Theory · online learning

The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no assumptions on prediction quality, a number of methods providing uncertainty quantification (UQ) on machine learning models have been developed in recent years, which could enable additional information about prediction quality at decision time. In this work, we investigate the problem of optimally utilizing uncertainty-quantified predictions in the design of online algorithms. In particular, we study two classic online problems, ski rental and online search, where the decision-maker is provided predictions augmented with UQ describing the likelihood of the ground truth falling within a particular range of values. We demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the UQ predictions. Moreover, we consider how to utilize more general forms of UQ, proposing an online learning framework that learns to exploit UQ to make decisions in multi-instance settings.

Measuring human feedback via randomized experimentation is a cornerstone of data-driven decision-making. The methodology used to estimate user preferences from their online behaviours is critically dependent on user identifiers. However, in today's digital landscape, consumers frequently interact with content across multiple devices, which are often recorded with different identifiers for the same consumer. The inability to match different device identities across consumers poses significant challenges for accurately estimating human preferences and other causal effects. Moreover, without strong assumptions about the device-user graph, the causal effects might not be identifiable. In this paper, we propose HIFIVE, a variational method to solve the problem of estimating global average treatment effects (GATE) from a fragmented view of exposures and outcomes. Experiments show that our estimator is superior to standard estimators, with a lower bias and greater robustness to network uncertainty.

In this paper, we study the problem of online tracking in linear control systems, where the objective is to follow a moving target. Unlike classical tracking control, the target is unknown, non-stationary, and its state is revealed sequentially, thus, fitting the framework of online non-stochastic control. We consider the case of quadratic costs and propose a new algorithm, called predictive linear online tracking (PLOT). The algorithm uses recursive least squares with exponential forgetting to learn a time-varying dynamic model of the target. The learned model is used in the optimal policy under the framework of receding horizon control. We show the dynamic regret of PLOT scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of the target dynamics and $T$ is the time horizon. Unlike prior work, our theoretical results hold for non-stationary targets. We implement our online control algorithm on a real quadrotor, thus, showcasing one of the first successful applications of online control methods on real hardware.

Training autonomous agents with sparse rewards is a long-standing problem in online reinforcement learning (RL), due to low data efficiency. Prior work overcomes this challenge by extracting useful knowledge from offline data, often accomplished through the learning of action distribution from offline data and utilizing the learned distribution to facilitate online RL. However, since the offline data are given and fixed, the extracted knowledge is inherently limited, making it difficult to generalize to new tasks. We propose a novel approach that leverages offline data to learn a generative diffusion model, coined as Adaptive Trajectory Diffuser (ATraDiff). This model generates synthetic trajectories, serving as a form of data augmentation and consequently enhancing the performance of online RL methods. The key strength of our diffuser lies in its adaptability, allowing it to effectively handle varying trajectory lengths and mitigate distribution shifts between online and offline data. Because of its simplicity, ATraDiff seamlessly integrates with a wide spectrum of RL methods. Empirical evaluation shows that ATraDiff consistently achieves state-of-the-art performance across a variety of environments, with particularly pronounced improvements in complicated settings. Our code and demo video are available at https://atradiff.github.io.

Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation of complex latent-state posteriors. In this work, we build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference by combining particle methods and variational inference. While standard VSMC operates in the offline mode, by re-processing repeatedly a given batch of data, we distribute the approximation of the gradient of the VSMC surrogate ELBO in time using stochastic approximation, allowing for online learning in the presence of streams of data. This results in an algorithm, online VSMC, that is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation. In addition, we provide rigorous theoretical results describing the algorithm's convergence properties as the number of data tends to infinity as well as numerical illustrations of its excellent convergence properties and usefulness also in batch-processing settings.

Despite the success of the Adam optimizer in practice, the theoretical understanding of its algorithmic components still remains limited. In particular, most existing analyses of Adam show the convergence rate that can be simply achieved by non-adative algorithms like SGD. In this work, we provide a different perspective based on online learning that underscores the importance of Adam's algorithmic components. Inspired by Cutkosky et al. (2023), we consider the framework called online learning of updates/increments, where we choose the updates/increments of an optimizer based on an online learner. With this framework, the design of a good optimizer is reduced to the design of a good online learner. Our main observation is that Adam corresponds to a principled online learning framework called Follow-the-Regularized-Leader (FTRL). Building on this observation, we study the benefits of its algorithmic components from the online learning perspective.

