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General Machine Learning · Online Learning, Active Learning and Bandits

Chengbo Zang, Mehmet Turkcan, Gil Zussman, Zoran Kostic, Javad Ghaderi

We propose a framework for adaptive data collection aimed at robust learning in multi-distribution scenarios under a fixed data collection budget. In each round, the algorithm selects a distribution source to sample from for data collection and updates the model parameters accordingly. The objective is to find the model parameters that minimize the expected loss across all the data sources. Our approach integrates upper-confidence-bound (UCB) sampling with online gradient descent (OGD) to dynamically collect and annotate data from multiple sources. By bridging online optimization and multi-armed bandits, we provide theoretical guarantees for our UCB-OGD approach, demonstrating that it achieves a minimax regret of $O(T^{\frac{1}{2}}(K\ln T)^{\frac{1}{2}})$ over $K$ data sources after $T$ rounds. We further provide a lower bound showing that the result is optimal up to a $\ln T$ factor. Extensive evaluations on standard datasets and a real-world testbed for object detection in smart-city intersections validate the consistent performance improvements of our method compared to baselines such as random sampling and various active learning methods.

General Machine Learning · Online Learning, Active Learning and Bandits

Xuchuang Wang, Qirun Zeng, Jinhang Zuo, Xutong Liu, Mohammad Hajiesmaili, John C. S. Lui, Adam Wierman

This paper investigates the fusion of absolute (reward) and relative (dueling) feedback in stochastic bandits, where both feedback types are gathered in each decision round. We derive a regret lower bound, demonstrating that an efficient algorithm may incur only the smaller among the reward and dueling-based regret for each individual arm. We propose two fusion approaches: (1) a simple elimination fusion algorithm that leverages both feedback types to explore all arms and unifies collected information by sharing a common candidate arm set, and (2) a decomposition fusion algorithm that selects the more effective feedback to explore the corresponding arms and randomly assigns one feedback type for exploration and the other for exploitation in each round. The elimination fusion experiences a suboptimal multiplicative term of the number of arms in regret due to the intrinsic suboptimality of dueling elimination. In contrast, the decomposition fusion achieves regret matching the lower bound up to a constant under a common assumption. Extensive experiments confirm the efficacy of our algorithms and theoretical results.

General Machine Learning · Online Learning, Active Learning and Bandits

Yifeng Wang, Xueying Zhan, Siyu Huang

As deep learning continues to evolve, the need for data efficiency becomes increasingly important. Considering labeling large datasets is both time-consuming and expensive, active learning (AL) provides a promising solution to this challenge by iteratively selecting the most informative subsets of examples to train deep neural networks, thereby reducing the labeling cost. However, the effectiveness of different AL algorithms can vary significantly across data scenarios, and determining which AL algorithm best fits a given task remains a challenging problem. This work presents the first differentiable AL strategy search method, named AutoAL, which is designed on top of existing AL sampling strategies. AutoAL consists of two neural nets, named SearchNet and FitNet, which are optimized concurrently under a differentiable bi-level optimization framework. For any given task, SearchNet and FitNet are iteratively co-optimized using the labeled data, learning how well a set of candidate AL algorithms perform on that task. With the optimal AL strategies identified, SearchNet selects a small subset from the unlabeled pool for querying their annotations, enabling efficient training of the task model. Experimental results demonstrate that AutoAL consistently achieves superior accuracy compared to all candidate AL algorithms and other selective AL approaches, showcasing its potential for adapting and integrating multiple existing AL methods across diverse tasks and domains.

Theory · Online Learning and Bandits

Adrienne Tuynman, Rémy Degenne

In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions.We are interested in batched methods, which change their sampling behaviour only a few times, between batches of observations.We give an instance-dependent lower bound on the number of batches used by any sample efficient algorithm for any pure exploration task.We then give a general batched algorithm and prove upper bounds on its expected sample complexity and batch complexity.We illustrate both lower and upper bounds on best-arm identification and thresholding bandits.

