NeurIPS 2024 Papers

We study online classification when the learner has access to predictions about future examples. We design an online learner whose expected regret is never worse than the worst-case regret, gracefully improves with the quality of the predictions, and can be significantly better than the worst-case regret when the predictions of future examples are accurate. As a corollary, we show that if the learner is always guaranteed to observe data where future examples are easily predictable, then online learning can be as easy as transductive online learning. Our results complement recent work in online algorithms with predictions and smoothed online classification, which go beyond a worse-case analysis by using machine-learned predictions and distributional assumptions respectively.

Image generation has shown remarkable results in generating high-fidelity realistic images, in particular with the advancement of diffusion-based models. However, the prevalence of AI-generated images may have side effects for the machine learning community that are not clearly identified. Meanwhile, the success of deep learning in computer vision is driven by the massive dataset collected on the Internet. The extensive quantity of synthetic data being added to the Internet would become an obstacle for future researchers to collect "clean" datasets without AI-generated content. Prior research has shown that using datasets contaminated by synthetic images may result in performance degradation when used for training. In this paper, we investigate the potential impact of contaminated datasets on Online Continual Learning (CL) research. We experimentally show that contaminated datasets might hinder the training of existing online CL methods. Also, we propose Entropy Selection with Real-synthetic similarity Maximization (ESRM), a method to alleviate the performance deterioration caused by synthetic images when training online CL models. Experiments show that our method can significantly alleviate performance deterioration, especially when the contamination is severe. For reproducibility, the source code of our work is available at https://github.com/maorong-wang/ESRM.

The secretary problem is one of the fundamental problems in online decision making; a tight competitive ratio for this problem of $1/e \approx 0.368$ has been known since the 1960s. Much more recently, the study of algorithms with predictions was introduced: The algorithm is equipped with a (possibly erroneous) additional piece of information upfront which can be used to improve the algorithm's performance. Complementing previous work on secretary problems with prior knowledge, we tackle the following question: _What is the weakest piece of information that allows us to break the $1/e$ barrier?_ To this end, we introduce the secretary problem with predicted additive gap. As in the classical problem, weights are fixed by an adversary and elements appear in random order. In contrast to previous variants of predictions, our algorithm only has access to a much weaker piece of information: an _additive gap_ $c$. This gap is the difference between the highest and $k$-th highest weight in the sequence. Unlike previous pieces of advice, knowing an exact additive gap does not make the problem trivial. Our contribution is twofold. First, we show that for any index $k$ and any gap $c$, we can obtain a competitive ratio of $0.4$ when knowing the exact gap (even if we do not know $k$), hence beating the prevalent bound for the classical problem by a constant. Second, a slightly modified version of our algorithm allows to prove standard robustness-consistency properties as well as improved guarantees when knowing a range for the error of the prediction.

We prove that single-parameter natural exponential families with subexponential tails are self-concordant with polynomial-sized parameters. For subgaussian natural exponential families we establish an exact characterization of the growth rate of the self-concordance parameter. Applying these findings to bandits allows us to fill gaps in the literature: We show that optimistic algorithms for generalized linear bandits enjoy regret bounds that are both second-order (scale with the variance of the optimal arm's reward distribution) and free of an exponential dependence on the bound of the problem parameter in the leading term. To the best of our knowledge, ours is the first regret bound for generalized linear bandits with subexponential tails, broadening the class of problems to include Poisson, exponential and gamma bandits.

We propose a new best-of-both-worlds algorithm for bandits with variably delayed feedback. In contrast to prior work, which required prior knowledge of the maximal delay $d_{\max}$ and had a linear dependence of the regret on it, our algorithm can tolerate arbitrary excessive delays up to order $T$ (where $T$ is the time horizon). The algorithm is based on three technical innovations, which may all be of independent interest: (1) We introduce the first implicit exploration scheme that works in best-of-both-worlds setting. (2) We introduce the first control of distribution drift that does not rely on boundedness of delays. The control is based on the implicit exploration scheme and adaptive skipping of observations with excessive delays. (3) We introduce a procedure relating standard regret with drifted regret that does not rely on boundedness of delays. At the conceptual level, we demonstrate that complexity of best-of-both-worlds bandits with delayed feedback is characterized by the amount of information missing at the time of decision making (measured by the number of outstanding observations) rather than the time that the information is missing (measured by the delays).

