From Contextual Combinatorial Semi-Bandits to Bandit List Classification: Improved Sample Complexity with Sparse Rewards

• URL: http://arxiv.org/abs/2502.09257v3
• Date: Sun, 26 Oct 2025 12:38:06 GMT
• Title: From Contextual Combinatorial Semi-Bandits to Bandit List Classification: Improved Sample Complexity with Sparse Rewards
• Authors: Liad Erez, Tomer Koren,
• Abstract summary: We study the problem of contextual semi-bandits, where input contexts are mapped into subsets of size $m$ of a collection of $K$ possible actions.<n>Motivated by prototypical applications of contextual bandits, we focus on the $s$-sparse regime.<n>Our framework generalizes the list multiclass classification problem with bandit feedback, which can be seen as a special case with binary reward vectors.
• Score: 26.147671458980117
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of contextual combinatorial semi-bandits, where input contexts are mapped into subsets of size $m$ of a collection of $K$ possible actions. In each round, the learner observes the realized reward of the predicted actions. Motivated by prototypical applications of contextual bandits, we focus on the $s$-sparse regime where we assume that the sum of rewards is bounded by some value $s\ll K$. For example, in recommendation systems the number of products purchased by any customer is significantly smaller than the total number of available products. Our main result is for the $(\epsilon,\delta)$-PAC variant of the problem for which we design an algorithm that returns an $\epsilon$-optimal policy with high probability using a sample complexity of $\tilde{O}((poly(K/m)+sm/\epsilon^2) \log(|\Pi|/\delta))$ where $\Pi$ is the underlying (finite) class and $s$ is the sparsity parameter. This bound improves upon known bounds for combinatorial semi-bandits whenever $s\ll K$, and in the regime where $s=O(1)$, the leading terms in our bound match the corresponding full-information rates, implying that bandit feedback essentially comes at no cost. Our algorithm is also computationally efficient given access to an ERM oracle for $\Pi$. Our framework generalizes the list multiclass classification problem with bandit feedback, which can be seen as a special case with binary reward vectors. In the special case of single-label classification corresponding to $s=m=1$, we prove an $O((K^7+1/\epsilon^2)\log(|H|/\delta))$ sample complexity bound, which improves upon recent results in this scenario. Additionally, we consider the regret minimization setting where data can be generated adversarially, and establish a regret bound of $\tilde O(|\Pi|+\sqrt{smT\log |\Pi|})$, extending the result of Erez et al. (2024) who consider the simpler single label classification setting.

