Yishay Mansour
Prof. Yishay Mansour got his PhD from MIT in 1990, following it he was
a postdoctoral fellow in Harvard and a Research Staff Member in IBM T.
J. Watson Research Center. Since 1992 he is at Tel-Aviv University,
where he is currently a Professor of Computer Science and has serves
as the first head of the Blavatnik School of Computer Science during
2000-2002. He was the founder and first director of the Israeli Center of Research
Excellence in Algorithms.
Prof. Mansour has published over 100 journal papers and over 200
proceeding papers in various areas of computer science with special
emphasis on machine learning, algorithmic game theory, communication
networks, and theoretical computer science and has supervised over a
dozen graduate students in those areas.
Prof. Mansour was named as an ACM fellow 2014, and he is currently an
associate editor in a number of distinguished journals and has been on
numerous conference program committees. He was both the program chair
of COLT (1998) and the STOC (2016) and served twice on the COLT
steering committee and is a member of the ALT steering committee.
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Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d. test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such as error rate are well-defined, and test error reliably approximates population error given sufficiently large datasets. In contrast, evaluation is more challenging for generative models due to their open-ended nature: it is unclear which metrics are appropriate and whether such metrics can be reliably evaluated from finite samples. In this work, we introduce a theoretical framework for evaluating language models and establish evaluability results for commonly used metrics. We study two categories of metrics: test-based metrics, including integral probability metrics (IPMs), and similarity-based metrics, including Rényi and KL divergences. We show that IPMs with respect to any bounded test class can be evaluated from finite samples up to multiplicative and additive approximation errors. Moreover, when the test class has finite fat-shattering dimension, IPMs can be evaluated with arbitrary precision. In contrast, similarity-based metrics, including Rényi and KL divergences, are not evaluable from finite samples, as their values can be critically determined by rare events. We also analyze the potential and limitations of perplexity as an evaluation method.
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Learning Conditional Averages
Marco Bressan
Nataly Brukhim
Nicolo Cesa-Bianchi
Emmanuel Esposito
Shay Moran
Maximilian Thiessen
COLT (2026)
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We introduce the problem of learning \emph{conditional averages} in the PAC framework.
The learner receives a sample labeled by an unknown target concept from a known concept class, as in standard PAC learning. However, instead of learning the target concept itself, the goal is to predict, for each instance, the average label over its \emph{neighborhood}---an arbitrary subset of points that contains the instance.
In the degenerate case where all neighborhoods are singletons, the problem reduces exactly to classic PAC learning. More generally, it extends PAC learning to a setting that captures learning tasks arising in several domains, including explainability, fairness, and recommendation systems. %including explainability, fairness, and recommendation systems.
Our main contribution is a complete characterization of when conditional averages are learnable, together with sample complexity bounds that are tight up to logarithmic factors. The characterization hinges on the joint finiteness of two novel combinatorial parameters, which depend on both the concept class and the neighborhood system, and are closely related to the independence number of the associated neighborhood graph.
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The fundamental theorem of statistical learning establishes that binary PAC learning is governed by a single parameter---the Vapnik-Chervonenkis ($\mathtt{VC}$) dimension---which controls both learnability and sample complexity. Extending this characterization to multiclass classification has long been challenging, since the early work of Natarajan in the late 80's that proposed the Natarajan dimension ($\mathtt{Nat}$) as a natural analogue of the VC dimension.
Daniely and Shalev-Shwartz (2014) introduced the $\mathtt{DS}$ dimension, later shown by Brukhim et al.\ (2022) to characterize multiclass \emph{learnability}.
Brukhim et al.\ (2022) also demonstrated that the Natarajan and $\mathtt{DS}$ dimensions can diverge arbitrarily, so that multiclass learning appears to be governed by $\mathtt{DS}$ rather than $\mathtt{Nat}$.
We show that the agnostic multiclass PAC sample complexity is in fact governed by \emph{two distinct dimensions}. Specifically, we prove nearly tight agnostic sample complexity bounds that, up to logarithmic factors, take the form
$$
\frac{\mathtt{DS}^{1.5}}{\epsilon} + \frac{\mathtt{Nat}}{\epsilon^2}
$$
where $\epsilon$ is the excess risk. This bound is tight up to a $\sqrt{\mathtt{DS}}$ factor in the first lower-order term, nearly matching known $\mathtt{Nat}/\epsilon^2$ and $\mathtt{DS}/\epsilon$ lower bounds.