While machine learning shows promise in automated knowledge generation, current techniques such as large language models and micro-targeted influence operations can be exploited for harmful purposes like the proliferation of disinformation. The European Union's Digital Services Act (DSA) is an exemplary policy response addressing these harms generated by online platforms. In this regard, it necessitates a comprehensive evaluation of its impact on curbing the harmful downstream effects of these opaque practices. Despite their harmful applications, we argue that machine learning techniques offer immense, yet under-exploited, potential for unraveling the impacts of regulations like the DSA. Following an analysis that reveals possible limitations in the DSA's provisions, we call for resolute efforts to address methodological barriers around appropriate data access, isolating marginal regulatory effects, and facilitating generalization across different contexts. Given the identified advantages of data-driven approaches to regulatory delivery, we advocate for machine learning research to help quantify the policy impacts on online harms.

Selecting appropriate thresholds for anomaly detection in online, unsupervised settings is a challenging task, especially in the presence of data distribution shifts. Addressing these challenges is critical in many practical large scale systems, such as infrastructure monitoring and network intrusion detection. This paper proposes an algorithm that connects online thresholding with constructing confidence sequences achieving (1) adaptive online threshold selection robust to distribution shifts, (2) statistical guarantees on false positive and false negative rates without any distributional assumptions, and (3) improved performance when given relevant offline data to warm-start the online algorithm, while having bounded degradation if the offline data is irrelevant. We complement our theoretical results by empirical evidence that our method outperforms commonly used baselines across synthetic and real world datasets.

Spiking Neural Networks (SNNs) are attracting great attention for their energy-efficient and fast-inference properties in neuromorphic computing. However, the efficient training of deep SNNs poses challenges in gradient calculation due to the non-differentiability of their binary spike-generating activation functions. The widely used surrogate gradient (SG) method, combined with the back-propagation through time (BPTT), has shown considerable effectiveness. Yet, BPTT's process of unfolding and back-propagating along the computation graph requires storing intermediate information at all time-steps, resulting in huge memory consumption and failing to meet online requirements. In this work, we propose Neuronal Dynamics-based Online Training (NDOT) for SNNs, which uses the neuronal dynamics-based temporal dependency/sensitivity in gradient computation. NDOT enables forward-in-time learning by decomposing the full gradient into temporal and spatial gradients. To illustrate the intuition behind NDOT, we employ the Follow-the-Regularized-Leader (FTRL) algorithm. FTRL explicitly utilizes historical information and addresses limitations in instantaneous loss. Our proposed NDOT method accurately captures temporal dependencies through neuronal dynamics, functioning similarly to FTRL's explicit utilizing historical information. Experiments on CIFAR-10, CIFAR-100, and CIFAR10-DVS demonstrate the superior performance of our NDOT method on large-scale static and neuromorphic datasets within a small number of time steps. The codes are available at https://github.com/HaiyanJiang/SNN-NDOT.

In this paper, we study offline-to-online Imitation Learning (IL) that pretrains an imitation policy from static demonstration data, followed by fast finetuning with minimal environmental interaction. We find the naive combination of existing offline IL and online IL methods tends to behave poorly in this context, because the initial discriminator (often used in online IL) operates randomly and discordantly against the policy initialization, leading to misguided policy optimization and *unlearning* of pretraining knowledge. To overcome this challenge, we propose a principled offline-to-online IL method, named OLLIE, that simultaneously learns a near-expert policy initialization along with an *aligned discriminator initialization*, which can be seamlessly integrated into online IL, achieving smooth and fast finetuning. Empirically, OLLIE consistently and significantly outperforms the baseline methods in **20** challenging tasks, from continuous control to vision-based domains, in terms of performance, demonstration efficiency, and convergence speed. This work may serve as a foundation for further exploration of pretraining and finetuning in the context of IL.