Deep Learning · Large Language Models

Yunlong Hou, Fengzhuo Zhang, Cunxiao Du, Xuan Zhang, Jiachun Pan, Tianyu Pang, Chao Du, Vincent Tan, Zhuoran Yang

Speculative decoding has emerged as a popular method to accelerate the inference of Large Language Models (LLMs) while retaining their superior text generation performance. Previous methods either adopt a fixed speculative decoding configuration regardless of the prefix tokens, or train draft models in an offline or online manner to align them with the context. This paper proposes a training-free online learning framework to adaptively choose the configuration of the hyperparameters for speculative decoding as text is being generated. We first formulate this hyperparameter selection problem as a Multi-Armed Bandit problem and provide a general speculative decoding framework BanditSpec. Furthermore, two bandit-based hyperparameter selection algorithms, UCBSpec and EXP3Spec, are designed and analyzed in terms of a novel quantity, the stopping time regret. We upper bound this regret under both stochastic and adversarial reward settings. By deriving an information-theoretic impossibility result, it is shown that the regret performance of UCBSpec is optimal up to universal constants. Finally, extensive empirical experiments with LLaMA3 and Qwen2 demonstrate that our algorithms are effective compared to existing methods, and the throughput is close to the oracle best hyperparameter in simulated real-life LLM serving scenarios with diverse input prompts.

General Machine Learning · Online Learning, Active Learning and Bandits

Jiahui Zhu, Kihyun Yu, Dabeen Lee, Xin Liu, Honghao Wei

Online safe reinforcement learning (RL) plays a key role in dynamic environments, with applications in autonomous driving, robotics, and cybersecurity. The objective is to learn optimal policies that maximize rewards while satisfying safety constraints modeled by constrained Markov decision processes (CMDPs). Existing methods achieve sublinear regret under stochastic constraints but often fail in adversarial settings, where constraints are unknown, time-varying, and potentially adversarially designed. In this paper, we propose the Optimistic Mirror Descent Primal-Dual (OMDPD) algorithm, the first to address online CMDPs with anytime adversarial constraints. OMDPD achieves optimal regret $\tilde{\mathcal{O}}(\sqrt{K})$ and strong constraint violation $\tilde{\mathcal{O}}(\sqrt{K})$ without relying on Slater’s condition or the existence of a strictly known safe policy. We further show that access to accurate estimates of rewards and transitions can further improve these bounds. Our results offer practical guarantees for safe decision-making in adversarial environments.

General Machine Learning · Sequential, Network, and Time Series Modeling

Yu-Yang Qian, Yuan-Ze Xu, Zhen-Yu Zhang, Peng Zhao, Zhi-Hua Zhou

Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates *continual learning* (CL) to update models online, enabling adaptation to new tasks while preserving past knowledge to prevent catastrophic forgetting. Nowadays, with the flourish of *large pre-trained models* (LPMs), *efficiency* has become increasingly critical for CL, due to their substantial computational demands and growing parameter sizes. In this paper, we introduce TreeLoRA (K-D Tree of Low-Rank Adapters), a novel approach that constructs *layer-wise* adapters by leveraging hierarchical gradient similarity to enable efficient CL, particularly for LPMs. To reduce the computational burden of task similarity estimation, we employ *bandit* techniques to develop an algorithm based on lower confidence bounds to efficiently explore the task structure. Furthermore, we use sparse gradient updates to facilitate parameter optimization, making the approach better suited for LPMs. Theoretical analysis is provided to justify the rationale behind our approach, and experiments on both *vision transformers* (ViTs) and *large language models* (LLMs) demonstrate the effectiveness and efficiency of our approach across various domains, including vision and natural language processing tasks.