The first term reflects the DS-controlled regime, while the second reveals that the Natarajan dimension still dictates asymptotic behavior for small $\epsilon$. Thus, unlike in binary or online classification---where a single dimension (VC or Littlestone) controls both phenomena---multiclass learning inherently involves \emph{two structural parameters}.
Our technical approach departs significantly from traditional agnostic learning methods based on uniform convergence or reductions-to-realizable techniques. A key ingredient is a novel online procedure, based on a self-adaptive multiplicative-weights algorithm which performs a label-space reduction. This approach may be of independent interest and find further applications.
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Modern machine learning systems, such as generative models and recommendation systems, often evolve through a cycle of deploying a model, observing user interactions, and updating the model intermittently based on feedback. This mode of learning contrasts with common supervised learning frameworks, which focus on loss or regret minimization over a shared sequence of prediction tasks. Motivated by this deployment-driven learning cycle, we revisit the classical model of learning from equivalence queries, introduced by Angluin, which provides a simple abstraction of such interactions: a learner repeatedly proposes hypotheses and, whenever the deployed hypothesis is inadequate, receives a counterexample tailored to that hypothesis. Under fully adversarial counterexample generation, however, this model exhibits overly pessimistic worst-case behavior. Moreover, most existing work on learning from equivalence queries considers the \emph{full-information} setting, where the learner observes not only a counterexample but also its correct label. This is an assumption that does not always align with natural interactive settings. To address these considerations, we restrict the environment to generate counterexamples in a less adversarial manner by introducing a broad class of counterexample generators, which we call \emph{symmetric}. Informally, such symmetric counterexample generators select counterexamples based only on the symmetric difference between the hypothesis and the target, and encompass natural feedback mechanisms such as random counterexamples, as well as generators that select counterexamples minimizing a prescribed complexity measure over the instance space. Within this framework, we study learning from equivalence queries under both full-information and bandit feedback. We establish tight bounds on the number of learning rounds in both settings and outline directions for future research. Our techniques rely on a game-theoretic perspective on symmetric adversaries and combine adaptive weighting algorithms with minimax arguments.
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We study contextual bandits in the stochastic i.i.d.\ setting, where a learner observes contexts drawn from an unknown distribution, selects actions from a finite set $\cA$, and aims to identify an approximately optimal policy from a given class based on bandit feedback.
Motivated by the important special case of bandit multiclass classification with zero-one rewards, we focus on the \emph{$s$-sparse} setting in which, for every context, the underlying reward vector has $L_1$-norm at most $s \ll |\cA|$. Our main result is the design of algorithms that, with probability at least~$1-\delta$, output an $\eps$-optimal policy compared to policy class $\Pi$ using
\begin{align*}
\wt{O} \brk*{\brk*{\frac{s}{\eps^2} + \frac{|\cA|}{\eps}} \log \frac{|\Pi|}{\delta}}
\end{align*}
samples.
We further extend this bound to general Natarajan classes and complement it with a matching lower bound (up to logarithmic factors), thereby closing a substantial gap left by prior work~\citep{erez2024real,erez2024fast,erez2025bandit}, which incurred an additional $\Theta(|\cA|^9)$ dependence.
We obtain these results via two complementary approaches. First, we analyze contextual bandits through the lens of contextual decision making with structured observations, designing an exploration-by-optimization algorithm whose sample complexity is governed by the \emph{decision-estimation coefficient} (DEC; \citealp{foster2021statistical,foster2022complexity}). We show that, with $s$-sparse rewards, the induced model class admits a sharp DEC bound that scales with $s$ and directly yields the optimal rate. Since this approach is largely information-theoretic and involves solving complex min-max optimization problems, we also develop a second, more specialized algorithmic method based on a low-variance exploration technique. This approach leads to concrete, tractable algorithms and naturally extends to contextual combinatorial semi-bandits, leading to improved sample complexity guarantees for bandit multiclass list classification.
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We study the stochastic linear bandits with parameter noise model, in which the reward of action $a$ is $a^\top \theta$ where $\theta$ is sampled i.i.d.
