理论 · online learning

The bandits with knapsacks (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio $\alpha$ when $B=\Omega(T)$ or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent $\tilde{\mathcal{O}}(T^{1/2})$ regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

Online-Within-Online (OWO) meta learning stands for the online multi-task learning paradigm in which both tasks and data within each task become available in a sequential order. In this work, we study the OWO meta learning of the initialization and step size of within-task online algorithms in the non-convex setting, and provide improved regret bounds under mild assumptions of loss functions. Previous work analyzing this scenario has obtained for bounded and piecewise Lipschitz functions an averaged regret bound $O((\frac{\sqrt{m}}{T^{1/4}}+\frac{(\log{m})\log{T}}{\sqrt{T}}+V)\sqrt{m})$ across $T$ tasks, with $m$ iterations per task and $V$ the task similarity. Our first contribution is to modify the existing non-convex OWO meta learning algorithm and improve the regret bound to $O((\frac{1}{T^{1/2-\alpha}}+\frac{(\log{T})^{9/2}}{T}+V)\sqrt{m})$, for any $\alpha \in (0,1/2)$. The derived bound has a faster convergence rate with respect to $T$, and guarantees a vanishing task-averaged regret with respect to $m$ (for any fixed $T$). Then, we propose a new algorithm of regret $O((\frac{\log{T}}{T}+V)\sqrt{m})$ for non-convex OWO meta learning. This regret bound exhibits a better asymptotic performance than previous ones, and holds for any bounded (not necessarily Lipschitz) loss functions. Besides the improved regret bounds, our contributions include investigating how to attain generalization bounds for statistical meta learning via regret analysis. Specifically, by online-to-batch arguments, we achieve a transfer risk bound for batch meta learning that assumes all tasks are drawn from a distribution. Moreover, by connecting multi-task generalization error with task-averaged regret, we develop for statistical multi-task learning a novel PAC-Bayes generalization error bound that involves our regret bound for OWO meta learning.

Although reinforcement learning methods offer a powerful framework for auto- matic skill acquisition, for practical learning-based control problems in domains such as robotics, imitation learning often provides a more convenient and accessible alternative. In particular, an interactive imitation learning method such as DAgger, which queries a near-optimal expert to intervene online to collect correction data for addressing the distributional shift challenges that afflict naïve behavioral cloning, can enjoy good performance both in theory and practice without requiring manually specified reward functions and other components of full reinforcement learning methods. In this paper, we explore how off-policy reinforcement learning can enable improved performance under assumptions that are similar but potentially even more practical than those of interactive imitation learning. Our proposed method uses reinforcement learning with user intervention signals themselves as rewards. This relaxes the assumption that intervening experts in interactive imita- tion learning should be near-optimal and enables the algorithm to learn behaviors that improve over the potential suboptimal human expert. We also provide a uni- fied framework to analyze our RL method and DAgger; for which we present the asymptotic analysis of the suboptimal gap for both methods as well as the non- asymptotic sample complexity bound of our method. We then evaluate our method on challenging high-dimensional continuous control simulation benchmarks as well as real-world robotic vision-based manipulation tasks. The results show that it strongly outperforms DAgger-like approaches across the different tasks, especially when the intervening experts are suboptimal. Additional ablations also empirically verify the proposed theoretical justification that the performance of our method is associated with the choice of intervention model and suboptimality of the expert. Code and videos can be found on the project website: https://rlif-page.github.io

We study a strategic variant of the multi-armed bandit problem, which we coin the strategic click-bandit. This model is motivated by applications in online recommendation where the choice of recommended items depends on both the click-through rates and the post-click rewards. Like in classical bandits, rewards follow a fixed unknown distribution. However, we assume that the click-rate of each arm is chosen strategically by the arm (e.g., a host on Airbnb) in order to maximize the number of times it gets clicked. The algorithm designer does not know the post-click rewards nor the arms' actions (i.e., strategically chosen click-rates) in advance, and must learn both values over time. To solve this problem, we design an incentive-aware learning algorithm, UCB-S, which achieves two goals simultaneously: (a) incentivizing desirable arm behavior under uncertainty; (b) minimizing regret by learning unknown parameters. We approximately characterize all Nash equilibria of the arms under UCB-S and show a $\tilde{\mathcal{O}} (\sqrt{KT})$ regret bound uniformly in every equilibrium. We also show that incentive-unaware algorithms generally fail to achieve low regret in the strategic click-bandit. Finally, we support our theoretical results by simulations of strategic arm behavior which confirm the effectiveness and robustness of our proposed incentive design.

