encoded representations within the learned context vectors. Our findings highlight the potential implications of NCF for foundational models in the physical sciences, offering a promising approach to improving the adaptability and generalization of NODEs in various scientific applications.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Angelo Porrello, Lorenzo Bonicelli, Pietro Buzzega, Monica Millunzi, Simone Calderara, Rita Cucchiara

The fine-tuning of deep pre-trained models has revealed compositional properties, with multiple specialized modules that can be arbitrarily composed into a single, multi-task model. However, identifying the conditions that promote compositionality remains an open issue, with recent efforts concentrating mainly on linearized networks. We conduct a theoretical study that attempts to demystify compositionality in standard non-linear networks through the second-order Taylor approximation of the loss function. The proposed formulation highlights the importance of staying within the pre-training basin to achieve composable modules. Moreover, it provides the basis for two dual incremental training algorithms: the one from the perspective of multiple models trained individually, while the other aims to optimize the composed model as a whole. We probe their application in incremental classification tasks and highlight some valuable skills. In fact, the pool of incrementally learned modules not only supports the creation of an effective multi-task model but also enables unlearning and specialization in certain tasks. Code available at <https://github.com/aimagelab/mammoth>

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Youngjun Lee, Doyoung Kim, Junhyeok Kang, Jihwan Bang, Hwanjun Song, Jae-Gil Lee

Vision-language models (VLMs) are known to be susceptible to distribution shifts between pre-training data and test data, and test-time adaptation (TTA) methods for VLMs have been proposed to mitigate the detrimental impact of the distribution shifts. However, the existing methods solely rely on the internal knowledge encoded within the model parameters, which are constrained to pre-training data. To complement the limitation of the internal knowledge, we propose **Retrieval-Augmented-TTA (RA-TTA)** for adapting VLMs to test distribution using **external** knowledge obtained from a web-scale image database. By fully exploiting the bi-modality of VLMs, RA-TTA **adaptively** retrieves proper external images for each test image to refine VLMs' predictions using the retrieved external images, where fine-grained **text descriptions** are leveraged to extend the granularity of external knowledge. Extensive experiments on 17 datasets demonstrate that the proposed RA-TTA outperforms the state-of-the-art methods by 3.01-9.63\% on average.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Hao Dong, Eleni Chatzi, Olga Fink

Test-time adaptation (TTA) has demonstrated significant potential in addressing distribution shifts between training and testing data. Open-set test-time adaptation (OSTTA) aims to adapt a source pre-trained model online to an unlabeled target domain that contains unknown classes. This task becomes more challenging when multiple modalities are involved. Existing methods have primarily focused on unimodal OSTTA, often filtering out low-confidence samples without addressing the complexities of multimodal data. In this work, we present Adaptive Entropy-aware Optimization (AEO), a novel framework specifically designed to tackle Multimodal Open-set Test-time Adaptation (MM-OSTTA) for the first time. Our analysis shows that the entropy difference between known and unknown samples in the target domain strongly correlates with MM-OSTTA performance. To leverage this, we propose two key components: Unknown-aware Adaptive Entropy Optimization (UAE) and Adaptive Modality Prediction Discrepancy Optimization (AMP). These components enhance the model’s ability to distinguish unknown class samples during online adaptation by amplifying the entropy difference between known and unknown samples. To thoroughly evaluate our proposed methods in the MM-OSTTA setting, we establish a new benchmark derived from existing datasets. This benchmark includes two downstream tasks – action recognition and 3D semantic segmentation – and incorporates five modalities: video, audio, and optical flow for action recognition, as well as LiDAR and camera for 3D semantic segmentation. Extensive experiments across various domain shift situations demonstrate the efficacy and versatility of the AEO framework. Additionally, we highlight the strong performance of AEO in long-term and continual MM-OSTTA settings, both of which are challenging and highly relevant to real-world applications. This underscores AEO’s robustness and adaptability in dynamic environments. Our source code and benchmarks are available at https://github.com/donghao51/AEO.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Gaurav Patel, Christopher M. Sandino, Behrooz Mahasseni, Ellen Zippi, Erdrin Azemi, Ali Moin, Juri Minxha