Reinforcement Learning · Planning

Tuan Dam

Monte-Carlo Tree Search (MCTS) has demonstrated success in online planning for deterministic environments, yet significant challenges remain in adapting it to stochastic Markov Decision Processes (MDPs), particularly in continuous state-action spaces. Existing methods, such as HOOT, which combines MCTS with the Hierarchical Optimistic Optimization (HOO) bandit strategy, address continuous spaces but rely on a logarithmic exploration bonus that lacks theoretical guarantees in non-stationary, stochastic settings. Recent advancements, such as Poly-HOOT, introduced a polynomial bonus term to achieve convergence in deterministic MDPs, though a similar theory for stochastic MDPs remains undeveloped. In this paper, we propose a novel MCTS algorithm, Stochastic-Power-HOOT, designed for continuous, stochastic MDPs. Stochastic-Power-HOOT integrates a power mean as a value backup operator, alongside a polynomial exploration bonus to address the non-stationarity inherent in continuous action spaces. Our theoretical analysis establishes that Stochastic-Power-HOOT converges at a polynomial rate of $\mathcal{O}(n^{-1/2})$, where \( n \) is the number of visited trajectories, thereby extending the non-asymptotic convergence guarantees of Poly-HOOT to stochastic environments. Experimental results on synthetic and stochastic tasks validate our theoretical findings, demonstrating the effectiveness of Stochastic-Power-HOOT in continuous, stochastic domains.

General Machine Learning · Online Learning, Active Learning and Bandits

Kiran Purohit, Venktesh V, Sourangshu Bhattacharya, Avishek Anand

The in-context learning paradigm with LLMs has been instrumental in advancing a wide range of natural language processing tasks. The selection of few-shot examples (exemplars / demonstration samples) is essential for constructing effective prompts under context-length budget constraints. In this paper, we formulate the exemplar selection task as a top-m best arms identification problem. A key challenge in this setup is the exponentially large number of arms that need to be evaluated to identify the m-best arms. We propose CASE (Challenger Arm Sampling for Exemplar selection), a novel sample-efficient selective exploration strategy that maintains a shortlist of “challenger” arms, which are current candidates for the top-m arms. In each iteration, only one of the arms from this shortlist or the current top-m set is pulled, thereby reducing sample complexity and, consequently, the number of LLM evaluations. Furthermore, we model the scores of exemplar subsets (arms) using a parameterized linear scoring function, leading to stochastic linear bandits setting. CASE achieves remarkable efficiency gains of up to 7× speedup in runtime while requiring 7× fewer LLM calls (87% reduction) without sacrificing performance compared to state-of-the-art exemplar selection methods. We release our code and data (https://github.com/kiranpurohit/CASE).

General Machine Learning · Online Learning, Active Learning and Bandits

Cun-Yuan Xing, Meng-Zhang Qian, Wu-Yang Chen, Wei Gao, Zhi-Hua Zhou

Feature evolvable learning studies the scenario where old features will vanish and new features will emerge when learning with data streams, and various methods have been developed by utilizing some useful relationships from old features to new features, rather than re-training from scratch. In this work, we focus on two fundamental problems: How to characterize the relationships between two different feature spaces, and how to exploit those relationships for feature evolvable learning. We introduce the Kernel Ortho-Mapping (KOM) discrepancy to characterize relationships between two different feature spaces via kernel functions, and correlate with the optimal classifiers learned from different feature spaces. Based on this discrepancy, we develop the one-pass algorithm for feature evolvable learning, which requires going through all instances only once without storing the entire or partial training data. Our basic idea is to take online kernel learning with the random Fourier features and incorporate some feature and label relationships via the KOM discrepancy for feature evolvable learning. We finally validate the effectiveness of our proposed method both theoretically and empirically.