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Key challenges in OCL include automatic adaptation to the specific non-stationary structure of the data and maintaining appropriate predictive uncertainty. To address these challenges we introduce a probabilistic Bayesian online learning approach that utilizes a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity in the linear predictor weights is modelled using a “parameter drift” transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allow for adaptation to the non-stationarity observed in the data. While the framework is developed assuming a linear Gaussian model, we extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the model's predictive ability and its flexibility in capturing non-stationarity.

Regularization-based methods have so far been among the *de facto* choices for continual learning. Recent theoretical studies have revealed that these methods all boil down to relying on the Hessian matrix approximation of model weights. However, these methods suffer from suboptimal trade-offs between knowledge transfer and forgetting due to fixed and unchanging Hessian estimations during training. Another seemingly parallel strand of Meta-Continual Learning (Meta-CL) algorithms enforces alignment between gradients of previous tasks and that of the current task. In this work we revisit Meta-CL and for the first time bridge it with regularization-based methods. Concretely, Meta-CL implicitly approximates Hessian in an online manner, which enjoys the benefits of timely adaptation but meantime suffers from high variance induced by random memory buffer sampling. We are thus highly motivated to combine the best of both worlds, through the proposal of Variance Reduced Meta-CL (VR-MCL) to achieve both timely and accurate Hessian approximation. Through comprehensive experiments across three datasets and various settings, we consistently observe that VR-MCL outperforms other SOTA methods, which further validates the effectiveness of VR-MCL.

The theories of offline and online reinforcement learning, despite having evolved in parallel, have begun to show signs of the possibility for a unification, with algorithms and analysis techniques for one setting often having natural counterparts in the other. However, the notion of *density ratio modeling*, an emerging paradigm in offline RL, has been largely absent from online RL, perhaps for good reason: the very existence and boundedness of density ratios relies on access to an exploratory dataset with good coverage, but the core challenge in online RL is to collect such a dataset without having one to start. In this work we show---perhaps surprisingly---that density ratio-based algorithms have online counterparts. Assuming only the existence of an exploratory distribution with good coverage, a structural condition known as *coverability* (Xie et al., 2023), we give a new algorithm (GLOW) that uses density ratio realizability and value function realizability to perform sample-efficient online exploration. GLOW addresses unbounded density ratios via careful use of truncation, and combines this with optimism to guide exploration. GLOW is computationally inefficient; we complement it with a more efficient counterpart, HyGLOW, for the Hybrid RL setting (Song et al., 2023) wherein online RL is augmented with additional offline data. HyGLOW is derived as a special case of a more general meta-algorithm that provides a provable black-box reduction from hybrid RL to offline RL, which may be of independent interest.

Hybrid RL is the setting where an RL agent has access to both offline data and online data by interacting with the real-world environment. In this work, we propose a new hybrid RL algorithm that combines an on-policy actor-critic method with offline data. On-policy methods such as policy gradient and natural policy gradient (NPG) have shown to be more robust to model misspecification, though sometimes it may not be as sample efficient as methods that rely on off-policy learning. On the other hand, offline methods that depend on off-policy training often require strong assumptions in theory and are less stable to train in practice. Our new approach integrates a procedure of off-policy training on the offline data into an on-policy NPG framework. We show that our approach, in theory, can obtain a *best-of-both-worlds* type of result --- it achieves the state-of-art theoretical guarantees of offline RL when offline RL-specific assumptions hold, while at the same time maintaining the theoretical guarantees of on-policy NPG regardless of the offline RL assumptions' validity. Experimentally, in challenging rich-observation environments, we show that our approach outperforms a state-of-the-art hybrid RL baseline which only relies on off-policy policy optimization, demonstrating the empirical benefit of combining on-policy and off-policy learning.

