AISTATS 2023 论文列表

In recent years there has been a significant research effort on incorporating predictions into online algorithms. However, work in this area often makes the underlying assumption that predictions come for free (e.g., without any computational or monetary costs). In this paper, we consider a cost associated with making predictions. We show that interesting algorithmic subtleties arise for even the most basic online problems, such as ski rental and its generalization, the Bahncard problem. In particular, we show that with costly predictions, care needs to be taken in (i) asking for the prediction at the right time, (ii) deciding if it is worth asking for the prediction, and (iii) how many predictions we ask for, in settings where it is natural to consider making multiple predictions. Specifically, (i) in the basic ski-rental setting, we compute the optimal delay before asking the predictor, (ii) in the same setting, given apriori information about the true number of ski-days through its mean and variance, we provide a simple algorithm that is near-optimal, under some natural parameter settings, in deciding if it is worth asking for the predictor and (iii) in the setting of the Bahncard problem, we provide a $(1+\varepsilon)$-approximation algorithm and quantify lower bounds on the number of queries required to do so. In addition, we show that solving the problem optimally would require almost complete information of the instance.

Although parallelism has been extensively used in Reinforcement Learning (RL), the quantitative effects of parallel exploration are not well understood theoretically. We study the benefits of simple parallel exploration for reward-free RL in linear Markov decision processes (MDPs) and two-player zero-sum Markov games (MGs). In contrast to the existing literature, which focuses on approaches that encourage agents to explore over a diverse set of policies, we show that using a single policy to guide exploration across all agents is sufficient to obtain an almost-linear speedup in all cases compared to their fully sequential counterpart. Furthermore, we demonstrate that this simple procedure is near-minimax optimal in the reward-free setting for linear MDPs. From a practical perspective, our paper shows that a single policy is sufficient and provably near-optimal for incorporating parallelism during the exploration phase.

We address the problem of Internal Regret in adversarial Sleeping Bandits and the relationship between different notions of sleeping regrets in multi-armed bandits. We propose a new concept called Internal Regret for sleeping multi-armed bandits (MAB) and present an algorithm that achieves sublinear Internal Regret, even when losses and availabilities are both adversarial. We demonstrate that a low internal regret leads to both low external regret and low policy regret for i.i.d. losses. Our contribution is unifying existing notions of regret in sleeping bandits and exploring their implications for each other. In addition, we extend our results to Dueling Bandits (DB), a preference feedback version of multi-armed bandits, and design a low-regret algorithm for sleeping dueling bandits with stochastic preferences and adversarial availabilities. We validate the effectiveness of our algorithms through empirical evaluations.

This paper studies a cooperative multi-agent multi-armed stochastic bandit problem where agents operate asynchronously – agent pull times and rates are unknown, irregular, and heterogeneous – and face the same instance of a K-armed bandit problem. Agents can share reward information to speed up the learning process at additional communication costs. We propose ODC, an on-demand communication protocol that tailors the communication of each pair of agents based on their empirical pull times. ODC is efficient when the pull times of agents are highly heterogeneous, and its communication complexity depends on the empirical pull times of agents. ODC is a generic protocol that can be integrated into most cooperative bandit algorithms without degrading their performance. We then incorporate ODC into the natural extensions of UCB and AAE algorithms and propose two communication-efficient cooperative algorithms. Our analysis shows that both algorithms are near-optimal in regret.

This paper investigates the efficiency of the K-fold cross-validation (CV) procedure and a debiased version thereof as a means of estimating the generalization risk of a learning algorithm. We work under the general assumption of uniform algorithmic stability. We show that the K-fold risk estimate may not be consistent under such general stability assumptions, by constructing non vanishing lower bounds on the error in realistic contexts such as regularized empirical risk minimisation and stochastic gradient descent. We thus advocate the use of a debiased version of the K-fold and prove an error bound with exponential tail decay regarding this version. Our result is applicable to the large class of uniformly stable algorithms, contrarily to earlier works focusing on specific tasks such as density estimation. We illustrate the relevance of the debiased K-fold CV on a simple model selection problem and demonstrate empirically the usefulness of the promoted approach on real world classification and regression datasets.

The geometric median, an instrumental component of the secure machine learning toolbox, is known to be effective when robustly aggregating models (or gradients), gathered from potentially malicious (or strategic) users. What is less known is the extent to which the geometric median incentivizes dishonest behaviors. This paper addresses this fundamental question by quantifying its strategyproofness. While we observe that the geometric median is not even approximately strategyproof, we prove that it is asymptotically $\alpha$-strategyproof: when the number of users is large enough, a user that misbehaves can gain at most a multiplicative factor $\alpha$, which we compute as a function of the distribution followed by the users. We then generalize our results to the case where users actually care more about specific dimensions, determining how this impacts $\alpha$. We also show how the skewed geometric medians can be used to improve strategyproofness.