In this paper, we propose a framework for efficient Source-Free Domain Adaptation (SFDA) in the context of time-series, focusing on enhancing both parameter efficiency and data-sample utilization. Our approach introduces an improved paradigm for source-model preparation and target-side adaptation, aiming to enhance training efficiency during target adaptation. Specifically, we reparameterize the source model's weights in a Tucker-style decomposed manner, factorizing the model into a compact form during the source model preparation phase. During target-side adaptation, only a subset of these decomposed factors is fine-tuned, leading to significant improvements in training efficiency. We demonstrate using PAC Bayesian analysis that this selective fine-tuning strategy implicitly regularizes the adaptation process by constraining the model's learning capacity. Furthermore, this re-parameterization reduces the overall model size and enhances inference efficiency, making the approach particularly well suited for resource-constrained devices. Additionally, we demonstrate that our framework is compatible with various SFDA methods and achieves significant computational efficiency, reducing the number of fine-tuned parameters and inference overhead in terms of MACs by over 90\% while maintaining model performance.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Haoran Chen, Micah Goldblum, Zuxuan Wu, Yu-Gang Jiang

Continual learning, also known as lifelong learning or incremental learning, refers to the process by which a model learns from a stream of incoming data over time. A common problem in continual learning is the classification layer’s bias towards the most recent task. Traditionally, methods have relied on incorporating data from past tasks during training to mitigate this issue. However, the recent shift in continual learning to memory-free environments has rendered these approaches infeasible. In this study, we propose a solution focused on the testing phase. We first introduce a simple Out-of-Task Detection method, OTD, designed to accurately identify samples from past tasks during testing. Leveraging OTD, we then propose: (1) an Adaptive Retention mechanism for dynamically tuning the classifier layer on past task data; (2) an Adaptive Correction mechanism for revising predictions when the model classifies data from previous tasks into classes from the current task. We name our approach Adaptive Retention & Correction (ARC). While designed for memory-free environments, ARC also proves effective in memorybased settings. Extensive experiments show that our proposed method can be plugged in to virtually any existing continual learning approach without requiring any modifications to its training procedure. Specifically, when integrated with state-of-the-art approaches, ARC achieves an average performance increase of 2.7% and 2.6% on the CIFAR-100 and Imagenet-R datasets, respectively

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Hanmo Liu, Shimin Di, Jialiang Wang, Zhili Wang, Jiachuan Wang, Xiaofang Zhou, Lei Chen

In recent years, the design and transfer of neural network models have been widely studied due to their exceptional performance and capabilities. However, the complex nature of datasets and the vast architecture space pose significant challenges for both manual and automated algorithms in creating high-performance models. Inspired by researchers who design, train, and document the performance of various models across different datasets, this paper introduces a novel schema that transforms the benchmark data into a Knowledge Benchmark Graph (KBG), which primarily stores the facts in the form of performance(data, model). Constructing the KBG facilitates the structured storage of design knowledge, aiding subsequent model design and transfer. However, it is a non-trivial task to retrieve or design suitable neural networks based on the KBG, as real-world data are often off the records. To tackle this challenge, we propose transferring existing models stored in KBG by establishing correlations between unseen and previously seen datasets. Given that measuring dataset similarity is a complex and open-ended issue, we explore the potential for evaluating the correctness of the similarity function. Then, we further integrate the KBG with Large Language Models (LLMs), assisting LLMs to think and retrieve existing model knowledge in a manner akin to humans when designing or transferring models. We demonstrate our method specifically in the context of Graph Neural Network (GNN) architecture design, constructing a KBG (with 26,206 models, 211,669 performance records, and 2,540,064 facts) and validating the effectiveness of leveraging the KBG to promote GNN architecture design.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Weicai Yan, Wang Lin, Zirun Guo, Ye Wang, Fangming Feng, Xiaoda Yang, zehan wang, Tao Jin

