Peng Zhao

Peng Zhao, Yan-Feng Xie, Lijun Zhang et al.

Non-stationary online learning has drawn much attention in recent years. In particular, dynamic regret and adaptive regret are proposed as two principled performance measures for online convex optimization in non-stationary environments. To optimize them, a two-layer online ensemble is usually deployed due to the inherent uncertainty of non-stationarity, in which multiple base-learners are maintained and a meta-algorithm is employed to track the best one on the fly. However, the two-layer structure raises concerns about computational complexity -- such methods typically maintain $O(\log T)$ base-learners simultaneously for a $T$-round online game and thus perform multiple projections onto the feasible domain per round, which becomes the computational bottleneck when the domain is complicated. In this paper, we present efficient methods for optimizing dynamic regret and adaptive regret that reduce the number of projections per round from $O(\log T)$ to $1$. The proposed algorithms require only one gradient query and one function evaluation at each round. Our technique hinges on the reduction mechanism developed in parameter-free online learning and requires non-trivial modifications for non-stationary online methods. Furthermore, we study an even stronger measure, namely "interval dynamic regret", and reduce the number of projections per round from $O(\log^2 T)$ to $1$ for minimizing it. Our reduction demonstrates broad generality and applies to two important applications: online stochastic control and online principal component analysis, resulting in methods that are both efficient and optimal. Finally, empirical studies verify our theoretical findings.

Yuheng Zhao, Yu-Hu Yan, Kfir Yehuda Levy et al.

Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can be understood through the lens of gradient-variation online learning. In this paper, we investigate online learning with Hölder smooth functions, a general class encompassing both smooth and non-smooth (Lipschitz) functions, and explore its implications for offline optimization. For (strongly) convex online functions, we design the corresponding gradient-variation online learning algorithm whose regret smoothly interpolates between the optimal guarantees in smooth and non-smooth regimes. Notably, our algorithms do not require prior knowledge of the Hölder smoothness parameter, exhibiting strong adaptivity over existing methods. Through online-to-batch conversion, this gradient-variation online adaptivity yields an optimal universal method for stochastic convex optimization under Hölder smoothness. However, achieving universality in offline strongly convex optimization is more challenging. We address this by integrating online adaptivity with a detection-based guess-and-check procedure, which, for the first time, yields a universal offline method that achieves accelerated convergence in the smooth regime while maintaining near-optimal convergence in the non-smooth one.

Yu-Yang Qian, Yuan-Ze Xu, Zhen-Yu Zhang et al.

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.

Long-Fei Li, Peng Zhao, Zhi-Hua Zhou

We study episodic linear mixture MDPs with the unknown transition and adversarial rewards under full-information feedback, employing dynamic regret as the performance measure. We start with in-depth analyses of the strengths and limitations of the two most popular methods: occupancy-measure-based and policy-based methods. We observe that while the occupancy-measure-based method is effective in addressing non-stationary environments, it encounters difficulties with the unknown transition. In contrast, the policy-based method can deal with the unknown transition effectively but faces challenges in handling non-stationary environments. Building on this, we propose a novel algorithm that combines the benefits of both methods. Specifically, it employs (i) an occupancy-measure-based global optimization with a two-layer structure to handle non-stationary environments; and (ii) a policy-based variance-aware value-targeted regression to tackle the unknown transition. We bridge these two parts by a novel conversion. Our algorithm enjoys an $\widetilde{\mathcal{O}}(d \sqrt{H^3 K} + \sqrt{HK(H + \bar{P}_K)})$ dynamic regret, where $d$ is the feature dimension, $H$ is the episode length, $K$ is the number of episodes, $\bar{P}_K$ is the non-stationarity measure. We show it is minimax optimal up to logarithmic factors by establishing a matching lower bound. To the best of our knowledge, this is the first work that achieves near-optimal dynamic regret for adversarial linear mixture MDPs with the unknown transition without prior knowledge of the non-stationarity measure.

Long-Fei Li, Yu-Yang Qian, Peng Zhao et al.

Reinforcement Learning from Human Feedback (RLHF) has shown remarkable success in aligning Large Language Models (LLMs) with human preferences. Traditional RLHF methods rely on a fixed dataset, which often suffers from limited coverage. To this end, online RLHF has emerged as a promising direction, enabling iterative data collection and refinement. Despite its potential, this paradigm faces a key bottleneck: the requirement to continuously integrate new data into the dataset and re-optimize the model from scratch at each iteration, resulting in computational and storage costs that grow linearly with the number of iterations. In this work, we address this challenge by proposing a one-pass reward modeling method that eliminates the need to store historical data and achieves constant-time updates per iteration. Specifically, we first formalize RLHF as a contextual preference bandit and develop a new algorithm based on online mirror descent with a tailored local norm, replacing the standard maximum likelihood estimation for reward modeling. We then apply it to various online RLHF settings, including passive data collection, active data collection, and deployment-time adaptation. We provide theoretical guarantees showing that our method enhances both statistical and computational efficiency. Finally, we design practical algorithms for LLMs and conduct experiments with the Llama-3-8B-Instruct and Qwen2.5-7B-Instruct models on Ultrafeedback and Mixture2 datasets, validating the effectiveness of our approach.

