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arXiv 最近完成扫描:2026-11-15 19:05 · 全站最近入库:2026-11-14 15:09各信源进度 →

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版本更新 · v3arXiv:2605.17609

Adaptive Generate-Rank-Verify: Inference-Time Search with Costly Verification

Shaddin Dughmi, Mahdi Haghifam, Yusuf Hakan Kalayci

原文摘要

Many inference-time language-model pipelines combine a cheap reward signal with an expensive verifier, such as exact answer checking in mathematical reasoning or hidden-test execution in code generation. We formalize this setting using a learning-theoretic lens as generative active search: a cost-sensitive first-positive search problem in which a policy adaptively samples candidates from an unknown distribution, observes cheap scores, and pays for verifier labels until it finds a positive example. For a fixed prompt, the generator and reward model induce two unknown objects: a distribution over reward scores and a score-conditioned success function. When these quantities are known, we characterize the distribution-aware optimal policy using a dynamic programming approach. In the realistic and practical setting where both the score distribution and success function are unknown, we propose ADAP, a shellwise adaptive generate-rank-verify algorithm that progressively increases the number of sampled responses and top-ranked verifications. Under the monotonicity assumption that higher reward scores are no less likely to pass verification, we show that ADAP achieves expected cost within a constant factor of the distribution-aware optimum. We complement this result with learning-theoretic lower bounds, based on a centered star number, showing that structural assumptions on the score--label relationship are necessary. Experiments on mathematical reasoning and competitive programming validate the predicted advantage over both fixed non-adaptive policies and difficulty-adaptive baselines.

cs.LG

版本更新 · v2arXiv:2609.20797

The Strong Secretary Conjecture is True for Linear Matroids

Kristóf Bérczi, Shaddin Dughmi, Vasilis Livanos, José A. Soto, Victor Verdugo

原文摘要

We prove a $1/e$ guarantee for Matroid Secretary on linear matroids: each element of a fixed optimal basis is selected with probability at least $1/e$. This settles the strong secretary conjecture for this class of matroids. Our result holds both when the matroid is known in advance and when a linear representation is given online. In the known-matroid model, the result extends to fully modular extendable matroids. We also obtain $1/e$ guarantees for a more general model on linear matroids, both when the matroid is known and when its representation is revealed online. In XOS Matroid Secretary, agents with XOS valuations over the elements arrive in uniformly random order, and the algorithm must assign each arriving agent a bundle of elements. The bundles must be pairwise disjoint, and their union must be an independent set of the matroid. We obtain an expected total value of at least $1/e$ times the offline optimum. This model contains Group Matroid Secretary, in which the elements are adversarially partitioned into groups that arrive in uniformly random order, and the algorithm selects a subset of each arriving group. For this special case, we select each element of a fixed optimal basis with probability at least $1/e$

cs.DS

新论文 · v1arXiv:2611.08673

Optimal Contention Resolution from Samples

Shaddin Dughmi, Vasilis Livanos, Pranav Nuti

原文摘要

Contention resolution schemes convert random sets which are ex-ante feasible for some constraint into sets which are feasible ex post, and their online variants have broad applications in Bayesian and stochastic optimization, including prophet inequalities and stochastic probing. In many such applications, however, full distributional knowledge is an unattainable requirement. This motivates the study of contention resolution schemes which employ a limited number of samples from the underlying distributions. We study sample-based contention resolution for $k$-uniform matroids, for both uniformly random and adversarial arrival orders, and compare their balance guarantees to the best possible with full distributional knowledge. For a single-item constraint, we show that one sample per element suffices for an optimal $(1-1/e)$-balanced ROCRS. For adversarial arrivals, however, we prove that no single-sample OCRS can be $1/2$-balanced, even for known arrival orders, separating contention resolution from prophet inequalities in the single-sample setting. Perhaps surprisingly, we show that two samples are necessary and sufficient for the optimal $1/2$ guarantee. We also present a single-sample $0.48$-balanced scheme. For general $k$, we give a simple single-sample ROCRS that achieves an optimal balance ratio of $1-e^{-k}k^k/k!$. In adversarial order, we obtain a single-sample $(1 - O(1/\sqrt{k}))$-balanced scheme, matching the optimal asymptotic dependence on $k$. Finally, we complete the picture by characterizing the minimum number of samples needed to match the optimal balance ratio achievable with full distributional knowledge. For random arrivals, one sample suffices for $k = 1,2,3,4$, and zero samples suffice for $k \geq 5$. For an adversarial arrival order, even known in advance, and any $k \geq 2$, we show that no constant number of samples suffices to achieve optimal balance.

cs.DS · cs.GT

版本更新 · v2arXiv:2608.26516

Algorithmic Principles For Multiclass Learning Are Hard To Come By: Limits of Regularization and Proper Learning

Julian Asilis, Shaddin Dughmi, Vatsal Sharan, Alec Sun, Shang-Hua Teng, Chang Wang

原文摘要

Two of the most fundamental questions in statistical learning theory are the following: which prediction problems are learnable, and how should they be learned? For the former, elegant answers often take the form of combinatorial dimensions. The latter question, however, has proved considerably more elusive: all known general-purpose multiclass learners rely on intricate orientations of exponentially large one-inclusion structures, and familiar algorithmic principles such as proper learning and regularization remain poorly understood. Motivated by prior work, we ask whether learning reduces to proper learning---possibly over a larger hypothesis class---and whether proper or improper multiclass learning can ultimately be captured by suitable regularizers. Our primary results answer both questions negatively, resolving three open problems from prior work. First, we exhibit a learnable multiclass problem that cannot be embedded in any properly learnable class, meaning learning cannot be reduced to proper learning by enlarging the hypothesis class. Second, we demonstrate that proper learning can require training error and characterize this phenomenon precisely: every properly learnable class admits a proper learner making $o(m)$ errors on samples of size $m$, but every prescribed sublinear scale $a_m=o(m)$ is necessary for some properly learnable problem. Third, regularization is not a general learner: we exhibit a properly learnable class that cannot be learned by any Structural Risk Minimization (SRM) learner, and a learnable class that cannot be learned by any local regularizer. We complement these impossibility results with a positive theory that gives two sufficient conditions for SRM learnability and characterizes SRM representability through integrability of revealed preferences.

cs.LG · stat.ML