We propose annealed entropic allocation, an adaptive sampling policy based on an annealed, weighted soft-min formulation of static budget allocation. We replace the maximin large-deviation rate objective with a weighted log-sum-exp surrogate that blends challenger-specific pairwise scores through soft-min weights, avoiding hard switching when several challengers are nearly active. To capture tail behavior beyond the leading exponent, the surrogate incorporates saddlepoint prefactors from refined pairwise tail asymptotics. Because these corrections are subexponential, decreasing the annealing temperature with the budget preserves the same first-order target allocation. For the static problem, we prove uniform convergence to the hard minimum, concentration of soft-min weights on active challengers, and continuity of the induced target-allocation map under fixed weights. Experiments show that the proposed methods are consistently competitive: the no-saddlepoint ablation performs best in symmetric Gaussian and exponential slippage settings, while saddlepoint weighting can help in heterogeneous or asymmetric cases.

The essence of 3DGaussian Splatting (3DGS) training is to smartly allocate Gaussian primitives, expressing complex regions with more primitives and vice versa. Prior researches typically mark out under-reconstructed regions in a renderingloss-driven manner. However, such a loss-driven strategy is often dominated by low-frequency regions, which leads to insufficient modeling of high-frequency details in texture-rich regions. As a result, it yields a suboptimal spatial allocation of Gaussian primitives. This inspires us to excavate the loss-agnostic visual prior in training views to identify complex regions that need more primitives to model.

Many ranking-and-selection (R&S) problems arise in settings where information is noisy, structured, and expensive. In multi-fidelity experimentation, one can query cheap but biased proxies or expensive high-fidelity measurements; in dueling bandits, feedback arrives only through pairwise comparisons rather than direct rewards. These models are increasingly natural in engineering design, simulation optimization, preference learning for LLMs, and human-in-the-loop evaluation, where absolute scores are often unavailable or prohibitively costly and decisions must be made with a prescribed level of confidence. What makes these settings especially challenging is that the usual single-winner template is no longer sufficient. First, the answer map may be set-valued: in good-alternative or subset-selection problems, several answers can be simultaneously correct. Second, even when the true instance is answerable, a noisy estimate may temporarily fall outside the answerable set.

We consider matroid allocation problems under opportunity fairness constraints: resources need to be allocated to a set of agents under matroid constraints (which include classical problems such as bipartite matching). Agents are divided into C groups according to a sensitive attribute, and an allocation is opportunity-fair if each group receives the same share proportional to the maximum feasible allocation it could achieve in isolation. We study the Price of Fairness (PoF), i.e., the ratio between maximum size allocations and maximum size opportunity-fair allocations. We first provide a characterization of the PoF leveraging the underlying polymatroid structure of the allocation problem. Based on this characterization, we prove bounds on the PoF in various settings from fully adversarial (worst-case) to fully random. Notably, one of our main results considers an arbitrary matroid structure with agents randomly divided into groups. In this setting, we prove a PoF bound as a function of the (relative) size of the largest group. Our result implies that, as long as there is no dominant group (i.e., the largest group is not too large), opportunity fairness constraints do not induce any loss of social welfare (defined as the allocation size). Overall, our results give insights into which aspects of the problem's structure affect the trade-off between opportunity fairness and social welfare.

While diffusion language models (DLMs) enable fine-grained refinement, their practical controllability remains fragile. We identify and formally characterize a central failure mode--update-forgetting--in which uniform, context-agnostic updates induce token-level fluctuations across timesteps, erasing earlier semantic edits and disrupting the cumulative refinement process, thereby degrading fluency and coherence. As this failure originates in uniform, context-agnostic updates, effective control demands explicit token ordering. We propose Token Timestep Allocation (TTA-DIFFUSION), which realizes soft, semantic token ordering via pertoken timestep schedules: critical tokens are frozen early, while uncertain tokens receive continued refinement. This timestep-based ordering can be instantiated as either a fixed policy or an adaptive policy driven by task signals, thereby supporting a broad spectrum of refinement strategies. Because it operates purely at inference time, it applies uniformly across various DLMs and naturally extends to diverse supervision sources. Empirically, TTA-DIFFUSION improves controllability and fluency: on sentiment control, it yields >20%higher accuracy and nearly halves perplexity using <1/5 the steps; in detoxification, it lowers maximum toxicity (12.2 vs. 14.5) and perplexity (26.0 vs. 32.0). Together, these results demonstrate that softened ordering via timestep allocation is the critical lever for mitigating update-forgetting and achieving stable and controllable diffusion text generation.