As predictive models are increasingly being employed to make consequential decisions, there is a growing emphasis on developing techniques that can provide algorithmic recourse to affected individuals. While such recourses can be immensely beneficial to affected individuals, potential adversaries could also exploit these recourses to compromise privacy. In this work, we make the first attempt at investigating if and how an adversary can leverage recourses to infer private information about the underlying model’s training data. To this end, we propose a series of novel membership inference attacks which leverage algorithmic recourse. More specifically, we extend the prior literature on membership inference attacks to the recourse setting by leveraging the distances between data instances and their corresponding counterfactuals output by state-of-the-art recourse methods. Extensive experimentation with real world and synthetic datasets demonstrates significant privacy leakage through recourses. Our work establishes unintended privacy leakage as an important risk in the widespread adoption of recourse methods.

Motivated by both theory and practice, we study how random pruning the weights affects a neural network’s neural tangent kernel (NTK). In particular, this work establishes an equivalence of the NTKs between a fully-connected neural network and its randomly pruned version. The equivalence is established under two cases. The first main result studies the infinite-width asymptotic. It is shown that given a pruning probability, for fully-connected neural networks with the weights randomly pruned at the initialization, as the width of each layer grows to infinity sequentially, the NTK of the pruned neural network converges to the limiting NTK of the original network with some extra scaling. If the network weights are rescaled appropriately after pruning, this extra scaling can be removed. The second main result considers the finite width case. It is shown that to ensure the NTK’s closeness to the limit, the dependence of width on the sparsity parameter is asymptotically linear, as the NTK’s gap to its limit goes down to zero. Moreover, if the pruning probability is set to zero (i.e., no pruning), the bound on the required width matches the bound for fully-connected neural networks in previous works up to logarithmic factors. The proof of this result requires developing novel analysis of a network structure which we called mask-induced pseudo-networks.Experiments are provided to evaluate our results.

The Elo score has been extensively used to rank players by their skill or strength in competitive games such as chess, go, or StarCraft II. The Elo score implicitly assumes games have a strong additive—hence transitive—component. In this paper, we investigate the challenge of identifying transitive components in games. As a starting point, we show that the Elo score provably fails to extract the transitive component of some elementary transitive games. Based on this observation, we propose an alternative ranking system which properly extracts the transitive components in these games. Finally, we conduct an in-depth empirical validation on real-world game payoff matrices: it shows significant prediction performance improvements compared to the Elo score.

Various logit-adjusted parameterizations of the cross-entropy (CE) loss have been proposed as alternatives to weighted CE for training large models on label-imbalanced data far beyond the zero train error regime. The driving force behind those designs has been the theory of implicit bias, which for linear(ized) models, explains why they successfully induce bias on the optimization path towards solutions that favor minorities. Aiming to extend this theory to non-linear models, we investigate the implicit geometry of classifiers and embeddings that are learned by different CE parameterizations. Our main result characterizes the global minimizers of a non-convex cost-sensitive SVM classifier for the unconstrained features model, which serves as an abstraction of deep-nets. We derive closed-form formulas for the angles and norms of classifiers and embeddings as a function of the number of classes, the imbalance and the minority ratios, and the loss hyperparameters. Using these, we show that logit-adjusted parameterizations can be appropriately tuned to learn symmetric geometries irrespective of the imbalance ratio. We complement our analysis with experiments and an empirical study of convergence accuracy in deep-nets.

Bilevel optimization has been applied to a wide variety of machine learning models and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the single-machine setting so that they are incapable of handling the distributed data. To address this issue, under the setting where all participants compose a network and perform peer-to-peer communication in this network, we developed two novel decentralized stochastic bilevel optimization algorithms based on the gradient tracking communication mechanism and two different gradient estimators. Additionally, we established their convergence rates for nonconvex-strongly-convex problems with novel theoretical analysis strategies. To our knowledge, this is the first work achieving these theoretical results. Finally, we applied our algorithms to practical machine learning models, and the experimental results confirmed the efficacy of our algorithms.

Decision tree learning algorithms such as CART are generally based on heuristics that maximizes the purity gain greedily. Though these algorithms are practically successful, theoretical properties such as consistency are far from clear. In this paper, we discover that the most serious obstacle encumbering consistency analysis for decision tree learning algorithms lies in the fact that the worst-case purity gain, i.e., the core heuristics for tree splitting, can be zero. Based on this recognition, we present a new algorithm, named Grid Classification And Regression Tree (GridCART), with a provable consistency rate $\mathcal{O}(n^{-1 / (d + 2)})$, which is the first consistency rate proved for heuristic tree learning algorithms.

In contextual linear bandits, the reward function is assumed to be a linear combination of an unknown reward vector and a given embedding of context-arm pairs. In practice, the embedding is often learned at the same time as the reward vector, thus leading to an online representation learning problem. Existing approaches to representation learning in contextual bandits are either very generic (e.g., model-selection techniques or algorithms for learning with arbitrary function classes) or specialized to particular structures (e.g., nested features or representations with certain spectral properties). As a result, the understanding of the cost of representation learning in contextual linear bandit is still limited. In this paper, we take a systematic approach to the problem and provide a comprehensive study through an instance-dependent perspective. We show that representation learning is fundamentally more complex than linear bandits (i.e., learning with a given representation). In particular, learning with a given set of representations is never simpler than learning with the worst realizable representation in the set, while we show cases where it can be arbitrarily harder. We complement this result with an extensive discussion of how it relates to existing literature and we illustrate positive instances where representation learning is as complex as learning with a fixed representation and where sub-logarithmic regret is achievable.