Ranking algorithms are fundamental to various online platforms across e-commerce sites to content streaming services. Our research addresses the challenge of adaptively ranking items from a candidate pool for heterogeneous users, a key component in personalizing user experience. We develop a user response model that considers diverse user preferences and the varying effects of item positions, aiming to optimize overall user satisfaction with the ranked list. We frame this problem within a contextual bandits framework, with each ranked list as an action. Our approach incorporates an upper confidence bound to adjust predicted user satisfaction scores and selects the ranking action that maximizes these adjusted scores, efficiently solved via maximum weight imperfect matching. We demonstrate that our algorithm achieves a cumulative regret bound of $O(d\sqrt{NKT})$ for ranking $K$ out of $N$ items in a $d$-dimensional context space over $T$ rounds, under the assumption that user responses follow a generalized linear model. This regret alleviates dependence on the ambient action space, whose cardinality grows exponentially with $N$ and $K$ (thus rendering direct application of existing adaptive learning algorithms -- such as UCB or Thompson sampling -- infeasible). Experiments conducted on both simulated and real-world datasets demonstrate our algorithm outperforms the baseline.

In real-world scenarios such as traffic and energy management, we frequently encounter large volumes of time-series data characterized by missing values, noise, and irregular sampling patterns. While numerous imputation methods have been proposed, the majority tend to operate within a local horizon, which involves dividing long sequences into batches of fixed-length segments for model training. This local horizon often leads to the overlooking of global trends and periodic patterns. More importantly, most methods assume the observations are sampled at regular timestamps, and fail to handle complex irregular sampled time series in various applications. Additionally, most existing methods are learned in an offline manner. Thus, it is not suitable for applications with rapidly arriving streaming data. To address these challenges, we propose BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition. Our method conceptualizes multivariate time series as the weighted combination of groups of low-rank temporal factors with different patterns. We employ a suite of Gaussian Processes (GPs),each with a unique kernel, as functional priors to model these factors. For computational efficiency, we further convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE), and developing a scalable algorithm for online inference. The proposed method can not only handle imputation over arbitrary timestamps, but also offer uncertainty quantification and interpretability for the downstream application. We evaluate our method on both synthetic and real-world datasets. We release the code at https://github.com/xuangu-fang/BayOTIDE.

We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the discounted regret in online convex optimization, and propose an adaptive (i.e., instance optimal), FTRL-based algorithm that improves the widespread non-adaptive baseline -- gradient descent with a constant learning rate. From a practical perspective, this refines the classical idea of regularization in lifelong learning: we show that designing better regularizers can be guided by the principled theory of adaptive online optimization. Complementing this result, we also consider the (Gibbs & Candes, 2021)-style online conformal prediction problem, where the goal is to sequentially predict the uncertainty sets of a black-box machine learning model. We show that the FTRL nature of our algorithm can simplify the conventional gradient-descent-based analysis, leading to instance-dependent performance guarantees.

Online Bayesian bipartite matching is a central problem in digital marketplaces and exchanges, including advertising, crowdsourcing, ridesharing, and kidney exchange. We introduce a graph neural network (GNN) approach that emulates the problem's combinatorially-complex optimal online algorithm, which selects actions (e.g., which nodes to match) by computing each action's *value-to-go (VTG)*—the expected weight of the final matching if the algorithm takes that action, then acts optimally in the future. We train a GNN to estimate VTG and show empirically that this GNN returns high-weight matchings across a variety of tasks. Moreover, we identify a common family of graph distributions in spatial crowdsourcing applications, such as rideshare, under which VTG can be efficiently approximated by aggregating information within local neighborhoods in the graphs. This structure matches the local behavior of GNNs, providing theoretical justification for our approach.

Large Language Models (LLMs) have a natural role in answering complex queries about data streams, but the high computational cost of LLM inference makes them infeasible in many such tasks. We propose *online cascade learning*, the first approach to address this challenge. The objective here is to learn a ``cascade'' of models, starting with lower-capacity models (such as logistic regression) and ending with a powerful LLM, along with a *deferral policy* that determines the model to be used on a given input. We formulate the task of learning cascades online as an imitation-learning problem, where smaller models are updated over time imitating the collected LLM demonstrations, and give a no-regret algorithm for the problem. Experimental results across four benchmarks show that our method parallels LLMs in accuracy while cutting down inference costs by as much as 90% with strong robustness against input distribution shifts, underscoring its efficacy and adaptability in stream processing. Our source code is available at https://github.com/flitternie/online_cascade_learning.

