论文检索

Theory · Online Learning and Bandits

Harin Lee, Taehyun Hwang, Min-hwan Oh

We consider a stochastic sparse linear bandit problem where only a sparse subset of context features affects the expected reward function, i.e., the unknown reward parameter has a sparse structure.In the existing Lasso bandit literature, the compatibility conditions, together with additional diversity conditions on the context features are imposed to achieve regret bounds that only depend logarithmically on the ambient dimension $d$.In this paper, we demonstrate that even without the additional diversity assumptions, the \textit{compatibility condition on the optimal arm} is sufficient to derive a regret bound that depends logarithmically on $d$, and our assumption is strictly weaker than those used in the lasso bandit literature under the single-parameter setting.We propose an algorithm that adapts the forced-sampling technique and prove that the proposed algorithm achieves $\mathcal{O}(\text{poly}\log dT)$ regret under the margin condition.To our knowledge, the proposed algorithm requires the weakest assumptions among Lasso bandit algorithms under the single-parameter setting that achieve $\mathcal{O}(\text{poly}\log dT)$ regret.Through numerical experiments, we confirm the superior performance of our proposed algorithm.

Theory · Online Learning and Bandits

Chuan Liu, Ruibing Song, Chunshu Wu, Pouya Haghi, Tong Geng

Time-series modeling is broadly adopted to capture underlying patterns present in historical data, allowing prediction of future values. However, one crucial aspect of such modeling is often overlooked: in highly dynamic environments, data distributions can shift drastically within a second or less. Under these circumstances, traditional predictive models, and even online learning methods, struggle to adapt to the ultra-fast and complex distribution shifts present in highly dynamic scenarios. To address this, we propose InstaTrain, a novel learning approach that enables ultra-fast model updates for real-world prediction tasks, thereby keeping pace with rapidly evolving data distributions. In this work, (1) we transform the slow and expensive training process into an ultra-fast natural annealing process within a dynamical system. (2) Leveraging a recently proposed electronic dynamical system, we augment the system with parameter update modules, extending its capabilities to encompass both rapid training and inference. Experimental results on highly dynamic datasets demonstrate that our method achieves orders-of-magnitude improvements in training speed and energy efficiency while delivering superior accuracy compared to baselines running on GPUs.

Theory · Online Learning and Bandits

Yu Chen, Jiatai Huang, Yan Dai, Longbo Huang

In this paper, we present a novel algorithm, `uniINF`, for the Heavy-Tailed Multi-Armed Bandits (HTMAB) problem, demonstrating robustness and adaptability in both stochastic and adversarial environments. Unlike the stochastic MAB setting where loss distributions are stationary with time, our study extends to the adversarial setup, where losses are generated from heavy-tailed distributions that depend on both arms and time. Our novel algorithm `uniINF` enjoys the so-called Best-of-Both-Worlds (BoBW) property, performing optimally in both stochastic and adversarial environments *without* knowing the exact environment type. Moreover, our algorithm also possesses a Parameter-Free feature, *i.e.*, it operates *without* the need of knowing the heavy-tail parameters $(\sigma, \alpha)$ a-priori.To be precise, `uniINF` ensures nearly-optimal regret in both stochastic and adversarial environments, matching the corresponding lower bounds when $(\sigma, \alpha)$ is known (up to logarithmic factors). To our knowledge, `uniINF` is the first parameter-free algorithm to achieve the BoBW property for the heavy-tailed MAB problem. Technically, we develop innovative techniques to achieve BoBW guarantees for Parameter-Free HTMABs, including a refined analysis for the dynamics of log-barrier, an auto-balancing learning rate scheduling scheme, an adaptive skipping-clipping loss tuning technique, and a stopping-time analysis for logarithmic regret.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Ze Yang, Shichao Dong, Ruibo Li, Nan Song, Guosheng Lin