Prompt learning has demonstrated promising results in fine-tuning pre-trained multimodal models. However, the performance improvement is limited when applied to more complex and fine-grained tasks. The reason is that most existing methods directly optimize the parameters involved in the prompt generation process through loss backpropagation, which constrains the richness and specificity of the prompt representations. In this paper, we propose Diffusion-Driven Prompt Generator (Diff-Prompt), aiming to use the diffusion model to generate rich and fine-grained prompt information for complex downstream tasks. Specifically, our approach consists of three stages. In the first stage, we train a Mask-VAE to compress the masks into latent space. In the second stage, we leverage an improved Diffusion Transformer (DiT) to train a prompt generator in the latent space, using the masks for supervision. In the third stage, we align the denoising process of the prompt generator with the pre-trained model in the semantic space, and use the generated prompts to fine-tune the model. We conduct experiments on a complex pixel-level downstream task, referring expression comprehension, and compare our method with various parameter-efficient fine-tuning approaches. Diff-Prompt achieves a maximum improvement of 8.87 in R@1 and 14.05 in R@5 compared to the foundation model and also outperforms other state-of-the-art methods across multiple metrics. The experimental results validate the effectiveness of our approach and highlight the potential of using generative models for prompt generation. Code is available at https://github.com/Kelvin-ywc/diff-prompt.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Jonathan Kahana, Eliahu Horwitz, Imri Shuval, Yedid Hoshen

Weight space learning aims to extract information about a neural network, such as its training dataset or generalization error. Recent approaches learn directly from model weights, but this presents many challenges as weights are high-dimensional and include permutation symmetries between neurons. An alternative approach, Probing, represents a model by passing a set of learned inputs (probes) through the model, and training a predictor on top of the corresponding outputs. Although probing is typically not used as a stand alone approach, our preliminary experiment found that a vanilla probing baseline worked surprisingly well. However, we discover that current probe learning strategies are ineffective. We therefore propose Deep Linear Probe Generators (ProbeGen), a simple and effective modification to probing approaches. ProbeGen adds a shared generator module with a deep linear architecture, providing an inductive bias towards structured probes thus reducing overfitting. While simple, ProbeGen performs significantly better than the state-of-the-art and is very efficient, requiring between 30 to 1000 times fewer FLOPs than other top approaches.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Zhekai Du, Yinjie Min, Jingjing Li, Ke Lu, Changliang Zou, Liuhua Peng, Tingjin Chu, Mingming Gong

Low-rank adaptation (LoRA) has become a prevalent method for adapting pre-trained large language models to downstream tasks. However, the simple low-rank decomposition form may constrain the optimization flexibility. To address this limitation, we introduce Location-aware Cosine Adaptation (LoCA), a novel frequency-domain parameter-efficient fine-tuning method based on inverse Discrete Cosine Transform (iDCT) with selective locations of learnable components. We begin with a comprehensive theoretical comparison between frequency-domain and low-rank decompositions for fine-tuning pre-trained large models. Our analysis reveals that frequency-domain approximation with carefully selected frequency components can surpass the expressivity of traditional low-rank-based methods. Furthermore, we demonstrate that iDCT offers a more efficient implementation compared to inverse Discrete Fourier Transform (iDFT), allowing for better selection and tuning of frequency components while maintaining equivalent expressivity to the optimal iDFT-based adaptation. By employing finite-difference approximation to estimate gradients for discrete locations of learnable coefficients on the DCT spectrum, LoCA dynamically selects the most informative frequency components during training. Experiments on diverse language and vision fine-tuning tasks demonstrate that LoCA offers enhanced parameter efficiency while maintains computational feasibility comparable to low-rank-based methods.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Minyoung Kim, Timothy Hospedales