We study the supervised learning paradigm called Learning Using Privileged Information, first suggested by Vapnik and Vashist (2009). In this paradigm, in addition to the examples and labels, additional (privileged) information is provided only for training examples. The goal is to use this information to improve the classification accuracy of the resulting classifier, where this classifier can only use the non-privileged information of new example instances to predict their label. We study the theory of privileged learning with the zero-one loss under the natural Privileged ERM algorithm proposed in Peshyony and Vapnik (2010). We provide a counter example to a claim made in that work regarding the VC dimension of the loss class induced by this problem; We conclude that the claim is incorrect. We then provide a correct VC dimension analysis which gives both lower and upper bounds on the capacity of the Privileged ERM loss class. We further show, via a generalization analysis, that worst-case guarantees for Privileged ERM cannot improve over standard non-privileged ERM, unless the capacity of the privileged information is similar or smaller to that of the non-privileged information. This result points to an important limitation of the Privileged ERM approach. In our closing discussion, we suggest another way in which Privileged ERM might still be helpful, even when the capacity of the privileged information is large.

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes error, and epistemic uncertainty via the size of the set. In this paper, we extend the notion of calibration, which is commonly used to evaluate the validity of the aleatoric uncertainty representation of a single probabilistic classifier, to assess the validity of an epistemic uncertainty representation obtained by sets of probabilistic classifiers. Broadly speaking, we call a set of probabilistic classifiers calibrated if one can find a calibrated convex combination of these classifiers. To evaluate this notion of calibration, we propose a novel nonparametric calibration test that generalizes an existing test for single probabilistic classifiers to the case of sets of probabilistic classifiers. Making use of this test, we empirically show that ensembles of deep neural networks are often not well calibrated.

We revisit the acceleration of the noise-tolerant power method for which, despite previous studies, the results remain unsatisfactory as they are either wrong or suboptimal, also lacking generality. In this work, we present a simple yet general and optimal analysis via noise-corrupted Chebyshev polynomials, which allows a larger iteration rank $p$ than the target rank $k$, requires less noise conditions in a new form, and achieves the optimal iteration complexity $\Theta\left(\sqrt{\frac{\lambda_{k}-\lambda_{q+1}}{\lambda_{k}}}\log\frac{1}{\epsilon}\right)$ for some $q$ satisfying $k\leq q\leq p$ in a certain regime of the momentum parameter. Interestingly, it shows dynamic dependence of the noise tolerance on the spectral gap, i.e., from linear at the beginning to square-root near convergence, while remaining commensurate with the previous in terms of overall tolerance. We relate our new form of noise norm conditions to the existing trigonometric one, which enables an improved analysis of generalized eigenspace computation and canonical correlation analysis. We conduct an extensive experimental study to showcase the great performance of the considered algorithm with a larger iteration rank $p>k$ across different applications.

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks. Several methods, ranging from temperature scaling to different Bayesian treatments of neural networks, have been proposed to mitigate overconfidence, most often supported by the numerical observation that they yield better calibrated uncertainty measures. In this work, we provide a sharp comparison between popular uncertainty measures for binary classification in a mathematically tractable model for overparametrized neural networks: the random features model. We discuss a trade-off between classification accuracy and calibration, unveiling a double descent behavior in the calibration curve of optimally regularised estimators as a function of overparametrization. This is in contrast with the empirical Bayes method, which we show to be well calibrated in our setting despite the higher generalization error and overparametrization.

A new portfolio selection strategy that adapts to a continuous side-information sequence is presented, with a universal wealth guarantee against a class of state-constant rebalanced portfolios with respect to a state function that maps each side-information symbol to a finite set of states. In particular, given that a state function belongs to a collection of functions of finite Natarajan dimension, the proposed strategy is shown to achieve, asymptotically to first order in the exponent, the same wealth as the best state-constant rebalanced portfolio with respect to the best state function, chosen in hindsight from observed market. This result can be viewed as an extension of the seminal work of Cover and Ordentlich (1996) that assumes a single-state function.

A common technique in reinforcement learning is to evaluate the value function from Monte Carlo simulations of a given policy, and use the estimated value function to obtain a new policy which is greedy with respect to the estimated value function. A well-known longstanding open problem in this context is to prove the convergence of such a scheme when the value function of a policy is estimated from data collected from a single sample path obtained from implementing the policy (see page 99 of [Sutton and Barto, 2018], page 8 of [Tsitsiklis, 2002]). We present a solution to the open problem by showing that a first-visit version of such a policy iteration scheme indeed converges to the optimal policy provided that the policy improvement step uses lookahead [Silver et al., 2016, Mnih et al., 2016, Silver et al., 2017b] rather than a simple greedy policy improvement. We provide results both for the original open problem in the tabular setting and also present extensions to the function approximation setting, where we show that the policy resulting from the algorithm performs close to the optimal policy within a function approximation error.