ALT 2025 论文列表

An important challenge in robust machine learning is when training data is provided by strategic sources who may intentionally report erroneous data for their own benefit. A line of work at the intersection of machine learning and mechanism design aims to deter strategic agents from reporting erroneous training data by designing learning algorithms that are strategyproof. Strategyproofness is a strong and desirable property, but it comes at a cost in the approximation ratio of even simple risk minimization problems. In this paper, we study strategyproof regression and classification problems in a model with advice. This model is part of a recent line on mechanism design with advice where the goal is to achieve both an improved approximation ratio when the advice is correct (consistency) and a bounded approximation ratio when the advice is incorrect (robustness). We provide the first non-trivial consistency-robustness tradeoffs for strategyproof regression and classification, which hold for simple yet interesting classes of functions. For classes of constant functions, we give a deterministic and strategyproof mechanism that is, for any $\gamma \in (0, 2]$, $1+\gamma$ consistent and $1 + 4/\gamma$ robust and provide a lower bound that shows that this tradeoff is optimal. We extend this mechanism and its guarantees to homogeneous linear regression over $\mathbb{R}$. In the binary classification problem of selecting from three or more labelings, we present strong impossibility results for both deterministic and randomized mechanism. Finally, we provide deterministic and randomized mechanisms for selecting from two labelings.

We study the sample complexity of the plug-in approach for learning $\varepsilon$-optimal policies in average-reward Markov decision processes (MDPs) with a generative model. The plug-in approach constructs a model estimate then computes an average-reward optimal policy in the estimated model. Despite representing arguably the simplest algorithm for this problem, the plug-in approach has never been theoretically analyzed. Unlike the more well-studied discounted MDP reduction method, the plug-in approach requires no prior problem information or parameter tuning. Our results fill this gap and address the limitations of prior approaches, as we show that the plug-in approach is optimal in several well-studied settings without using prior knowledge. Specifically it achieves the optimal diameter- and mixing-based sample complexities of $\widetilde{O}\left(SA \frac{D}{\varepsilon^2}\right)$ and $\widetilde{O}\left(SA \frac{\tau_{\mathrm{unif}}}{\varepsilon^2}\right)$, respectively, without knowledge of the diameter $D$ or uniform mixing time $\tau_{\mathrm{unif}}$. We also obtain span-based bounds for the plug-in approach, and complement them with algorithm-specific lower bounds suggesting that they are unimprovable. Our results require novel techniques for analyzing long-horizon problems which may be broadly useful and which also improve results for the discounted plug-in approach, removing effective-horizon-related sample size restrictions and obtaining the first optimal complexity bounds for the full range of sample sizes without reward perturbation.

While previous optimization results have suggested that deep neural networks tend to favor low-rank weight matrices, the implications of this inductive bias on generalization bounds remain underexplored. In this paper, we apply a chain rule for Gaussian complexity (Maurer, 2016) to analyze how low-rank layers in deep networks can prevent the accumulation of rank and dimensionality factors that typically multiply across layers. This approach yields generalization bounds for rank and spectral norm constrained networks. We compare our results to prior generalization bounds for deep networks, highlighting how deep networks with low-rank layers can achieve better generalization than those with full-rank layers. Additionally, we discuss how this framework provides new perspectives on the generalization capabilities of deep networks exhibiting neural collapse.

We present a novel technique for computing a center-based approximation of a drifting distribution. Given $k \geq 1$ and a sequence of data, whose distribution is changing over time, the goal is to compute, at each step, the best $k$ centers representation of the current distribution, despite possibly having only a single sample from the most recent distribution. In data mining, this is traditionally attempted through the sliding-window mechanism, where the analysis is performed on the most recent fixed-size segment of the data. The problems with this approach are twofold: (1) setting the correct window size is challenging; and (2) a fixed window size cannot effectively track changes in the distribution happening at variable speed. In this paper, we propose a new methodology that dynamically adjusts the window size based on the recent drift of the data. The challenge is that it is not possible to explicitly estimate the drift, as we may have only a single data point from each distribution. Our main contribution lies in providing a rigorous mathematical analysis, establishing both an upper bound via a dynamic window size algorithm, and a lower bound that shows the tightness of our approach.