Theory · Online Learning and Bandits

Pierre Laforgue, Giulia Clerici, Nicolò Cesa-Bianchi

Nonstationary phenomena, such as satiation effects in recommendations, have mostly been modeled using bandits with finitely many arms. However, the richer action space provided by linear bandits is often preferred in practice. In this work, we introduce a novel nonstationary linear bandit model, where current rewards are influenced by the learner's past actions in a fixed-size window. Our model, which recovers stationary linear bandits as a special case, leverages two parameters: the window size $m \ge 0$, and an exponent $\gamma$ that captures the rotting ($\gamma < 0)$ or rising ($\gamma > 0$) nature of the phenomenon. When both $m$ and $\gamma$ are known, we propose and analyze a variant of OFUL which minimizes regret against cyclic policies. By choosing the cycle length so as to trade-off approximation and estimation errors, we then prove a bound of order $\sqrt{d}\,(m+1)^{\frac{1}{2}+\max\{\gamma,0\}}\,T^{3/4}$ (ignoring log factors) on the regret against the optimal sequence of actions, where $T$ is the horizon and $d$ is the dimension of the linear action space. Through a bandit model selection approach, our results are then extended to the case where both $m$ and $\gamma$ are unknown. Finally, we complement our theoretical results with experiments comparing our approach to natural baselines.

Theory · Online Learning and Bandits

Rohan Deb, Mohammad Ghavamzadeh, Arindam Banerjee

Conservative Contextual Bandits (CCBs) address safety in sequential decision making by requiring that an agent's policy, along with minimizing regret, also satisfies a safety constraint: the performance is not worse than a baseline policy (e.g., the policy that the company has in production) by more than $(1+\alpha)$ factor. Prior work developed UCB-stylealgorithms for this problem in the multi-armed (Wu et al., 2016) and contextuallinear (Kazerouni et al., 2017) settings.However, in practice the cost of the armsis often a non-linear function, and therefore existing UCB algorithms are ineffective in such settings. In this paper, we consider CCBs beyond the linear case and develop two algorithms $\mathtt{C\text{-}SquareCB}$ and $\mathtt{C\text{-}FastCB}$, using Inverse Gap Weighting (IGW) based exploration and an online regression oracle. We show that the safety constraint is satisfied in high probability and that the regret for $\mathtt{C\text{-}SquareCB}$ is sub-linear in horizon $T$, while the the regret for $\mathtt{C\text{-}FastCB}$ is first-order and is sub-linear in $L^*$, the cumulative loss of the optimal policy. Subsequently, we use a neural network for function approximation and online gradient descent as the regression oracle to provide $\tilde{\mathcal{O}}\big(\sqrt{KT} + K/\alpha\big) $ and $\tilde{\mathcal{O}}\big(\sqrt{KL^*} + K (1 + 1/\alpha)\big)$ regret bounds respectively. Finally, we demonstrate the efficacy of our algorithms on real world data, and show that they significantly outperform the existing baseline while maintaining the performance guarantee.

Theory · Online Learning and Bandits

Xiaoyi Zhu, Zengfeng Huang

This paper considers the Lipschitz bandit problem, where the set of arms is continuous and the expected reward is a Lipschitz function over the arm space. This problem has been extensively studied. Prior algorithms need to store the reward information of all visited arms, leading to significant memory consumption. We address this issue by introducing an algorithm named Log-space Lipschitz bandits (Log-Li), which achieves an optimal (up to logarithmic factors) regret of $\widetilde{O}\left(T^{\frac{d_z+1}{d_z+2}}\right)$ while only uses $O\left(\log T\right)$ bits of memory. Additionally, we provide a complexity analysis for this problem, demonstrating that $\Omega\left(\log T\right)$ bits of space are necessary for any algorithm to achieve the optimal regret. We also conduct numerical simulations, and the results show that our new algorithm achieves regret comparable to the state-of-the-art while reducing memory usage by orders of magnitude.