We tackle the problem of parameter-efficient fine-tuning (PEFT) of a pre-trained large deep model on many different but related tasks. Instead of the simple but strong baseline strategy of task-wise independent fine-tuning, we aim to meta-learn the core shared information that can be used for unseen test tasks to improve the prediction performance further. That is, we propose a method for {\em learning-to-fine-tune} (LiFT). LiFT introduces a novel hierarchical Bayesian model that can be superior to both existing general meta learning algorithms like MAML and recent LoRA zoo mixing approaches such as LoRA-Retriever and model-based clustering. In our Bayesian model, the parameters of the task-specific LoRA modules are regarded as random variables where these task-wise LoRA modules are governed/regularized by higher-level latent random variables, which represents the prior of the LoRA modules that capture the shared information across all training tasks. To make the posterior inference feasible, we propose a novel SGLD-Gibbs sampling algorithm that is computationally efficient. To represent the posterior samples from the SGLD-Gibbs, we propose an online EM algorithm that maintains a Gaussian mixture representation for the posterior in an online manner in the course of iterative posterior sampling. We demonstrate the effectiveness of LiFT on NLP and vision multi-task meta learning benchmarks.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Frederic Z. Zhang, Paul Albert, Cristian Rodriguez-Opazo, Anton van den Hengel, Ehsan Abbasnejad

Pre-trained models produce strong generic representations that can be adapted via fine-tuning on specialised datasets. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning that enables the model to capture these specialised representations. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks enables modular learning that effectively leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labelled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a parameter-efficient fine-tuning method, particularly with less data, and demonstrate that it can be easily scaled up for higher performance.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Emir Konuk, Christos Matsoukas, Moein Sorkhei, Phitchapha Lertsiravarameth, Kevin Smith

We introduce Learning from Offline Foundation Features with Tensor Augmentations (LOFF-TA), an efficient training scheme designed to harness the capabilities of foundation models in limited resource settings where their direct development is not feasible. LOFF-TA involves training a compact classifier on cached feature embeddings from a frozen foundation model, resulting in up to $37\times$ faster training and up to $26\times$ reduced GPU memory usage. Because the embeddings of augmented images would be too numerous to store, yet the augmentation process is essential for training, we propose to apply tensor augmentations to the cached embeddings of the original non-augmented images. LOFF-TA makes it possible to leverage the power of foundation models, regardless of their size, in settings with limited computational capacity. Moreover, LOFF-TA can be used to apply foundation models to high-resolution images without increasing compute. In certain scenarios, we find that training with LOFF-TA yields better results than directly fine-tuning the foundation model.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Jiechao Guan, Hui Xiong

Hierarchical Bayesian bandit refers to the multi-task bandit problem in which bandit tasks are assumed to be drawn from the same distribution. In this work, we provide improved Bayes regret bounds for hierarchical Bayesian bandit algorithms in the multi-task linear bandit and semi-bandit settings. For the multi-task linear bandit, we first analyze the preexisting hierarchical Thompson sampling (HierTS) algorithm, and improve its gap-independent Bayes regret bound from $O(m\sqrt{n\log{n}\log{(mn)}})$ to $O(m\sqrt{n\log{n}})$ in the case of infinite action set, with $m$ being the number of tasks and $n$ the number of iterations per task. In the case of finite action set, we propose a novel hierarchical Bayesian bandit algorithm, named hierarchical BayesUCB (HierBayesUCB), that achieves the logarithmic but gap-dependent regret bound $O(m\log{(mn)}\log{n})$ under mild assumptions. All of the above regret bounds hold in many variants of hierarchical Bayesian linear bandit problem, including when the tasks are solved sequentially or concurrently. Furthermore, we extend the aforementioned HierTS and HierBayesUCB algorithms to the multi-task combinatorial semi-bandit setting. Concretely, our combinatorial HierTS algorithm attains comparable Bayes regret bound $O(m\sqrt{n}\log{n})$ with respect to the latest one. Moreover, our combinatorial HierBayesUCB yields a sharper Bayes regret bound $O(m\log{(mn)}\log{n})$. Experiments are conducted to validate the soundness of our theoretical results for multi-task bandit algorithms.