Panoptic segmentation, which unifies semantic and instance segmentation into a single task, has witnessed considerable success on predefined tasks. However, traditional methods tend to struggle with catastrophic forgetting and poor generalization when learning from a continuous stream of new tasks. While continual learning aims to mitigate these challenges, our study reveals that existing continual panoptic segmentation (CPS) methods often suffer from efficiency or scalability issues. To address these limitations, we propose an efficient adaptation framework that incorporates attentive self-distillation and dual-decoder prediction fusion to efficiently preserve prior knowledge while facilitating model generalization. Specifically, we freeze the majority of model weights, enabling a shared forward pass between the teacher and student models during distillation. Attentive self-distillation then adaptively distills useful knowledge from the old classes without being distracted from non-object regions, which effectively enhances knowledge retention. Additionally, query-level fusion (QLF) is devised to seamlessly integrate the output of the dual decoders without incurring scale inconsistency. Our method achieves state-of-the-art performance on ADE20K and COCO benchmarks. Code is available at https://github.com/Ze-Yang/ADAPT.

Theory · Online Learning and Bandits

Solenne Gaucher, Martino Bernasconi, Matteo Castiglioni, Andrea Celli, Vianney Perchet

Bilateral trade models the problem of facilitating trades between a seller and a buyer having private valuations for the item being sold. In the online version of the problem, the learner faces a new seller and buyer at each time step, and has to post a price for each of the two parties without any knowledge of their valuations. We consider a scenario where, at each time step, before posting prices the learner observes a context vector containing information about the features of the item for sale. The valuations of both the seller and the buyer follow an unknown linear function of the context. In this setting, the learner could leverage previous transactions in an attempt to estimate private valuations. We characterize the regret regimes of different settings, taking as a baseline the best context-dependent prices in hindsight. First, in the setting in which the learner has two-bit feedback and strong budget balance constraints, we propose an algorithm with $O(\log T)$ regret. Then, we study the same set-up with noisy valuations, providing a tight $\widetilde O(T^{2/3})$ regret upper bound. Finally, we show that loosening budget balance constraints allows the learner to operate under more restrictive feedback. Specifically, we show how to address the one-bit, global budget balance setting through a reduction from the two-bit, strong budget balance setup. This established a fundamental trade-off between the quality of the feedback and the strictness of the budget constraints.

Theory · Online Learning and Bandits

Xuchuang Wang, Maoli Liu, Jinhang Zuo, Xutong Liu, John C.S. Lui, Mohammad Hajiesmaili

This paper investigates stochastic multi-armed bandit algorithms that are robust to adversarial attacks, where an attacker can first observe the learner's action and *then* alter their reward observation.We study two cases of this model, with or without the knowledge of an attack budget $C$, defined as an upper bound of the summation of the difference between the actual and altered rewards. For both cases, we devise two types of algorithms with regret bounds having additive or multiplicative $C$ dependence terms.For the known attack budget case, we prove our algorithms achieve the regret bound of ${O}((K/\Delta)\log T + KC)$ and $\tilde{O}(\sqrt{KTC})$ for the additive and multiplicative $C$ terms, respectively, where $K$ is the number of arms, $T$ is the time horizon, $\Delta$ is the gap between the expected rewards of the optimal arm and the second-best arm, and $\tilde{O}$ hides the logarithmic factors.For the unknown case, we prove our algorithms achieve the regret bound of $\tilde{O}(\sqrt{KT} + KC^2)$ and $\tilde{O}(KC\sqrt{T})$ for the additive and multiplicative $C$ terms, respectively.In addition to these upper bound results, we provide several lower bounds showing the tightness of our bounds and the optimality of our algorithms.These results delineate an intrinsic separation between the bandits with attacks and corruption models.