Let $\mathsf{TH}\_{k}$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}\_k$ function using noisy readings of the Boolean variables, where each reading is incorrect with some fixed and known probability $p \in (0,1/2)$. As our main result, we show that it is sufficient to use $(1+o(1)) \frac{n\log \frac{m}{\delta}}{D\_{\mathsf{KL}}(p \| 1-p)}$ queries in expectation to compute the $\mathsf{TH}\_k$ function with a vanishing error probability $\delta = o(1)$, where $m\triangleq \min(k,n-k+1)$ and $D\_{\mathsf{KL}}(p \| 1-p)$ denotes the Kullback-Leibler divergence between $\mathsf{Bern}(p)$ and $\mathsf{Bern}(1-p)$ distributions. Conversely, we show that any algorithm achieving an error probability of $\delta = o(1)$ necessitates at least $(1-o(1))\frac{(n-m)\log\frac{m}{\delta}}{D\_{\mathsf{KL}}(p \| 1-p)}$ queries in expectation. The upper and lower bounds are tight when $m=o(n)$, and are within a multiplicative factor of $\frac{n}{n-m}$ when $m=\Theta(n)$. In particular, when $k=n/2$, the $\mathsf{TH}\_k$ function corresponds to the $\mathsf{MAJORITY}$ function, in which case the upper and lower bounds are tight up to a multiplicative factor of two. Compared to previous work, our result tightens the dependence on $p$ in both the upper and lower bounds.

We study the problem of classifying the nodes of a given graph in the self-directed learning setup. This learning setting is a variant of online learning, where rather than an adversary determining the sequence in which nodes are presented, the learner autonomously and adaptively selects them. While self-directed learning of Euclidean halfspaces, linear functions, and general multiclass hypothesis classes was recently considered, no results previously existed specifically for self-directed node classification on graphs. In this paper, we address this problem developing efficient algorithms for it. More specifically, we focus on the case of (geodesically) convex clusters, i.e., for every two nodes sharing the same label, all nodes on every shortest path between them also share the same label. In particular, we devise an algorithm with runtime polynomial in $n$ that makes only $3(h(G)+1)^4 \ln n$ mistakes on graphs with two convex clusters, where $n$ is the total number of nodes and $h(G)$ is the Hadwiger number, i.e., the size of the largest clique minor of the graph $G$. We also show that our algorithm is robust to the case that clusters are slightly non-convex, still achieving a mistake bound logarithmic in $n$. Finally, we devise a simple and efficient algorithm for homophilic clusters, where strongly connected nodes tend to belong to the same class.

We study the mixing time of two popular discrete-time Markov chains in continuous space, the Unadjusted Langevin Algorithm and the Proximal Sampler, which are discretizations of the Langevin dynamics. We extend mixing time analyses for these Markov chains to hold in $\Phi$-divergence. We show that any $\Phi$-divergence arising from a twice-differentiable strictly convex function $\Phi$ converges to $0$ exponentially fast along these Markov chains, under the assumption that their stationary distributions satisfy the corresponding $\Phi$-Sobolev inequality, which holds for example when the target distribution of the Langevin dynamics is strongly log-concave. Our setting includes as special cases popular mixing time regimes, namely the mixing in chi-squared divergence under a Poincaré inequality, and the mixing in relative entropy under a log-Sobolev inequality. Our results follow by viewing the sampling algorithms as noisy channels and bounding the contraction coefficients arising in the appropriate strong data processing inequalities.

We revisit the classic problem of aggregating binary advice from conditionally independent experts, also known as the Naive Bayes setting. Our quantity of interest is the error probability of the optimal decision rule. In the case of symmetric errors (sensitivity = specificity), reasonably tight bounds on the optimal error probability are known. In the general asymmetric case, we are not aware of any nontrivial estimates on this quantity. Our contribution consists of sharp upper and lower bounds on the optimal error probability in the general case, which recover and sharpen the best known results in the symmetric special case. Since this turns out to be closely connected to bounding the total variation distance between two product distributions, our results also have bearing on this important and challenging problem.

We consider a repeatedly played generalized Nash equilibrium game. This induces a multi-agent online learning problem with joint constraints. An important challenge in this setting is that the feasible set for each agent depends on the simultaneous moves of the other agents and, therefore, varies over time. As a consequence, the agents face time-varying constraints, which are not adversarial but rather endogenous to the system. Prior work in this setting focused on convergence to a feasible solution in the limit via integrating the constraints in the objective as a penalty function. However, no existing work can guarantee that the constraints are satisfied for all iterations while simultaneously guaranteeing convergence to a generalized Nash equilibrium. This is a problem of fundamental theoretical interest and practical relevance. In this work, we introduce a new online feasible point method. Under the assumption that limited communication between the agents is allowed, this method guarantees feasibility. We identify the class of benign generalized Nash equilibrium problems, for which the convergence of our method to the equilibrium is guaranteed. We set this class of benign generalized Nash equilibrium games in context with existing definitions and illustrate our method with examples.