We show a regret upper bound of $\tO \brk{\sqrt{d T \logKdelta \sigmax}}$ for a horizon $T$, general action set of size $K$ of dimension $d$, and where $\sigmax$ is the maximal variance of the reward for any action.
We further provide a lower bound of $\tOmega \brk{d \sqrt{T \sigmax}}$ which is tight (up to logarithmic factors) whenever $\log \brk{K} \approx d$.
For more specific action sets, $\ell_p$ unit balls with $p \leq 2$ and dual norm $q$, we show that the minimax regret is $\tTheta \brk{\sqrt{dT \vsigq}}$, where $\vsigq$ is a variance-dependent quantity that is always at most $4$.
This is in contrast to the minimax regret attainable for such sets in the classic additive noise model, where the regret is of order $d \sqrt{T}$.
Surprisingly, we show that this optimal (up to logarithmic factors) regret bound is attainable using a very simple explore-exploit algorithm.
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e introduce a new Bayesian perspective on the concept of data reconstruction, and leverage this viewpoint to propose a new security definition that, in certain settings, provably prevents reconstruction attacks. We use our paradigm to shed new light on one of the most notorious attacks in the privacy and memorization literature - fingerprinting code attacks (FPC). We argue that these attacks are really a form of membership inference attacks, rather than reconstruction attacks. Furthermore, we show that if the goal is solely to prevent reconstruction (but not membership inference), then in some cases the impossibility results derived from FPC no longer apply.
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In this paper we introduce \emph{OPO-CMDP}, the first policy optimization algorithm for stochastic Contextual Markov Decision Process (CMDPs) under general offline function approximation. We establish a high probability regret bound of
$\widetilde{O}\left(H^4\sqrt{T|S||A|\log(|\mathcal{F}||\mathcal{P}|)}\right),$
where $S$ and $A$ denote the state and action spaces, $H$ the horizon length, $T$ the number of episodes, and $\mathcal{F}, \mathcal{P}$ the function classes used to approximate the losses and dynamics, respectively. This result improves the dependence on $|S|$ and $|A|$ compared to the previously known state-of-the-art bound of \citet*{DBLP:conf/nips/QianHS24}. Our analysis introduces sophisticated confidence bounds for stochastic policies that eliminate restrictive assumptions required in prior work. Our results demonstrate that simple policy optimization over optimistic model approximations can achieve better, near-optimal regret bound for CMDPs.
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Of Dice and Games: A Theory of Generalized Boosting
Marco Bressan
Nataly Brukhim
Nicolo Cesa-Bianchi
Emmanuel Esposito
Shay Moran
Maximilian Thiessen
COLT (2025)
Preview abstract
Cost-sensitive loss functions are crucial in many real-world prediction problems, where different types of errors are penalized differently; for example, in medical diagnosis, a false negative prediction can lead to severe consequences. However, traditional PAC learning theory has mostly focused on the symmetric 0-1 loss, leaving cost-sensitive losses largely unaddressed.
In this work, we extend the celebrated theory of boosting to incorporate both cost-sensitive and multi-objective losses.
Cost-sensitive losses assign costs to the entries of a confusion matrix, and are used to control the sum of prediction errors accounting for the cost of each error type. Multi-objective losses, on the other hand, simultaneously track multiple cost-sensitive losses,
and are useful when the goal is to satisfy several criteria at once (e.g., minimizing false positives while keeping false negatives below a critical threshold).
We develop a comprehensive theory of cost-sensitive and multi-objective boosting, providing a taxonomy of weak learning guarantees that distinguishes which guarantees are trivial (i.e., they can always be achieved), which are boostable (i.e., they imply strong learning), and which are intermediate, implying non-trivial yet not arbitrarily accurate learning. For binary classification, we establish a dichotomy: a weak learning guarantee is either trivial or boostable. In the multiclass setting, we describe a more intricate landscape of intermediate weak learning guarantees. Our characterization relies on a geometric interpretation of boosting, revealing a useful duality between cost-sensitive and multi-objective losses.
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We consider non-stationary multi-arm bandit (MAB) where the expected reward of each action follows a linear function of the number of times we executed the action.
Our main result is a tight regret bound of $\tilde{\Theta}(T^{4/5}K^{3/5})$, by providing both upper and lower bounds.
We extend our results to derive instance dependent regret bounds, which depend on the unknown parametrization of the linear drift of the rewards.
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