Reinforcement Learning · Online

GUOJUN XIONG, Ujwal Dinesha, Debajoy Mukherjee, Jian Li, Srinivas Shakkottai

Restless multi-armed bandits (RMAB) has been widely used to model constrained sequential decision making problems, where the state of each restless arm evolves according to a Markov chain and each state transition generates a scalar reward. However, the success of RMAB crucially relies on the availability and quality of reward signals. Unfortunately, specifying an exact reward function in practice can be challenging and even infeasible. In this paper, we introduce Pref-RMAB, a new RMAB model in the presence of preference signals, where the decision maker only observes pairwise preference feedback rather than scalar reward from the activated arms at each decision epoch. Preference feedback, however, arguably contains less information than the scalar reward, which makes Pref-RMAB seemingly more difficult. To address this challenge, we present a direct online preference learning (DOPL) algorithm for Pref-RMAB to efficiently explore the unknown environments, adaptively collect preference data in an online manner, and directly leverage the preference feedback for decision-makings. We prove that DOPL yields a sublinear regret. To our best knowledge, this is the first algorithm to ensure $\tilde{\mathcal{O}}(\sqrt{T\ln T})$ regret for RMAB with preference feedback. Experimental results further demonstrate the effectiveness of DOPL.

Theory · Online Learning and Bandits

Jack Sandberg, Niklas Åkerblom, Morteza Haghir Chehreghani

We consider the combinatorial volatile Gaussian process (GP) semi-bandit problem. Each round, an agent is provided a set of available base arms and must select a subset of them to maximize the long-term cumulative reward. We study the Bayesian setting and provide novel Bayesian cumulative regret bounds for three GP-based algorithms: GP-UCB, GP-BayesUCB and GP-TS. Our bounds extend previous results for GP-UCB and GP-TS to the \emph{infinite}, \emph{volatile} and \emph{combinatorial} setting, and to the best of our knowledge, we provide the first regret bound for GP-BayesUCB. Volatile arms encompass other widely considered bandit problems such as contextual bandits.Furthermore, we employ our framework to address the challenging real-world problem of online energy-efficient navigation, where we demonstrate its effectiveness compared to the alternatives.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Evgenii Dzhivelikian, Petr Kuderov, Aleksandr Panov

This paper presents a novel approach to address the challenge of online sequence learning for decision making under uncertainty in non-stationary, partially observable environments. The proposed algorithm, Distributed Hebbian Temporal Memory (DHTM), is based on the factor graph formalism and a multi-component neuron model. DHTM aims to capture sequential data relationships and make cumulative predictions about future observations, forming Successor Features (SFs). Inspired by neurophysiological models of the neocortex, the algorithm uses distributed representations, sparse transition matrices, and local Hebbian-like learning rules to overcome the instability and slow learning of traditional temporal memory algorithms such as RNN and HMM. Experimental results show that DHTM outperforms LSTM, RWKV and a biologically inspired HMM-like algorithm, CSCG, on non-stationary data sets. Our results suggest that DHTM is a promising approach to address the challenges of online sequence learning and planning in dynamic environments.

Theory · Online Learning and Bandits

Joe Suk, Arpit Agarwal

In $K$-armed dueling bandits, the learner receives preference feedback between arms, and the regret of an arm is defined in terms of its suboptimality to a winner arm. The non-stationary variant of the problem, motivated by concerns of changing user preferences, has received recent interest (Saha and Gupta, 2022; Buening and Saha, 2023; Suk and Agarwal, 2023). The goal here is to design algorithms with low dynamic regret, ideally without foreknowledge of the amount of change. The notion of regret here is tied to a notion of winner arm, most typically taken to be a so-called Condorcet winner or a Borda winner. However, the aforementioned results mostly focus on the Condorcet winner. In comparison, the Borda version of this problem has received less attention which is the focus of this work. We establish the first optimal and adaptive dynamic regret upper bound $\tilde{O}(\tilde{L}^{1/3} K^{1/3} T^{2/3})$, where $\tilde{L}$ is the unknown number of significant Borda winner switches. We also introduce a novel weighted Borda score framework which generalizes both the Borda and Condorcet problems. This framework surprisingly allows a Borda-style regret analysis of the Condorcet problem and establishes improved bounds over the theoretical state-of-art in regimes with a large number of arms or many spurious changes in Condorcet winner. Such a generalization was not known and could be of independent interest.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Minhyuk Seo, Hyunseo Koh, Jonghyun Choi

