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General Machine Learning · Online Learning, Active Learning and Bandits

Jiajun Chen, Jin Tian, Chris Quinn

Artificial intelligence will play a significant role in decision making in numerous aspects of society. Numerous fairness criteria have been proposed in the machine learning community, but there remains limited investigation into fairness as defined through specified attributes in a sequential decision-making framework. In this paper, we focus on causal logistic bandit problems where the learner seeks to make fair decisions, under a notion of fairness that accounts for counterfactual reasoning. We propose and analyze an algorithm by leveraging primal-dual optimization for constrained causal logistic bandits where the non-linear constraints are a priori unknown and must be learned in time. We obtain sub-linear regret guarantees with leading term similar to that for unconstrained logistic bandits (Lee et al., 2024) while guaranteeing sub-linear constraint violations. We show how to achieve zero cumulative constraint violations with a small increase in the regret bound.

General Machine Learning · Online Learning, Active Learning and Bandits

Negin Golrezaei, Sourav Sahoo

We study the bidding problem in repeated uniform price multi-unit auctions from the perspective of a single *value-maximizing* buyer who aims to maximize their cumulative value over $T$ rounds while adhering to return-on-investment (RoI) constraints in each round. Buyers adopt $m$-*uniform bidding* format, where they submit $m$ bid-quantity pairs $(b_i, q_i)$ to demand $q_i$ units at bid $b_i$. We introduce *safe* bidding strategies as those that satisfy RoI constraints in every auction, regardless of competing bids. We show that these strategies depend only on the bidder’s valuation curve, and the bidder can focus on a finite subset of this class without loss of generality. While the number of strategies in this subset is exponential in $m$, we develop a polynomial-time algorithm to learn the optimal safe strategy that achieves sublinear regret in the online setting, where regret is measured against a clairvoyant benchmark that knows the competing bids *a priori* and selects a fixed hindsight optimal safe strategy. We then evaluate the performance of safe strategies against a clairvoyant that selects the optimal strategy from a richer class of strategies in the online setting. In this scenario, we compute the *richness ratio*, $\alpha\in(0, 1]$ for the class of strategies chosen by the clairvoyant and show that our algorithm, designed to learn safe strategies, achieves $\alpha$-approximate sublinear regret against these stronger benchmarks. Experiments on semi-synthetic data from real-world auctions show that safe strategies substantially outperform the derived theoretical bounds, making them quite appealing in practice.

General Machine Learning · Online Learning, Active Learning and Bandits

Jae-Hong Lee

Test-time adaptation (TTA) addresses the machine learning challenge of adapting models to unlabeled test data from shifting distributions in dynamic environments. A key issue in this online setting arises from using unsupervised learning techniques, which introduce explicit gradient noise that degrades model weights. To invest in weight degradation, we propose a Bayesian weight enhancement framework, which generalizes existing weight-based TTA methods that effectively mitigate the issue. Our framework enables robust adaptation to distribution shifts by accounting for diverse weights by modeling weight distributions.Building on our framework, we identify a key limitation in existing methods: their neglect of time-varying covariance reflects the influence of the gradient noise. To address this gap, we propose a novel steady-state adaptation (SSA) algorithm that balances covariance dynamics during adaptation. SSA is derived through the solution of a stochastic differential equation for the TTA process and online inference. The resulting algorithm incorporates a covariance-aware learning rate adjustment mechanism. Through extensive experiments, we demonstrate that SSA consistently improves state-of-the-art methods in various TTA scenarios, datasets, and model architectures, establishing its effectiveness in instability and adaptability.