We study the problem of online prediction, in which at each time step $t \in \{1,2, \cdots T\}$, an individual $x_t$ arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris][1] and [Lee et al][2] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes (e.g., the set of all linear models, as used in linear regression). We show that a simple modification of the sleeping experts technique of [Blum & Lykouris][1] yields an efficient *reduction* to the well-understood problem of obtaining diminishing external regret *absent group considerations*. Our approach gives similar regret guarantees compared to [Blum & Lykouris][1]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris][1]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets --- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Fairness, especially group fairness, is an important consideration in the context of machine learning systems. The most commonly adopted group fairness-enhancing techniques are in-processing methods that rely on a mixture of a fairness objective (e.g., demographic parity) and a task-specific objective (e.g., cross-entropy) during the training process. However, when data arrives in an online fashion – one instance at a time – optimizing such fairness objectives poses several challenges. In particular, group fairness objectives are defined using expectations of predictions across different demographic groups. In the online setting, where the algorithm has access to a single instance at a time, estimating the group fairness objective requires additional storage and significantly more computation (e.g., forward/backward passes) than the task-specific objective at every time step. In this paper, we propose Aranyani, an ensemble of oblique decision trees, to make fair decisions in online settings. The hierarchical tree structure of Aranyani enables parameter isolation and allows us to efficiently compute the fairness gradients using aggregate statistics of previous decisions, eliminating the need for additional storage and forward/backward passes. We also present an efficient framework to train Aranyani and theoretically analyze several of its properties. We conduct empirical evaluations on 5 publicly available benchmarks (including vision and language datasets) to show that Aranyani achieves a better accuracy-fairness trade-off compared to baseline approaches.

Spiking neural networks (SNNs), attributed to the binary, event-driven nature of spikes, possess heightened biological plausibility and enhanced energy efficiency on neuromorphic hardware compared to analog neural networks (ANNs). Mainstream SNN training schemes apply backpropagation-through-time (BPTT) with surrogate gradients to replace the non-differentiable spike emitting process during backpropagation. While achieving competitive performance, the requirement for storing intermediate information at all time-steps incurs higher memory consumption and fails to fulfill the online property crucial to biological brains. Our work focuses on online training techniques, aiming for memory efficiency while preserving biological plausibility. The limitation of not having access to future information in early time steps in online training has constrained previous efforts to incorporate advantageous modules such as batch normalization. To address this problem, we propose Online Spiking Renormalization (OSR) to ensure consistent parameters between testing and training, and Online Threshold Stabilizer (OTS) to stabilize neuron firing rates across time steps. Furthermore, we design a novel online approach to compute the sample mean and variance over time for OSR. Experiments conducted on various datasets demonstrate the proposed method's superior performance among SNN online training algorithms. Our code is available at https://github.com/zhuyaoyu/SNN-online-normalization.

Solving a linear system ${\bf Ax}={\bf b}$ is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter $\omega$ has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm—using only the number of iterations as feedback—can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed $\omega$ as the sequence length increases. Furthermore, when given additional structural information, we show that a _contextual_ bandit method asymptotically achieves the performance of the _instance-optimal_ policy, which selects the best $\omega$ for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Recent works have shown a reduction from contextual bandits to online regression under a realizability assumption (Foster and Rakhlin, 2020; Foster and Krishnamurthy, 2021). In this work, we investigate the use of neural networks for such online regression and associated Neural Contextual Bandits (NeuCBs). Using existing results for wide networks, one can readily show a ${\mathcal{O}}(\sqrt{T})$ regret for online regression with square loss, which via the reduction implies a ${\mathcal{O}}(\sqrt{K} T^{3/4})$ regret for NeuCBs. Departing from this standard approach, we first show a $\mathcal{O}(\log T)$ regret for online regression with almost convex losses that satisfy QG (Quadratic Growth) condition, a generalization of the PL (Polyak-\L ojasiewicz) condition, and that have a unique minima. Although not directly applicable to wide networks since they do not have unique minima, we show that adding a suitable small random perturbation to the network predictions surprisingly makes the loss satisfy QG with unique minima. Based on such a perturbed prediction, we show a ${\mathcal{O}}(\log T)$ regret for online regression with both squared loss and KL loss, and subsequently convert these respectively to $\tilde{\mathcal{O}}(\sqrt{KT})$ and $\tilde{\mathcal{O}}(\sqrt{KL^*} + K)$ regret for NeuCB, where $L^*$ is the loss of the best policy. Separately, we also show that existing regret bounds for NeuCBs are $\Omega(T)$ or assume i.i.d. contexts, unlike this work. Finally, our experimental results on various datasets demonstrate that our algorithms, especially the one based on KL loss, persistently outperform existing algorithms.