We study a data pricing problem, where a seller has access to $N$ homogeneous data points (e.g. drawn i.i.d. from some distribution). There are $m$ types of buyers in the market, where buyers of the same type $i$ have the same valuation curve $v_i:[N]\rightarrow [0,1]$, where $v_i(n)$ is the value for having $n$ data points. *A priori*, the seller is unaware of the distribution of buyers, but can repeat the market for $T$ rounds so as to learn the revenue-optimal pricing curve $p:[N] \rightarrow [0, 1]$. To solve this online learning problem, we first develop novel discretization schemes to approximate any pricing curve. When compared to prior work, the size of our discretization schemes scales gracefully with the approximation parameter, which translates to better regret in online learning. Under assumptions like smoothness and diminishing returns which are satisfied by data, the discretization size can be reduced further. We then turn to the online learning problem, both in the stochastic and adversarial settings. On each round, the seller chooses an *anonymous* pricing curve $p_t$. A new buyer appears and may choose to purchase some amount of data. She then reveals her type *only if* she makes a purchase. Our online algorithms build on classical algorithms such as UCB and FTPL, but require novel ideas to account for the asymmetric nature of this feedback and to deal with the vastness of the space of pricing curves. Using the improved discretization schemes previously developed, we are able to achieve $\widetilde{O}(m\sqrt{T})$ regret in the stochastic setting and $\widetilde{\mathcal{O}}(m^{3/2}\sqrt{T})$ regret in the adversarial setting.

We study online classification with general hypothesis classes where the true labels are determined by some function within the class, but are corrupted by *unknown* stochastic noise, and the features are generated adversarially. Predictions are made using observed *noisy* labels and noiseless features, while the performance is measured via minimax risk when comparing against *true* labels. The noisy mechanism is modeled via a general noisy kernel that specifies, for any individual data point, a set of distributions from which the actual noisy label distribution is chosen. We show that minimax risk is *tightly* characterized (up to a logarithmic factor of the hypothesis class size) by the *Hellinger gap* of the noisy label distributions induced by the kernel, *independent* of other properties such as the means and variances of the noise. Our main technique is based on a novel reduction to an online comparison scheme of two hypotheses, along with a new *conditional* version of Le Cam-Birgé testing suitable for online settings. Our work provides the first comprehensive characterization of noisy online classification with guarantees that apply to the *ground truth* while addressing *general* noisy observations.

Modern machine learning models are becoming increasingly expensive to train for real-world image and text classification tasks, where massive web-scale data is collected in a streaming fashion. To reduce the training cost, online batch selection techniques have been developed to choose the most informative datapoints. However, many existing techniques are not robust to class imbalance and distributional shifts, and can suffer from poor worst-class generalization performance. This work introduces REDUCR, a robust and efficient data downsampling method that uses class priority reweighting. REDUCR reduces the training data while preserving worst-class generalization performance. REDUCR assigns priority weights to datapoints in a class-aware manner using an online learning algorithm. We demonstrate the data efficiency and robust performance of REDUCR on vision and text classification tasks. On web-scraped datasets with imbalanced class distributions, REDUCR significantly improves worst-class test accuracy (and average accuracy), surpassing state-of-the-art methods by around 15\%.

We study online control for continuous-time linear systems with finite sampling rates, where the objective is to design an online procedure that learns under non-stochastic noise and performs comparably to a fixed optimal linear controller. We present a novel two-level online algorithm, by integrating a higher-level learning strategy and a lower-level feedback control strategy. This method offers a practical and robust solution for online control, which achieves sublinear regret. Our work provides the first nonasymptotic results for controlling continuous-time linear systems with finite number of interactions with the system. Moreover, we examine how to train an agent in domain randomization environments from a non-stochastic control perspective. By applying our method to the SAC (Soft Actor-Critic) algorithm, we achieved improved results in multiple reinforcement learning tasks within domain randomization environments. Our work provides new insights into non-asymptotic analyses of controlling continuous-time systems. Furthermore, our work brings practical intuition into controller learning under non-stochastic environments.

Conformal prediction is an uncertainty quantification method that constructs a prediction set for a previously unseen datum, ensuring the true label is included with a predetermined coverage probability. Adaptive conformal prediction has been developed to address data distribution shifts in dynamic environments. However, the efficiency of prediction sets varies depending on the learning model used. Employing a single fixed model may not consistently offer the best performance in dynamic environments with unknown data distribution shifts. To address this issue, we introduce a novel adaptive conformal prediction framework, where the model used for creating prediction sets is selected ‘on the fly’ from multiple candidate models. The proposed algorithm is proven to achieve strongly adaptive regret over all intervals while maintaining valid coverage. Experiments on both real and synthetic datasets corroborate that the proposed approach consistently yields more efficient prediction sets while maintaining valid coverage, outperforming alternative methods.

Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content matching or online labor markets), the knowledge about preferences may not be readily available and must be learned, i.e., one side of the market (aka agents) may not know their preferences over the other side (aka arms). Recent research on online settings has focused primarily on welfare optimization aspects (i.e. minimizing the overall regret) while paying little attention to the game-theoretic properties such as the stability of the final matching. In this paper, we exploit the structure of stable solutions to devise algorithms that improve the likelihood of finding stable solutions. We initiate the study of the sample complexity of finding a stable matching, and provide theoretical bounds on the number of samples needed to reach a stable matching with high probability. Finally, our empirical results demonstrate intriguing tradeoffs between stability and optimality of the proposed algorithms, further complementing our theoretical findings.

In online bilateral trade, a platform posts prices to incoming pairs of buyers and sellers that have private valuations for a certain good. If the price is lower than the buyers' valuation and higher than the sellers' valuation, then a trade takes place. Previous work focused on the platform perspective, with the goal of setting prices maximizing the *gain from trade* (the sum of sellers' and buyers' utilities). Gain from trade is, however, potentially unfair to traders, as they may receive highly uneven shares of the total utility. In this work we enforce fairness by rewarding the platform with the _fair gain from trade_, defined as the minimum between sellers' and buyers' utilities. After showing that any no-regret learning algorithm designed to maximize the sum of the utilities may fail badly with fair gain from trade, we present our main contribution: a complete characterization of the regret regimes for fair gain from trade when, after each interaction, the platform only learns whether each trader accepted the current price. Specifically, we prove the following regret bounds: $\Theta(\ln T)$ in the deterministic setting, $\Omega(T)$ in the stochastic setting, and $\tilde{\Theta}(T^{2/3})$ in the stochastic setting when sellers' and buyers' valuations are independent of each other. We conclude by providing tight regret bounds when, after each interaction, the platform is allowed to observe the true traders' valuations.

In this work, we study the experts problem in the distributed setting where an expert's cost needs to be aggregated across multiple servers. Our study considers various communication models such as the message-passing model and the broadcast model, along with multiple aggregation functions, such as summing and taking the $\ell_p$ norm of an expert's cost across servers. We propose the first communication-efficient protocols that achieve near-optimal regret in these settings, even against a strong adversary who can choose the inputs adaptively. Additionally, we give a conditional lower bound showing that the communication of our protocols is nearly optimal. Finally, we implement our protocols and demonstrate empirical savings on the HPO-B benchmarks.

We study how to learn $\epsilon$-optimal strategies in zero-sum imperfect information games (IIG) with *trajectory feedback*. In this setting, players update their policies sequentially, based on their observations over a fixed number of episodes denoted by $T$. Most existing procedures suffer from high variance due to the use of importance sampling over sequences of actions. To reduce this variance, we consider a *fixed sampling* approach, where players still update their policies over time, but with observations obtained through a given fixed sampling policy. Our approach is based on an adaptive Online Mirror Descent (OMD) algorithm that applies OMD locally to each information set, using individually decreasing learning rates and a *regularized loss*. We show that this approach guarantees a convergence rate of $\tilde{\mathcal{O}}(T^{-1/2})$ with high probability and has a near-optimal dependence on the game parameters when applied with the best theoretical choices of learning rates and sampling policies. To achieve these results, we generalize the notion of OMD stabilization, allowing for time-varying regularization with convex increments.

Imagine a smart camera trap selectively clicking pictures to understand animal movement patterns within a particular habitat. These "snapshots", or pieces of data captured from a data stream at adaptively chosen times, provide a glimpse of different animal movements unfolding through time. Learning a continuous-time process through snapshots, such as smart camera traps, is a central theme governing a wide array of online learning situations. In this paper, we adopt a learning-theoretic perspective in understanding the fundamental nature of learning different classes of functions from both discrete data streams and continuous data streams. In our first framework, the *update-and-deploy* setting, a learning algorithm discretely queries from a process to update a predictor designed to make predictions given as input the data stream. We construct a uniform sampling algorithm that can learn with bounded error any concept class with finite Littlestone dimension. Our second framework, known as the *blind-prediction* setting, consists of a learning algorithm generating predictions independently of observing the process, only engaging with the process when it chooses to make queries. Interestingly, we show a stark contrast in learnability where non-trivial concept classes are unlearnable. However, we show that adaptive learning algorithms are necessary to learn sets of time-dependent and data-dependent functions, called pattern classes, in either framework. Finally, we develop a theory of pattern classes under discrete data streams for the blind-prediction setting.