We study revenue maximization for agents with additive preferences, subject to downward-closed constraints on the set of feasible allocations. In seminal work, Alaei [Ala14] introduced a powerful multi-to-single agent reduction based on an ex-ante relaxation of the multi-agent problem. This reduction employs a rounding procedure which is an online contention resolution scheme (OCRS) in disguise, a now widely-used method for rounding fractional solutions in online Bayesian and stochastic optimization problems. In this paper, we leverage our vantage point, 10 years after the work of Alaei, with a rich OCRS toolkit and modern approaches to analyzing multi-agent mechanisms; we introduce a general framework for designing non-sequential and sequential multi-agent, revenue-maximizing mechanisms, capturing a wide variety of problems Alaei's framework could not address. Our framework uses an interim relaxation, that is rounded to a feasible mechanism using what we call a two-level OCRS, which allows for some structured dependence between the activation of its input elements. For a wide family of constraints, we can construct such schemes using existing OCRSs as a black box; for other constraints, such as knapsack, we construct such schemes from scratch. We demonstrate numerous applications of our framework, including a sequential mechanism that guarantees a 2ee 1 3.16 approximation to the optimal revenue for the case of additive agents subject to matroid feasibility constraints. The simplicity of our developed two-level CRSs and OCRSs highlights the strength of our framework: even with a simple analysis, it yields state-of-the-art approximation guarantees across a wide range of settings. Finally, we show how it naturally extends to multi-parameter procurement auctions.

Pretrained Large Language Models (LLMs) achieve strong performance across a wide range of tasks, yet exhibit substantial variability in the various layers' training quality with respect to specific downstream applications, limiting their downstream performance. It is therefore critical to estimate layer-wise training quality in a manner that accounts for both model architecture and training data. However, existing approaches predominantly rely on model-centric heuristics (such as spectral statistics, outlier detection, or uniform allocation) while overlooking the influence of data. To address these limitations, we propose LAYERIF, a datadriven framework that leverages Influence Functions to quantify the training quality of individual layers in a principled and task-sensitive manner. By isolating each layer's gradients and measuring the sensitivity of the validation loss to training examples by computing layer-wise influences, we derive data-driven estimates of layer importance. Notably, our method produces task-specific layer importance estimates for the same LLM, revealing how layers specialize for different test-time evaluation tasks. We demonstrate the utility of our scores by leveraging them for two downstream applications: (a) expert allocation in LoRA-MoE architectures and (b) layer-wise sparsity distribution for LLM pruning. Experiments across multiple LLM architectures demonstrate that our model-agnostic, influence-guided allocation leads to consistent gains in task performance.

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-theart, achieving over 10% improvements on the challenging benchmarks.

Large Language Models have excelled in various domains but face efficiency challenges due to the growing Key-Value (KV) cache required for long-sequence inference. Recent efforts aim to reduce KV cache size by evicting vast non-critical cache elements during runtime while preserving generation quality. However, these methods typically allocate compression budgets uniformly across all attention heads, ignoring the unique attention patterns of each head. In this paper, we establish a theoretical loss upper bound between pre-and post-eviction attention output, explaining the optimization target of prior cache eviction methods, while guiding the optimization of adaptive budget allocation. Base on this, we propose Ada-KV, the first head-wise adaptive budget allocation strategy. It offers plug-and-play benefits, enabling seamless integration with prior cache eviction methods. Extensive evaluations on 13 datasets from Ruler and 16 datasets from LongBench, all conducted under both question-aware and question-agnostic scenarios, demonstrate substantial quality improvements over existing methods. Our code is available at https://github.com/FFY0/AdaKV.

Best Arm Identification (BAI) algorithms are deployed in data-sensitive applications, such as adaptive clinical trials or user studies. Driven by the privacy concerns of these applications, we study the problem of fixed-confidence BAI under global Differential Privacy (DP) for Bernoulli distributions. While numerous asymptotically optimal BAI algorithms exist in the non-private setting, a significant gap remains between the best lower and upper bounds in the global DP setting. This work reduces this gap to a small multiplicative constant, for any privacy budget ϵ. First, we provide a tighter lower bound on the expected sample complexity of any δ-correct and ϵ-global DP strategy.