The majority of online continual learning (CL) advocates single-epoch training and imposes restrictions on the size of replay memory. However, single-epoch training would incur a different amount of computations per CL algorithm, and the additional storage cost to store logit or model in addition to replay memory is largely ignored in calculating the storage budget. Arguing different computational and storage budgets hinder fair comparison among CL algorithms in practice, we propose to use floating point operations (FLOPs) and total memory size in Byte as a metric for computational and memory budgets, respectively, to compare and develop CL algorithms in the same ‘total resource budget.’ To improve a CL method in a limited total budget, we propose adaptive layer freezing that does not update the layers for less informative batches to reduce computational costs with a negligible loss of accuracy. In addition, we propose a memory retrieval method that allows the model to learn the same amount of knowledge as using random retrieval in fewer iterations. Empirical validations on the CIFAR-10/100, CLEAR-10/100, and ImageNet-1K datasets demonstrate that the proposed approach outperforms the state-of-the-art methods within the same total budget. Furthermore, we validate its effectiveness in the Multi-modal Concept incremental Learning setup with multimodal large language models, such as LLaVA-1.5-7B. Code is available at https://github.com/snumprlab/budgeted-cl.

Theory · Online Learning and Bandits

Arun Verma, Zhongxiang Dai, Xiaoqiang Lin, Patrick Jaillet, Bryan Kian Hsiang Low

Contextual dueling bandit is used to model the bandit problems, where a learner's goal is to find the best arm for a given context using observed noisy human preference feedback over the selected arms for the past contexts. However, existing algorithms assume the reward function is linear, which can be complex and non-linear in many real-life applications like online recommendations or ranking web search results. To overcome this challenge, we use a neural network to estimate the reward function using preference feedback for the previously selected arms. We propose upper confidence bound- and Thompson sampling-based algorithms with sub-linear regret guarantees that efficiently select arms in each round. We also extend our theoretical results to contextual bandit problems with binary feedback, which is in itself a non-trivial contribution. Experimental results on the problem instances derived from synthetic datasets corroborate our theoretical results.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Yuwei Luo, Mohsen Bayati

This paper is motivated by recent research in the $d$-dimensional stochastic linear bandit literature, which has revealed an unsettling discrepancy: algorithms like Thompson sampling and Greedy demonstrate promising empirical performance, yet this contrasts with their pessimistic theoretical regret bounds. The challenge arises from the fact that while these algorithms may perform poorly in certain problem instances, they generally excel in typical instances. To address this, we propose a new data-driven technique that tracks the geometric properties of the uncertainty ellipsoid around the main problem parameter. This methodology enables us to formulate a data-driven frequentist regret bound, which incorporates the geometric information, for a broad class of base algorithms, including Greedy, OFUL, and Thompson sampling. This result allows us to identify and ``course-correct" problem instances in which the base algorithms perform poorly. The course-corrected algorithms achieve the minimax optimal regret of order $\tilde{\mathcal{O}}(d\sqrt{T})$ for a $T$-period decision-making scenario, effectively maintaining the desirable attributes of the base algorithms, including their empirical efficacy. We present simulation results to validate our findings using synthetic and real data.