We study the preference-based pure exploration problem for bandits with vector-valued rewards and a set of preferences imposed over them. Specifically, we aim to identify the most preferred policy over a set of arms according to the preferences induced on the reward vectors by an ordering cone $C$. First, to quantify the impact of preferences, we derive a novel lower bound on the sample complexity for identifying the most preferred arm with confidence level $1-\delta$. Our lower bound shows that how the geometry of the preferences and reward vectors changes the hardness of this problem. We further explicate this geometry for Gaussian distributions of rewards, and provide a convex reformulation of the lower bound solvable with linear programming. Then, we leverage this convex reformulation of the lower bound to design the Track and Stop with Preferences (TSwP) algorithm that identifies the most preferred policy. Finally, we derive a new concentration result for vector-valued rewards, and show that TSwP achieves a matching sample complexity upper bound.

We study the generalized linear contextual bandit problem within the constraints of limited adaptivity. In this paper, we present two algorithms, B-GLinCB and RS-GLinCB, that address, respectively, two prevalent limited adaptivity settings. Given a budget $M$ on the number of policy updates, in the first setting, the algorithm needs to decide upfront $M$ rounds at which it will update its policy, while in the second setting it can adaptively perform $M$ policy updates during its course. For the first setting, we design an algorithm B-GLinCB, that incurs $\tilde{O}(\sqrt{T})$ regret when $M = \Omega( \log{\log T} )$ and the arm feature vectors are generated stochastically. For the second setting, we design an algorithm RS-GLinCB that updates its policy $\tilde{O}(\log^2 T)$ times and achieves a regret of $\tilde{O}(\sqrt{T})$ even when the arm feature vectors are adversarially generated. Notably, in these bounds, we manage to eliminate the dependence on a key instance dependent parameter $\kappa$, that captures non-linearity of the underlying reward model. Our novel approach for removing this dependence for generalized linear contextual bandits might be of independent interest.

Online learning methods, like the seminal Passive-Aggressive (PA) classifier, are still highly effective for high-dimensional streaming data, out-of-core processing, and other throughput-sensitive applications. Many such algorithms rely on fast adaptation to individual errors as a key to their convergence. While such algorithms enjoy low theoretical regret, in real-world deployment they can be sensitive to individual outliers that cause the algorithm to over-correct. When such outliers occur at the end of the data stream, this can cause the final solution to have unexpectedly low accuracy. We design a weighted reservoir sampling (WRS) approach to obtain a stable ensemble model from the sequence of solutions without requiring additional passes over the data, hold-out sets, or a growing amount of memory. Our key insight is that good solutions tend to be error-free for more iterations than bad solutions, and thus, the number of passive rounds provides an estimate of a solution's relative quality. Our reservoir thus contains $K$ previous intermediate weight vectors with high survival times. We demonstrate our WRS approach on the Passive-Aggressive Classifier (PAC) and First-Order Sparse Online Learning (FSOL), where our method consistently and significantly outperforms the unmodified approach. We show that the risk of the ensemble classifier is bounded with respect to the regret of the underlying online learning method.

The remarkable instruction-following capability of large language models (LLMs) has sparked a growing interest in automatically finding good prompts, i.e., prompt optimization. Most existing works follow the scheme of selecting from a pre-generated pool of candidate prompts. However, these designs mainly focus on the generation strategy, while limited attention has been paid to the selection method. Especially, the cost incurred during the selection (e.g., accessing LLM and evaluating the responses) is rarely explicitly considered. To overcome this limitation, this work provides a principled framework, TRIPLE, to efficiently perform prompt selection under an explicit budget constraint. TRIPLE is built on a novel connection established between prompt optimization and fixed-budget best arm identification (BAI-FB) in multi-armed bandits (MAB); thus, it is capable of leveraging the rich toolbox from BAI-FB systematically and also incorporating unique characteristics of prompt optimization. Extensive experiments on multiple well-adopted tasks using various LLMs demonstrate the remarkable performance improvement of TRIPLE over baselines while satisfying the limited budget constraints. As an extension, variants of TRIPLE are proposed to efficiently select examples for few-shot prompts, also achieving superior empirical performance.