Modern machine learning usually involves predictors in the overparameterised setting (number of trained parameters greater than dataset size), and their training yields not only good performance on training data, but also good generalisation capacity. This phenomenon challenges many theoretical results, and remains an open problem. To reach a better understanding, we provide novel generalisation bounds involving gradient terms. To do so, we combine the PAC-Bayes toolbox with Poincaré and Log-Sobolev inequalities, avoiding an explicit dependency on the dimension of the predictor space. Our results highlight the positive influence of flat minima (being minima with a neighbourhood nearly minimising the learning problem as well) on generalisation performance, involving directly the benefits of the optimisation phase.

There has been a recent interest in understanding and characterizing the sample complexity of list learning tasks, where the learning algorithm is allowed to make a short list of $k$ predictions, and we simply require one of the predictions to be correct. This includes recent works characterizing the PAC sample complexity of standard list classification and online list classification. Adding to this theme, in this work, we provide a complete characterization of list PAC _regression_. We propose two combinatorial dimensions, namely the $k$-OIG dimension and the $k$-fat-shattering dimension, and show that they characterize realizable and agnostic $k$-list regression respectively. These quantities generalize known dimensions for standard regression. Our work thus extends existing list learning characterizations from classification to regression.

We introduce a novel online learning framework that unifies and generalizes pre-established models, such as delayed and corrupted feedback, to encompass adversarial environments where action feedback evolves over time. In this setting, the observed loss is arbitrary and may not correlate with the true loss incurred, with each round updating previous observations adversarially. We propose regret minimization algorithms for both the full-information and bandit settings, with regret bounds quantified by the average feedback accuracy relative to the true loss. Our algorithms match the known regret bounds across many special cases, while also introducing previously unknown bounds.

We propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our proposed method is the result of applying a Metropolis-Hastings filter to the Markov chain formed by a single step of the preconditioned Langevin algorithm with a metric $\mathscr{G}$, and is motivated by the natural gradient descent algorithm for optimisation. We derive non-asymptotic upper bounds for the mixing time of this method for sampling from target distributions whose potentials are bounded relative to $\mathscr{G}$, and for exponential distributions restricted to the support. Our analysis suggests that if $\mathscr{G}$ satisfies stronger notions of self-concordance introduced in Kook and Vempala (2024), then these mixing time upper bounds have a strictly better dependence on the dimension than when $\mathscr{G}$ is merely self-concordant. Our method is a high-accuracy sampler due to the polylogarithmic dependence on the error tolerance in our mixing time upper bounds.

We establish disintegrated PAC-Bayesian generalisation bounds for models trained with gradient descent methods or continuous gradient flows. Contrary to standard practice in the PAC-Bayesian setting, our result applies to optimisation algorithms that are deterministic, without requiring any de-randomisation step. Our bounds are fully computable, depending on the density of the initial distribution and the Hessian of the training objective over the trajectory. We show that our framework can be applied to a variety of iterative optimisation algorithms, including stochastic gradient descent (SGD), momentum-based schemes, and damped Hamiltonian dynamics.

Comparative learning, a recently introduced variation of the PAC (Probably Approximately Correct) framework, interpolates between the two standard extreme settings of realizable and agnostic PAC learning. In comparative learning the labeling is assumed to be from one hypothesis class (the source class) while the learner's performance is to be measured against another hypothesis class (the benchmark class). This setup allows for incorporating more specific prior knowledge into PAC type learning bounds, which are known to be otherwise overly pessimistic. It also naturally represents model distillation tasks, where a predictor with specific requirements (such as being bounded in size or being interpretable) is trained on the labels from another model. A first sample complexity analysis of comparative learning established upper and lower bounds for general comparative learning. In this work, we propose a more fine grained view on this setting, distinguishing between proper learning and general (improper) learning. We derive novel upper and lower sample complexity bounds for both settings. In particular, we identify conditions for each of the regimes, and thereby exhibit how the rate depends on the relatedness of the two classes in perhaps unexpected ways.

We propose a learning problem, which we call reliable active apprenticeship learning, for which we define a learning algorithm providing optimal performance guarantees, which we further show are sharply characterized by the eluder dimension of a policy class. In this setting, a learning algorithm is tasked with behaving optimally in an unknown environment given by a Markov decision process. The correct actions are specified by an unknown optimal policy in a given policy class. The learner initially does not know the optimal policy, but it has the ability to query an expert, which returns the optimal action for the current state. A learner is said to be reliable if, whenever it takes an action without querying the expert, its action is guaranteed to be optimal. We are then interested in designing a reliable learner which does not query the expert too often. We propose a reliable learning algorithm which provably makes the minimal possible number of queries, which we show is precisely characterized by the eluder dimension of the policy class. We further extend this to allow for imperfect experts, modeled as an oracle with noisy responses. We study two variants of this, inspired by noise conditions from classification: namely, Massart noise and Tsybakov noise. In both cases, we propose a reliable learning strategy which achieves a nearly-minimal number of queries, and prove upper and lower bounds on the optimal number of queries in terms of the noise conditions and the eluder dimension of the policy class.