Youming Tao, Yulian Wu, Peng Zhao et al.

In this paper we investigate the problem of stochastic multi-armed bandits (MAB) in the (local) differential privacy (DP/LDP) model. Unlike previous results that assume bounded/sub-Gaussian reward distributions, we focus on the setting where each arm's reward distribution only has $(1+v)$-th moment with some $v\in (0, 1]$. In the first part, we study the problem in the central $ε$-DP model. We first provide a near-optimal result by developing a private and robust Upper Confidence Bound (UCB) algorithm. Then, we improve the result via a private and robust version of the Successive Elimination (SE) algorithm. Finally, we establish the lower bound to show that the instance-dependent regret of our improved algorithm is optimal. In the second part, we study the problem in the $ε$-LDP model. We propose an algorithm that can be seen as locally private and robust version of SE algorithm, which provably achieves (near) optimal rates for both instance-dependent and instance-independent regret. Our results reveal differences between the problem of private MAB with bounded/sub-Gaussian rewards and heavy-tailed rewards. To achieve these (near) optimal rates, we develop several new hard instances and private robust estimators as byproducts, which might be used to other related problems. Finally, experiments also support our theoretical findings and show the effectiveness of our algorithms.

Peng Zhao, Lijun Zhang, Yuan Jiang et al.

This paper investigates the problem of non-stationary linear bandits, where the unknown regression parameter is evolving over time. Existing studies develop various algorithms and show that they enjoy an $\widetilde{\mathcal{O}}(T^{2/3}P_T^{1/3})$ dynamic regret, where $T$ is the time horizon and $P_T$ is the path-length that measures the fluctuation of the evolving unknown parameter. In this paper, we discover that a serious technical flaw makes their results ungrounded, and then present a fix, which gives an $\widetilde{\mathcal{O}}(T^{3/4}P_T^{1/4})$ dynamic regret without modifying original algorithms. Furthermore, we demonstrate that instead of using sophisticated mechanisms, such as sliding window or weighted penalty, a simple restarted strategy is sufficient to attain the same regret guarantee. Specifically, we design an UCB-type algorithm to balance exploitation and exploration, and restart it periodically to handle the drift of unknown parameters. Our approach enjoys an $\widetilde{\mathcal{O}}(T^{3/4}P_T^{1/4})$ dynamic regret. Note that to achieve this bound, the algorithm requires an oracle knowledge of the path-length $P_T$. Combining the bandits-over-bandits mechanism by treating our algorithm as the base learner, we can further achieve the same regret bound in a parameter-free way. Empirical studies also validate the effectiveness of our approach.

Peng Zhao, Yu-Hu Yan, Yu-Xiang Wang et al.

We study the problem of Online Convex Optimization (OCO) with memory, which allows loss functions to depend on past decisions and thus captures temporal effects of learning problems. In this paper, we introduce dynamic policy regret as the performance measure to design algorithms robust to non-stationary environments, which competes algorithms' decisions with a sequence of changing comparators. We propose a novel algorithm for OCO with memory that provably enjoys an optimal dynamic policy regret in terms of time horizon, non-stationarity measure, and memory length. The key technical challenge is how to control the switching cost, the cumulative movements of player's decisions, which is neatly addressed by a novel switching-cost-aware online ensemble approach equipped with a new meta-base decomposition of dynamic policy regret and a careful design of meta-learner and base-learner that explicitly regularizes the switching cost. The results are further applied to tackle non-stationarity in online non-stochastic control (Agarwal et al., 2019), i.e., controlling a linear dynamical system with adversarial disturbance and convex cost functions. We derive a novel gradient-based controller with dynamic policy regret guarantees, which is the first controller provably competitive to a sequence of changing policies for online non-stochastic control.

Bo-Jian Hou, Yu-Hu Yan, Peng Zhao et al.

Feature evolvable learning has been widely studied in recent years where old features will vanish and new features will emerge when learning with streams. Conventional methods usually assume that a label will be revealed after prediction at each time step. However, in practice, this assumption may not hold whereas no label will be given at most time steps. A good solution is to leverage the technique of manifold regularization to utilize the previous similar data to assist the refinement of the online model. Nevertheless, this approach needs to store all previous data which is impossible in learning with streams that arrive sequentially in large volume. Thus we need a buffer to store part of them. Considering that different devices may have different storage budgets, the learning approaches should be flexible subject to the storage budget limit. In this paper, we propose a new setting: Storage-Fit Feature-Evolvable streaming Learning (SF$^2$EL) which incorporates the issue of rarely-provided labels into feature evolution. Our framework is able to fit its behavior to different storage budgets when learning with feature evolvable streams with unlabeled data. Besides, both theoretical and empirical results validate that our approach can preserve the merit of the original feature evolvable learning i.e., can always track the best baseline and thus perform well at any time step.