General Machine Learning · Online Learning, Active Learning and Bandits

Rohan Ghuge, Vidya Muthukumar, Sahil Singla

We study *online multicalibration*, a framework for ensuring calibrated predictions across multiple groups in adversarial settings, across $T$ rounds. Although online calibration is typically studied in the $\ell_1$ norm, prior approaches to online multicalibration have taken the indirect approach of obtaining rates in other norms (such as $\ell_2$ and $\ell_{\infty}$) and then transferred these guarantees to $\ell_1$ at additional loss. In contrast, we propose a direct method that achieves improved and oracle-efficient rates of $\widetilde{\mathcal{O}}(T^{-1/3})$ and $\widetilde{\mathcal{O}}(T^{-1/4})$ respectively, for online $\ell_1$-multicalibration. Our key insight is a novel reduction of online $\ell_1$-multicalibration to an online learning problem with product-based rewards, which we refer to as *online linear-product optimization* ($\mathtt{OLPO}$). To obtain the improved rate of $\widetilde{\mathcal{O}}(T^{-1/3})$, we introduce a linearization of $\mathtt{OLPO}$ and design a no-regret algorithm for this linearized problem. Although this method guarantees the desired sublinear rate (nearly matching the best rate for online calibration), it is computationally expensive when the group family $\mathcal{H}$ is large or infinite, since it enumerates all possible groups. To address scalability, we propose a second approach to $\mathtt{OLPO}$ that makes only a polynomial number of calls to an offline optimization (*multicalibration evaluation*) oracle, resulting in *oracle-efficient* online $\ell_1$-multicalibration with a corresponding rate of $\widetilde{\mathcal{O}}(T^{-1/4})$. Our framework also extends to certain infinite families of groups (e.g., all linear functions on the context space) by exploiting a $1$-Lipschitz property of the $\ell_1$-multicalibration error with respect to $\mathcal{H}$.

General Machine Learning · Online Learning, Active Learning and Bandits

Saumya Gaurang Shah, Abishek Sankararaman, Balakrishnan Narayanaswamy, Vikramank Singh

Can we efficiently choose the best Anomaly Detection (AD) algorithm for a data-stream without requiring anomaly labels? Streaming anomaly detection is hard. SOTA AD algorithms are sensitive to their hyperparameters and no single method works well on all datasets. The best algorithm/hyper-parameter combination for a given data-stream can change over time with data drift. 'What is an anomaly?' is often application, context and dataset dependent. We propose SEAD (Streaming Ensemble of Anomaly Detectors), the first model selection algorithm for streaming, unsupervised AD. All prior AD model selection algorithms are either supervised, or only work in the offline setting when all data from the test set is available upfront. We show that SEAD is {\em(i)} unsupervised, i.e., requires no true anomaly labels, {\em(ii)} efficiently implementable in a streaming setting, {\em (iii)} agnostic to the choice of the base algorithms among which it chooses from, and {\em (iv)} adaptive to non-stationarity in the data-stream. Experiments on 14 non-trivial public datasets and an internal dataset corroborate our claims.

General Machine Learning · Online Learning, Active Learning and Bandits

Jiujia Zhang, Ashok Cutkosky

This paper addresses online learning with ''corrupted'' feedback. Our learner is provided with potentially corrupted gradients $\tilde g_t$ instead of the ''true'' gradients $g_t$. We make no assumptions about how the corruptions arise: they could be the result of outliers, mislabeled data, or even malicious interference. We focus on the difficult ``unconstrained'' setting in which our algorithm must maintain low regret with respect to any comparison point $u \in \mathbb{R}^d$. The unconstrained setting is significantly more challenging as existing algorithms suffer extremely high regret even with very tiny amounts of corruption (which is not true in the case of a bounded domain). Our algorithms guarantee regret $ \|u\|G (\sqrt{T} + k) $ when $G \ge \max_t \|g_t\|$ is known, where $k$ is a measure of the total amount of corruption. When $G$ is unknown we incur an extra additive penalty of $(\|u\|^2+G^2) k$.

General Machine Learning · Online Learning, Active Learning and Bandits

Shion Takeno, Yoshito Okura, Yu Inatsu, Tatsuya Aoyama, Tomonari Tanaka, Satoshi Akahane, Hiroyuki Hanada, Noriaki Hashimoto, Taro Murayama, Hanju Lee 等

Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with fewer data labels, is an important problem. However, existing AL methods do not theoretically guarantee prediction accuracy for target distribution. Furthermore, as discussed in the distributionally robust learning literature, specifying the target distribution is often difficult. Thus, this paper proposes two AL methods that effectively reduce the worst-case expected error for GPR, which is the worst-case expectation in target distribution candidates. We show an upper bound of the worst-case expected squared error, which suggests that the error will be arbitrarily small by a finite number of data labels under mild conditions. Finally, we demonstrate the effectiveness of the proposed methods through synthetic and real-world datasets.

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.

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 · 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.

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.

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.

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.

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.

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.