Alon Cohen
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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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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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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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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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We present regret minimization algorithms for the contextual multi-armed bandit (CMAB) problem over $K$ actions in the presence of delayed feedback, a scenario where loss observations arrive with delays chosen by an adversary.
As a preliminary result, assuming direct access to a finite policy class $\Pi$ we establish an optimal expected regret bound of $ O (\sqrt{KT \log |\Pi|} + \sqrt{D \log |\Pi|)} $ where $D$ is the sum of delays.
For our main contribution, we study the general function approximation setting over a (possibly infinite) contextual loss function class $ \mathcal{F} $ with access to an online least-square regression oracle $\mathcal{O}$ over $\mathcal{F}$. In this setting, we achieve an expected regret bound of $O(\sqrt{KT\mathcal{R}_T(\mathcal{O})} + \sqrt{ d_{\max} D \beta})$ assuming FIFO order, where $d_{\max}$ is the maximal delay, $\mathcal{R}_T(\mathcal{O})$ is an upper bound on the oracle's regret and $\beta$ is a stability parameter associated with the oracle. We complement this general result by presenting a novel stability analysis of a Hedge-based version of Vovk's aggregating forecaster as an oracle implementation for least-square regression over a finite function class $\mathcal{F}$ and show that its stability parameter $\beta$ is bounded by $\log |\F|$, resulting in an expected regret bound of $O(\sqrt{KT \log |\mathcal{F}|} + \sqrt{d_{\max} D \log |\mathcal{F}|})$
which is a $\sqrt{d_{\max}}$ factor away from the lower bound of $\Omega(\sqrt{KT \log |\mathcal{F}|} + \sqrt{D \log |\mathcal{F}|})$ that we also present.
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We study regret minimization in online episodic linear Markov Decision Processes,
and propose a policy optimization algorithm that is computationally efficient, and obtains rate optimal $\wtO (\sqrt K)$ regret where $K$ denotes the number of episodes.
Our work is the first to establish the optimal rate (in terms of~$K$) of convergence in the stochastic setting with bandit feedback using a policy optimization based approach, and the first to establish the optimal rate in the adversarial setup with full information feedback, for which no algorithm with an optimal rate guarantee was previously known.
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We present the E-UC$^3$RL algorithm for regret minimization in Stochastic Contextual Markov Decision Processes (CMDPs). The algorithm operates under the minimal assumptions of realizable function class and access to \emph{offline} least squares and log loss regression oracles.
Our algorithm is efficient (assuming efficient offline regression oracles) and enjoys
a regret guarantee of
$
\widetilde{O}(H^3 \sqrt{T |S| |A|d_{\mathrm{E}}(\mathcal{P}) \log (|\mathcal{F}| |\mathcal{P}|/ \delta) )})
$
, with $T$ being the number of episodes, $S$ the state space, $A$ the action space, $H$ the horizon, $\mathcal{P}$ and $\mathcal{F}$ are finite function classes used to approximate the context-dependent dynamics and rewards, respectively, and $d_{\mathrm{E}}(\mathcal{P})$ is the Eluder dimension of $\mathcal{P}$ w.r.t the Hellinger distance.
To the best of our knowledge, our algorithm is the first efficient and rate-optimal regret minimization algorithm for CMDPs that operates under the general offline function approximation setting. In addition, we extend the Eluder dimension to general bounded metrics which may be of independent interest.
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We present the OMG-CMDP! algorithm for regret minimization in adversarial Contextual MDPs. The algorithm operates under the minimal assumptions of realizable function class and access to online least squares and log loss regression oracles. Our algorithm is efficient (assuming efficient online regression oracles), simple and robust to approximation errors. It enjoys an
$\widetilde{O}(H^{2.5} \sqrt{ T|S||A| (
} \linebreak[1]
\overline{ \mathcal{R}(\mathcal{O})
+ H \log(\delta^{-1}) )})$ regret guarantee,
with $T$ being the number of episodes, $S$ the state space, $A$ the action space, $H$ the horizon and $\mathcal{R}(\mathcal{O}) = \mathcal{R}(\mathcal{O}_{\mathrm{sq}}^\mathcal{F}) + \mathcal{R}(\mathcal{O}_{\mathrm{log}}^\mathcal{P})$
is the sum of the regression oracles' regret, used to approximate the context-dependent rewards and dynamics, respectively. To the best of our knowledge, our algorithm is the first efficient and rate optimal regret minimization algorithm for adversarial CMDPs which operates under the minimal and standard assumption of online function approximation. Our technique relies on standard convex optimization algorithms, and we show that it is robust to approximation errors.
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Shared computational principles for language processing in humans and deep language models
Ariel Goldstein
Zaid Zada
Eliav Buchnik
Amy Price
Bobbi Aubrey
Samuel A. Nastase
Harshvardhan Gazula
Gina Choe
Aditi Rao
Catherine Kim
Colton Casto
Lora Fanda
Werner Doyle
Daniel Friedman
Patricia Dugan
Lucia Melloni
Roi Reichart
Sasha Devore
Adeen Flinker
Liat Hasenfratz
Omer Levy,
Kenneth A. Norman
Orrin Devinsky
Uri Hasson
Nature Neuroscience (2022)
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Departing from traditional linguistic models, advances in deep learning have resulted in a new type of predictive (autoregressive) deep language models (DLMs). Using a self-supervised next-word prediction task, these models generate appropriate linguistic responses in a given context. In the current study, nine participants listened to a 30-min podcast while their brain responses were recorded using electrocorticography (ECoG). We provide empirical evidence that the human brain and autoregressive DLMs share three fundamental computational principles as they process the same natural narrative: (1) both are engaged in continuous next-word prediction before word onset; (2) both match their pre-onset predictions to the incoming word to calculate post-onset surprise; (3) both rely on contextual embeddings to represent words in natural contexts. Together, our findings suggest that autoregressive DLMs provide a new and biologically feasible computational framework for studying the neural basis of language.
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Building a Clinically-Focused Problem List From Medical Notes
Ayelet Benjamini
Birju Patel
Cathy Cheung
Hengrui Liu
Liwen Xu
Peter Clardy
Rachana Fellinger
Uri Lerner
LOUHI 2022: The 13th International Workshop on Health Text Mining and Information Analysis (2022)
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Clinical notes often contain vital information not observed in other structured data, but their unstructured nature can lead to critical patient-related information being lost. To make sure this valuable information is utilized for patient care, algorithms that summarize notes into a problem list are often proposed. Focusing on identifying medically-relevant entities in the free-form text, these solutions are often detached from a canonical ontology and do not allow downstream use of the detected text-spans. As a solution, we present here a system for generating a canonical problem list from medical notes, consisting of two major stages. At the first stage, annotation, we use a transformer model to detect all clinical conditions which are mentioned in a single note. These clinical conditions are then grounded to a predefined ontology, and are linked to spans in the text. At the second stage, summarization, we aggregate over the set of clinical conditions detected on all of the patient's note, and produce a concise patient summary that organizes their important conditions.
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