Theory · Online Learning and Bandits

Yuwei Cheng, Fan Yao, Xuefeng Liu, Haifeng Xu

This paper studies Learning from Imperfect Human Feedback (LIHF), addressing the potential irrationality or imperfect perception when learning from comparative human feedback. Building on evidences that human's imperfection decays over time (i.e., humans learn to improve), we cast this problem as a concave-utility continuous-action dueling bandit but under a restricted form of corruption: i.e., the corruption scale is decaying over time as $t^{\rho-1}$ for some ``imperfection rate'' $\rho \in [0, 1]$. With $T$ as the total number of iterations, we establish a regret lower bound of $ \Omega(\max\{\sqrt{T}, T^{\rho}\})$ for LIHF, even when $\rho$ is known. For the same setting, we develop the Robustified Stochastic Mirror Descent for Imperfect Dueling (RoSMID) algorithm, which achieves nearly optimal regret $\tilde{\mathcal{O}}(\max\{\sqrt{T}, T^{\rho}\})$. Core to our analysis is a novel framework for analyzing gradient-based algorithms for dueling bandit under corruption, and we demonstrate its general applicability by showing how this framework can be easily applied to obtain corruption-robust guarantees for other popular gradient-based dueling bandit algorithms. Our theoretical results are validated by extensive experiments.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Jaehyun Park, Dongmin Park, Jae-Gil Lee

*Continual learning (CL)* enables deep neural networks to adapt to ever-changing data distributions. In practice, there may be scenarios where annotation is costly, leading to *active continual learning (ACL)*, which performs *active learning (AL)* for the CL scenarios when reducing the labeling cost by selecting the most informative subset is preferable. However, conventional AL strategies are not suitable for ACL, as they focus solely on learning the new knowledge, leading to *catastrophic forgetting* of previously learned tasks. Therefore, ACL requires a new AL strategy that can balance the prevention of catastrophic forgetting and the ability to quickly learn new tasks. In this paper, we propose **AccuACL**, **Accu**mulated informativeness-based **A**ctive **C**ontinual **L**earning, by the novel use of the Fisher information matrix as a criterion for sample selection, derived from a theoretical analysis of the Fisher-optimality preservation properties within the framework of ACL, while also addressing the scalability issue of Fisher information-based AL. Extensive experiments demonstrate that AccuACL significantly outperforms AL baselines across various CL algorithms, increasing the average accuracy and forgetting by 23.8% and 17.0%, respectively, on average.

Theory · Online Learning and Bandits

Jung-hun Kim, Min-hwan Oh

In this study, we investigate the problem of dynamic multi-product selection and pricing by introducing a novel framework based on a *censored multinomial logit* (C-MNL) choice model. In this model, sellers present a set of products with prices, and buyers filter out products priced above their valuation, purchasing at most one product from the remaining options based on their preferences. The goal is to maximize seller revenue by dynamically adjusting product offerings and prices, while learning both product valuations and buyer preferences through purchase feedback. To achieve this, we propose a Lower Confidence Bound (LCB) pricing strategy. By combining this pricing strategy with either an Upper Confidence Bound (UCB) or Thompson Sampling (TS) product selection approach, our algorithms achieve regret bounds of $\tilde{O}(d^{\frac{3}{2}}\sqrt{T/\kappa})$ and $\tilde{O}(d^{2}\sqrt{T/\kappa})$, respectively. Finally, we validate the performance of our methods through simulations, demonstrating their effectiveness.

Theory · Online Learning and Bandits

Fang Kong, Jingqi Tang, Mingzhu Li, Pinyan Lu, John C.S. Lui, Shuai Li

A rich line of recent works studies how participants in matching markets learn their unknown preferences through iterative interactions with each other. The two sides of participants in the market can be respectively formulated as players and arms in the bandit problem. To ensure market stability, the objective is to minimize the stable regret of each player. Though existing works provide significant theoretical upper bounds for players' stable regret, the results heavily rely on the assumption that each participant has a strict preference ranking. However, in real applications, multiple candidates (e.g., workers in the labor market and students in school admission) usually demonstrate comparable performance levels, making it challenging for participants (e.g., employers and schools) to differentiate and rank their preferences. To deal with the potential indifferent preferences, we propose an adaptive exploration algorithm based on arm-guided Gale-Shapley (AE-AGS). We show that its stable regret is of order $O(NK \log T / \Delta^2)$, where $N$ is the number of players, $K$ the number of arms, $T$ the total time horizon, and $\Delta$ the minimum non-zero preference gap. Extensive experiments demonstrate the algorithm's effectiveness in handling such complex situations and its consistent superiority over baselines.