Related papers

• Beyond Minimax Rates in Group Distributionally Robust Optimization via a Novel Notion of Sparsity [14.396304498754688]
  We show a novel notion of sparsity that we dub $(lambda, beta)$-sparsity.<n>In short, there is a set of at most $beta$ groups whose risks at $theta$ all are at least $lambda$ larger than the risks of the other groups.<n>We show how to get a dimension-free semi-adaptive sample complexity bound with a computationally efficient method.
  arXiv  Detail & Related papers  (2024-10-01T13:45:55Z)
• Fast Rates for Bandit PAC Multiclass Classification [73.17969992976501]
  We study multiclass PAC learning with bandit feedback, where inputs are classified into one of $K$ possible labels and feedback is limited to whether or not the predicted labels are correct. Our main contribution is in designing a novel learning algorithm for the agnostic $(varepsilon,delta)$PAC version of the problem.
  arXiv  Detail & Related papers  (2024-06-18T08:54:04Z)
• The Real Price of Bandit Information in Multiclass Classification [73.17969992976501]
  We revisit the classical problem of multiclass classification with bandit feedback. We present a new bandit classification algorithm that guarantees regret $smashwidetildeO(|H|+sqrtT)$.
  arXiv  Detail & Related papers  (2024-05-16T12:11:09Z)
• Provably Efficient High-Dimensional Bandit Learning with Batched Feedbacks [93.00280593719513]
  We study high-dimensional multi-armed contextual bandits with batched feedback where the $T$ steps of online interactions are divided into $L$ batches. In specific, each batch collects data according to a policy that depends on previous batches and the rewards are revealed only at the end of the batch. Our algorithm achieves regret bounds comparable to those in fully sequential setting with only $mathcalO( log T)$ batches.
  arXiv  Detail & Related papers  (2023-11-22T06:06:54Z)
• Distribution-Independent Regression for Generalized Linear Models with Oblivious Corruptions [49.69852011882769]
  We show the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We present an algorithm that tackles newthis problem in its most general distribution-independent setting. This is the first newalgorithmic result for GLM regression newwith oblivious noise which can handle more than half the samples being arbitrarily corrupted.
  arXiv  Detail & Related papers  (2023-09-20T21:41:59Z)
• Context-lumpable stochastic bandits [49.024050919419366]
  We consider a contextual bandit problem with $S$ contexts and $K$ actions. We give an algorithm that outputs an $epsilon$-optimal policy after using at most $widetilde O(r (S +K )/epsilon2)$ samples. In the regret setting, we give an algorithm whose cumulative regret up to time $T$ is bounded by $widetilde O(sqrtr3(S+K)T)$.
  arXiv  Detail & Related papers  (2023-06-22T17:20:30Z)
• Phase Transitions in the Detection of Correlated Databases [12.010807505655238]
  We study the problem of detecting the correlation between two Gaussian databases $mathsfXinmathbbRntimes d$ and $mathsfYntimes d$, each composed of $n$ users with $d$ features. This problem is relevant in the analysis of social media, computational biology, etc.
  arXiv  Detail & Related papers  (2023-02-07T10:39:44Z)
• List-Decodable Sparse Mean Estimation via Difference-of-Pairs Filtering [42.526664955704746]
  We develop a novel, conceptually simpler technique for list-decodable sparse mean estimation. In particular, for distributions with "certifiably bounded" $t-th moments in $k$-sparse directions, our algorithm achieves error of $(1/alpha)O (1/t)$ with sample complexity $m = (klog(n))O(t)/alpha(mnt)$. For the special case of Gaussian inliers, our algorithm achieves the optimal error guarantee of $Theta (sqrtlog
  arXiv  Detail & Related papers  (2022-06-10T17:38:18Z)
• Self-training Converts Weak Learners to Strong Learners in Mixture Models [86.7137362125503]
  We show that a pseudolabeler $boldsymbolbeta_mathrmpl$ can achieve classification error at most $C_mathrmerr$. We additionally show that by running gradient descent on the logistic loss one can obtain a pseudolabeler $boldsymbolbeta_mathrmpl$ with classification error $C_mathrmerr$ using only $O(d)$ labeled examples.
  arXiv  Detail & Related papers  (2021-06-25T17:59:16Z)
• Semi-supervised Active Regression [21.51757844385258]
  This paper studies the use of partially labelled, potentially biased data for learning tasks. The learner has access to a dataset $X in mathbbRd | X min_beta in mathbbRd | X beta - Y |2 end2 equation while making few additional label queries.
  arXiv  Detail & Related papers  (2021-06-12T03:28:43Z)
• Near-Optimal Regret Bounds for Contextual Combinatorial Semi-Bandits with Linear Payoff Functions [53.77572276969548]
  We show that the C$2$UCB algorithm has the optimal regret bound $tildeO(dsqrtkT + dk)$ for the partition matroid constraints. For general constraints, we propose an algorithm that modifies the reward estimates of arms in the C$2$UCB algorithm.
  arXiv  Detail & Related papers  (2021-01-20T04:29:18Z)
• Active Local Learning [22.823171570933397]
  We consider active local learning: given a query point $x$, and active access to an unlabeled training set $S$, output the prediction $h(x)$ of a near-optimal $h in H$. In particular, the number of label queries should be independent of the complexity of $H$, and the function $h$ should be well-defined, independent of $x$. This immediately also implies an algorithm for distance estimation: estimating the value $opt(H)$ from many fewer labels than needed to actually learn a near-optimal $h in
  arXiv  Detail & Related papers  (2020-08-31T05:39:35Z)
• Stochastic Bandits with Linear Constraints [69.757694218456]
  We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies. We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB)
  arXiv  Detail & Related papers  (2020-06-17T22:32:19Z)
• $Q$-learning with Logarithmic Regret [60.24952657636464]
  We prove that an optimistic $Q$-learning enjoys a $mathcalOleft(fracSAcdot mathrmpolyleft(Hright)Delta_minlogleft(SATright)right)$ cumulative regret bound, where $S$ is the number of states, $A$ is the number of actions, $H$ is the planning horizon, $T$ is the total number of steps, and $Delta_min$ is the minimum sub-optimality gap.
  arXiv  Detail & Related papers  (2020-06-16T13:01:33Z)
• Model-Free Reinforcement Learning: from Clipped Pseudo-Regret to Sample Complexity [59.34067736545355]
  Given an MDP with $S$ states, $A$ actions, the discount factor $gamma in (0,1)$, and an approximation threshold $epsilon > 0$, we provide a model-free algorithm to learn an $epsilon$-optimal policy. For small enough $epsilon$, we show an improved algorithm with sample complexity.
  arXiv  Detail & Related papers  (2020-06-06T13:34:41Z)
• A Multiclass Classification Approach to Label Ranking [2.6905021039717987]
  In multiclass classification, the goal is to learn how to predict a random label $Y$, valued in $mathcalY=1,; ldots,; K $ with $Kgeq 3$. This article is devoted to the analysis of this statistical learning problem, halfway between multiclass classification and posterior probability estimation.
  arXiv  Detail & Related papers  (2020-02-21T17:12:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.