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

Itai Shufaro, Nadav Merlis, Nir Weinberger, Shie Mannor

In many sequential decision problems, an agent performs a repeated task. He then suffers regret and obtains information that he may use in the following rounds. However, sometimes the agent may also obtain information and avoid suffering regret by querying external sources. We study the trade-off between the information an agent accumulates and the regret it suffers. We invoke information-theoretic methods for obtaining regret lower bounds, that also allow us to easily re-derive several known lower bounds. We introduce the first Bayesian regret lower bounds that depend on the information an agent accumulates. We also prove regret upper bounds using the amount of information the agent accumulates. These bounds show that information measured in bits, can be traded off for regret, measured in reward. Finally, we demonstrate the utility of these bounds in improving the performance of a question-answering task with large language models, allowing us to obtain valuable insights.

Theory · Online Learning and Bandits

Zhuohua Li, Maoli Liu, Xiangxiang Dai, John C.S. Lui

The contextual multi-armed bandit (MAB) problem is crucial in sequential decision-making. A line of research, known as online clustering of bandits, extends contextual MAB by grouping similar users into clusters, utilizing shared features to improve learning efficiency. However, existing algorithms, which rely on the upper confidence bound (UCB) strategy, struggle to gather adequate statistical information to accurately identify unknown user clusters. As a result, their theoretical analyses require several strong assumptions about the "diversity" of contexts generated by the environment, leading to impractical settings, complicated analyses, and poor practical performance. Removing these assumptions has been a long-standing open problem in the clustering of bandits literature. In this work, we provide two partial solutions. First, we introduce an additional exploration phase to accelerate the identification of clusters. We integrate this general strategy into both graph-based and set-based algorithms and propose two new algorithms, UniCLUB and UniSCLUB. Remarkably, our algorithms require substantially weaker assumptions and simpler theoretical analyses while achieving superior cumulative regret compared to previous studies. Second, inspired by the smoothed analysis framework, we propose a more practical setting that eliminates the requirement for i.i.d. context generation used in previous studies, thus enhancing the performance of existing algorithms for online clustering of bandits. Extensive evaluations on both synthetic and real-world datasets demonstrate that our proposed algorithms outperform existing approaches.

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

Wonho Bae, Danica Sutherland, Gabriel Oliveira

Most active learning research has focused on methods which perform well when many labels are available, but can be dramatically worse than random selection when label budgets are small.Other methods have focused on the low-budget regime, but do poorly as label budgets increase.As the line between "low" and "high" budgets varies by problem,this is a serious issue in practice.We propose *uncertainty coverage*,an objective which generalizes a variety of low- and high-budget objectives,as well as natural, hyperparameter-light methods to smoothly interpolate between low- and high-budget regimes.We call greedy optimization of the estimate Uncertainty Herding;this simple method is computationally fast,and we prove that it nearly optimizes the distribution-level coverage.In experimental validation across a variety of active learning tasks,our proposal matches or beats state-of-the-art performance in essentially all cases;it is the only method of which we are aware that reliably works well in both low- and high-budget settings.

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

Giuseppe Serra, Florian Buettner

Given the ability to model more realistic and dynamic problems, Federated Continual Learning (FCL) has been increasingly investigated recently. A well-known problem encountered in this setting is the so-called catastrophic forgetting, for which the learning model is inclined to focus on more recent tasks while forgetting the previously learned knowledge. The majority of the current approaches in FCL propose generative-based solutions to solve said problem. However, this setting requires multiple training epochs over the data, implying an offline setting where datasets are stored locally and remain unchanged over time. Furthermore, the proposed solutions are tailored for vision tasks solely. To overcome these limitations, we propose a new approach to deal with different modalities in the online scenario where new data arrive in streams of mini-batches that can only be processed once. To solve catastrophic forgetting, we propose an uncertainty-aware memory-based approach. Specifically, we suggest using an estimator based on the Bregman Information (BI) to compute the model's variance at the sample level. Through measures of predictive uncertainty, we retrieve samples with specific characteristics, and – by retraining the model on such samples – we demonstrate the potential of this approach to reduce the forgetting effect in realistic settings while maintaining data confidentiality and competitive communication efficiency compared to state-of-the-art approaches.