Non-parametric detection of change points in streaming time series data that belong to Euclidean spaces has been extensively studied in the literature. Nevertheless, when the data belongs to a Riemannian manifold, existing approaches are no longer applicable as they fail to account for the structure and geometry of the manifold. In this paper, we introduce a non-parametric algorithm for online change point detection in manifold-valued data streams. This algorithm monitors the generalized Karcher mean of the data, computed using stochastic Riemannian optimization. We provide theoretical bounds on the detection and false alarm rate performances of the algorithm, using a new result on the non-asymptotic convergence of the stochastic Riemannian gradient descent. We apply our algorithm to two different Riemannian manifolds. Experimental results with both synthetic and real data illustrate the performance of the proposed method.

Online Continual Learning (OCL) addresses the problem of training neural networks on a continuous data stream where multiple classification tasks emerge in sequence. In contrast to offline Continual Learning, data can be seen only once in OCL, which is a very severe constraint. In this context, replay-based strategies have achieved impressive results and most state-of-the-art approaches heavily depend on them. While Knowledge Distillation (KD) has been extensively used in offline Continual Learning, it remains under-exploited in OCL, despite its high potential. In this paper, we analyze the challenges in applying KD to OCL and give empirical justifications. We introduce a direct yet effective methodology for applying Momentum Knowledge Distillation (MKD) to many flagship OCL methods and demonstrate its capabilities to enhance existing approaches. In addition to improving existing state-of-the-art accuracy by more than $10\%$ points on ImageNet100, we shed light on MKD internal mechanics and impacts during training in OCL. We argue that similar to replay, MKD should be considered a central component of OCL. The code is available at https://github.com/Nicolas1203/mkd_ocl.

This paper considers the parameter learning and data clustering problem for MLR with multiple sub-models and arbitrary mixing weights. To deal with the data streaming case, we propose an online learning algorithm to estimate the unknown parameters. By utilizing Ljung's ODE method, we establish the almost sure convergence results of this MLR problem without the traditional i.i.d. assumption on the input data for the first time. Based on the convergence property and using the classical stochastic Lyapunov function method, we also obtain the convergence rate analysis of the proposed algorithm for the first time. In addition, the data clustering can asymptotically achieve the same performance as the case with known parameters. Future work will consider how to relax the asymptotically stationary and ergodic assumption on the input data, and how to design algorithms with global convergence performance for the MLR problem.

For a specific online optimization problem, for example, online bipartite matching (OBM), research efforts could be made in two directions before it is finally closed, i.e., the optimal competitive online algorithm is found. One is to continuously design algorithms with better performance. To this end, reinforcement learning (RL) has demonstrated great success in literature. However, little is known on the other direction: whether RL helps explore how hard an online problem is. In this paper, we study a generalized model of OBM, named online matching with stochastic rewards (OMSR, FOCS 2012), for which the optimal competitive ratio is still unknown. We adopt an adversarial RL approach that trains two RL agents adversarially and iteratively: the algorithm agent learns for algorithms with larger competitive ratios, while the adversarial agent learns to produce a family of hard instances. Through such a framework, agents converge at the end with a robust algorithm, which empirically outperforms the state of the art (STOC 2020). Much more significantly, it allows to track how the hard instances are generated. We succeed in distilling two structural properties from the learned graph patterns, which remarkably reduce the action space, and further enable theoretical improvement on the best-known hardness result of OMSR, from $0.621$ (FOCS 2012) to $0.597$. To the best of our knowledge, this gives the first evidence that RL can help enhance the theoretical understanding of an online problem.

We propose a novel algorithm for online resource allocation with non-stationary customer arrivals and unknown click-through rates. We assume multiple types of customers arriving in a nonstationary stochastic fashion, with unknown arrival rates in each period. Additionally, customers' click-through rates are assumed to be unknown and only learnable online. By leveraging results from the stochastic contextual bandit with knapsack and online matching with adversarial arrivals, we develop an online scheme to allocate the resources to nonstationary customers. We prove that under mild conditions, our scheme achieves a ``best-of-both-world'' result: the scheme has a sublinear regret when the customer arrivals are near-stationary, and enjoys an optimal competitive ratio under general (non-stationary) customer arrival distributions. Finally, we conduct extensive numerical experiments to show our approach generates near-optimal revenues for all different customer scenarios.