We study data-dependent regret bounds for the Online Portfolio Selection (OPS) problem. As opposed to worst-case bounds that hold uniformly over all sequence of returns, data-dependent bounds adapt to the specific sequence of returns seen by the investor. Consider a market of $n$ assets and $T$ time periods, consisting of the returns $r_1,\dots,r_T \in \mathbb{R}^n_+$. The regret of our proposed algorithm, Log-Barrier Adaptive-Curvature Online Newton Step (LB-AdaCurv ONS) is bounded by $O(\min(nR\log T, \sqrt{nT\log T}))$, where $R = \max_{t,i,j} \frac{r_t(i)}{r_t(j)}$ is a data dependent quantity that is not known to the algorithm. Thus, LB-AdaCurv ONS has a worst case regret of $O(\sqrt{nT \log T})$ while simultaneously having a data-dependent regret of $O(nR\log T)$. Next, we consider the more practical setting of OPS with predicted returns, where the investor has access to predictions that can be incorporated into the portfolio selection process. We propose the Optimistic Expected Utility LB-FTRL (OUE-LB-FTRL) algorithm that incorporates the predictions using a utility function. If the predictions are accurate, OUE-LB-FTRL's regret is $O(n \log T)$ and even if the predictions are arbitrary, regret is always bounded by $O(\sqrt{nT\log T})$. We provide a meta-algorithm called Best-of-Both Worlds for OPS (BoB-OPS), that combines the portfolios of an expected utility investor and a regret minimizing investor. By properly instantiating BoB-OPS, we show that the regret with respect to the expected utility investor is $O(\log T)$ and the static regret is $O(n \log T)$. Finally, we also show new First-Order, Second-Order and Gradual-Variation regret bounds for OPS. In our analysis, we developed new regret inequalities for optimistic FTRL with convex hint functions. This extends prior work on optimistic FTRL that used only linear hints, and so could be of independent interest.

The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the *uniform convergence* of empirical error in $H$ to its mean, or equivalently, to the problem of *density estimation*, learnability of the underlying marginal distribution with respect to events in $H$. This seminal equivalence relies strongly on PAC learning's `distribution-free' assumption, that the adversary may choose any marginal distribution over data. Unfortunately, the distribution-free model is known to be overly adversarial in practice, failing to predict the success of modern machine learning algorithms, but without the Fundamental Theorem our theoretical understanding of learning under distributional constraints remains highly limited. In this work, we revisit the connection between PAC learning, uniform convergence, and density estimation beyond the distribution-free setting when the adversary is restricted to choosing a marginal distribution from a known family $\mathscr{P}$. We prove that while the traditional Fundamental Theorem fails, a finer-grained connection between the three fundamental notions continues to hold: 1. PAC-Learning is strictly sandwiched between two relaxed models of density estimation, differing only in whether the learner knows the set of well-estimated events in $\mathcal{H}$. 2. Under reasonable assumptions on $\mathcal{H}$ and $\mathscr{P}$, density estimation is equivalent to *uniform estimation*, a weakening of uniform convergence allowing non-empirical estimators. Together, our results give a clearer picture of how the Fundamental Theorem extends beyond the distribution-free setting and shed new light on the classically challenging problem of learning under arbitrary distributional assumptions.

We study the problem of multiclass online learning under $\textit{bandit feedback}$ within the framework of $\textit{universal learning}$ [Bousquet, Hanneke, Moran, van Handel, and Yehudayoff; STOC '21]. In multiclass online learning under bandit feedback, it is well known that no concept class $\mathcal{C}$ is $\textit{uniformly}$ learnable when the effective label space is unbounded, or in other words, no online learner guarantees a finite bound on the expected number of mistakes holding uniformly over all realizable data sequences. In contrast, surprisingly, we show that in the case of $\textit{universal}$ learnability of concept classes $\mathcal{C}$, there is an exact equivalence between multiclass online learnability under bandit feedback and full supervision, in both the realizable and agnostic settings. More specifically, our first main contribution is a theory that establishes an inherent dichotomy in multiclass online learning under bandit feedback within the realizable setting. In particular, for any concept class $\mathcal{C}$ even when the effective label space is unbounded, we have: (1) If $\mathcal{C}$ does not have an infinite multiclass Littlestone tree, then there is a deterministic online learner that makes only finitely many mistakes against any realizable adversary, crucially without placing a uniform bound on the number of mistakes. (2) If $\mathcal{C}$ has an infinite multiclass Littlestone tree, then there is a strategy for the realizable adversary that forces any learner, including randomized, to make linear expected number of mistakes. Furthermore, our second main contribution reveals a similar trend in the agnostic setting.