Theory · Online Learning and Bandits

Qing Feng, Tianyi Ma, Ruihao Zhu

Motivated by the concept of satisficing in decision-making, we consider the problem of satisficing exploration in bandit optimization. In this setting, the learner aims at finding a satisficing arm whose mean reward exceeds a certain threshold. The performance is measured by satisficing regret, which is the cumulative deficit of the chosen arm's mean reward compared to the threshold. We propose $\texttt{SELECT}$, a general algorithmic template for Satisficing REgret Minimization via SampLing and LowEr Confidence bound Testing, that attains constant satisficing regret for a wide variety of bandit optimization problems in the realizable case (i.e., whenever a satisficing arm exists). Specifically, given a class of bandit optimization problems and a corresponding learning oracle with sub-linear (standard) regret upper bound, $\texttt{SELECT}$ iteratively makes use of the oracle to identify a potential satisficing arm. Then, it collects data samples from this arm, and continuously compares the lower confidence bound of the identified arm's mean reward against the threshold value to determine if it is a satisficing arm. As a complement, $\texttt{SELECT}$ also enjoys the same (standard) regret guarantee as the oracle in the non-realizable case. Finally, we conduct numerical experiments to validate the performance of $\texttt{SELECT}$ for several popular bandit optimization settings.

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

Tommaso Cesari, Roberto Colomboni

We explore brokerage between traders in an online learning framework.At any round $t$, two traders meet to exchange an asset, provided the exchange is mutually beneficial.The broker proposes a trading price, and each trader tries to sell their asset or buy the asset from the other party, depending on whether the price is higher or lower than their private valuations.A trade happens if one trader is willing to sell and the other is willing to buy at the proposed price.Previous work provided guidance to a broker aiming at enhancing traders' total earnings by maximizing the *gain from trade*, defined as the sum of the traders' net utilities after each interaction.This classical notion of reward can be highly unfair to traders with small profit margins, and far from the real-life utility of the broker.For these reasons, we investigate how the broker should behave to maximize the trading volume, i.e., the *total number of trades*.We model the traders' valuations as an i.i.d. process with an unknown distribution.If the traders' valuations are revealed after each interaction (full-feedback), and the traders' valuations cumulative distribution function (cdf) is continuous, we provide an algorithm achieving logarithmic regret and show its optimality up to constants.If only their willingness to sell or buy at the proposed price is revealed after each interaction ($2$-bit feedback), we provide an algorithm achieving poly-logarithmic regret when the traders' valuations cdf is Lipschitz and show its near-optimality.We complement our results by analyzing the implications of dropping the regularity assumptions on the unknown traders' valuations cdf. If we drop the continuous cdf assumption, the regret rate degrades to $\Theta(\sqrt{T})$ in the full-feedback case, where $T$ is the time horizon. If we drop the Lipschitz cdf assumption, learning becomes impossible in the $2$-bit feedback case.

Theory · Online Learning and Bandits

Aadirupa Saha, Pierre Gaillard

We address the problem of active online assortment optimization problem with preference feedback, which is a framework for modeling user choices and subsetwise utility maximization. The framework is useful in various real-world applications including ad placement, online retail, recommender systems, and fine-tuning language models, amongst many others. The problem, although has been studied in the past, lacks an intuitive and practical solution approach with simultaneously efficient algorithm and optimal regret guarantee. E.g., popularly used assortment selection algorithms often require the presence of a ``strong reference" which is always included in the choice sets, further they are also designed to offer the same assortments repeatedly until the reference item gets selected---all such requirements are quite unrealistic for practical applications. In this paper, we designed efficient algorithms for the problem of regret minimization in assortment selection with \emph{Plackett Luce} (PL) based user choices. We designed a novel concentration guarantee for estimating the score parameters of the PL model using `\emph{Pairwise Rank-Breaking}', which builds the foundation of our proposed algorithms. Moreover, our methods are practical, provably optimal, and devoid of the aforementioned limitations of the existing methods.