Theory · Online Learning and Bandits

Zihan Zhang, Xiangyang Ji, Yuan Zhou

We study the optimal batch-regret tradeoff for batch linear contextual bandits. For this problem, we design batch learning algorithms and prove that they achieve the optimal regret bounds (up to logarithmic factors) for any batch number $M$, number of actions $K$, time horizon $T$, and dimension $d$. Therefore, we establish the \emph{full-parameter-range} (almost) optimal batch-regret tradeoff for the batch linear contextual bandit problem. Along our analysis, we also prove a new matrix concentration inequality with dependence on their dynamic upper bounds, which, to the best of our knowledge, is the first of its kind in literature and maybe of independent interest.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Aldo Pacchiano

Many works have developed no-regret algorithms for contextual bandits with function approximation, where the mean rewards over context-action pairs belong to a function class $\mathcal{F}$. Although there are many approaches to this problem, algorithms based on the principle of optimism, such as optimistic least squares have gained in importance. It can be shown the regret of this algorithm scales as $\widetilde{\mathcal{O}}\left(\sqrt{d_{\mathrm{eluder}}(\mathcal{F}) \log(\mathcal{F}) T }\right)$ where $d_{\mathrm{eluder}}(\mathcal{F})$ is a statistical measure of the complexity of the function class $\mathcal{F}$ known as eluder dimension. Unfortunately, even if the variance of the measurement noise of the rewards at time $t$ equals $\sigma_t^2$ and these are close to zero, the optimistic least squares algorithm’s regret scales with $\sqrt{T}$. In this work we are the first to develop algorithms that satisfy regret bounds for contextual bandits with function approximation of the form $\widetilde{\mathcal{O}}\left( \sigma \sqrt{\log(\mathcal{F})d_{\mathrm{eluder}}(\mathcal{F}) T } + d_{\mathrm{eluder}}(\mathcal{F}) \cdot \log(|\mathcal{F}|)\right) $ when the variances are unknown and satisfy $\sigma_t^2 = \sigma$ for all $t$ and $\widetilde{\mathcal{O}}\left( d_{\mathrm{eluder}}(\mathcal{F})\sqrt{\log(\mathcal{F})\sum_{t=1}^T \sigma_t^2 } + d_{\mathrm{eluder}}(\mathcal{F}) \cdot \log(|\mathcal{F}|)\right) $ when the variances change every time-step. These bounds generalize existing techniques for deriving second order bounds in contextual linear problems.

Theory · Online Learning and Bandits

T-H. Hubert Chan, Shaofeng Jiang, Tianyi Wu, Mengshi Zhao

We give online algorithms for $k$-Means(more generally, $(k, z)$-Clustering) with nearly optimal consistency (a notion suggested by Lattanzi & Vassilvitskii (2017)). Our result turns any $\alpha$-approximate offline algorithm for clustering into an $(1+\epsilon)\alpha^2$-competitive online algorithm for clustering with $O(k \text{poly} \log n)$ consistency. This consistency bound is optimal up to $\text{poly} \log(n)$ factors. Plugging in the offline algorithm that returns the exact optimal solution, we obtain the first$(1 + \epsilon)$-competitive online algorithm for clustering that achieves a linear in $k$ consistency.This simultaneously improves several previous results (Lattanzi & Vassilvitskii, 2017; Fichtenberger et al., 2021). We validate the performance of our algorithm on real datasets by plugging in the practically efficient $k$-Means++ algorithm. Our online algorithm makes $k$-Means++ achieve good consistency with little overhead to the quality of solutions.