Peng Zhao, Yu-Jie Zhang, Lijun Zhang et al.

We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length that essentially reflects the non-stationarity of environments, the state-of-the-art dynamic regret is $\mathcal{O}(\sqrt{T(1+P_T)})$. Although this bound is proved to be minimax optimal for convex functions, in this paper, we demonstrate that it is possible to further enhance the dynamic regret by exploiting the smoothness condition. Specifically, we propose novel online algorithms that are capable of leveraging smoothness and replace the dependence on $T$ in the dynamic regret by problem-dependent quantities: the variation in gradients of loss functions, the cumulative loss of the comparator sequence, and the minimum of the previous two terms. These quantities are at most $\mathcal{O}(T)$ while could be much smaller in benign environments. Therefore, our results are adaptive to the intrinsic difficulty of the problem, since the bounds are tighter than existing results for easy problems and meanwhile guarantee the same rate in the worst case.

Peng Zhao, Lijun Zhang

In this paper, we present an improved analysis for dynamic regret of strongly convex and smooth functions. Specifically, we investigate the Online Multiple Gradient Descent (OMGD) algorithm proposed by Zhang et al. (2017). The original analysis shows that the dynamic regret of OMGD is at most $\mathcal{O}(\min\{\mathcal{P}_T,\mathcal{S}_T\})$, where $\mathcal{P}_T$ and $\mathcal{S}_T$ are path-length and squared path-length that measures the cumulative movement of minimizers of the online functions. We demonstrate that by an improved analysis, the dynamic regret of OMGD can be improved to $\mathcal{O}(\min\{\mathcal{P}_T,\mathcal{S}_T,\mathcal{V}_T\})$, where $\mathcal{V}_T$ is the function variation of the online functions. Note that the quantities of $\mathcal{P}_T, \mathcal{S}_T, \mathcal{V}_T$ essentially reflect different aspects of environmental non-stationarity -- they are not comparable in general and are favored in different scenarios. Therefore, the dynamic regret presented in this paper actually achieves a \emph{best-of-three-worlds} guarantee and is strictly tighter than previous results.

Peng Zhao, Jia-Wei Shan, Yu-Jie Zhang et al.

In conventional supervised learning, a training dataset is given with ground-truth labels from a known label set, and the learned model will classify unseen instances to known labels. This paper studies a new problem setting in which there are unknown classes in the training data misperceived as other labels, and thus their existence appears unknown from the given supervision. We attribute the unknown unknowns to the fact that the training dataset is badly advised by the incompletely perceived label space due to the insufficient feature information. To this end, we propose the exploratory machine learning, which examines and investigates training data by actively augmenting the feature space to discover potentially hidden classes. Our method consists of three ingredients including rejection model, feature exploration, and model cascade. We provide theoretical analysis to justify its superiority, and validate the effectiveness on both synthetic and real datasets.

Yu-Jie Zhang, Peng Zhao, Zhi-Hua Zhou

This paper studies the problem of learning with augmented classes (LAC), where augmented classes unobserved in the training data might emerge in the testing phase. Previous studies generally attempt to discover augmented classes by exploiting geometric properties, achieving inspiring empirical performance yet lacking theoretical understandings particularly on the generalization ability. In this paper we show that, by using unlabeled training data to approximate the potential distribution of augmented classes, an unbiased risk estimator of the testing distribution can be established for the LAC problem under mild assumptions, which paves a way to develop a sound approach with theoretical guarantees. Moreover, the proposed approach can adapt to complex changing environments where augmented classes may appear and the prior of known classes may change simultaneously. Extensive experiments confirm the effectiveness of our proposed approach.

Peng Zhao, Guanghui Wang, Lijun Zhang et al.

Bandit Convex Optimization (BCO) is a fundamental framework for modeling sequential decision-making with partial information, where the only feedback available to the player is the one-point or two-point function values. In this paper, we investigate BCO in non-stationary environments and choose the \emph{dynamic regret} as the performance measure, which is defined as the difference between the cumulative loss incurred by the algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length of the comparator sequence that reflects the non-stationarity of environments. We propose a novel algorithm that achieves $O(T^{3/4}(1+P_T)^{1/2})$ and $O(T^{1/2}(1+P_T)^{1/2})$ dynamic regret respectively for the one-point and two-point feedback models. The latter result is optimal, matching the $Ω(T^{1/2}(1+P_T)^{1/2})$ lower bound established in this paper. Notably, our algorithm is more adaptive to non-stationary environments since it does not require prior knowledge of the path-length $P_T$ ahead of time, which is generally unknown.

Peng Zhao, Le-Wen Cai, Zhi-Hua Zhou

In many real-world applications, data are often collected in the form of stream, and thus the distribution usually changes in nature, which is referred as concept drift in literature. We propose a novel and effective approach to handle concept drift via model reuse, leveraging previous knowledge by reusing models. Each model is associated with a weight representing its reusability towards current data, and the weight is adaptively adjusted according to the model performance. We provide generalization and regret analysis. Experimental results also validate the superiority of our approach on both synthetic and real-world datasets.