On the conceptual front, we identify connections between these three problems and present a framework that brings all these challenges under a common umbrella. We then present a (randomized) algorithm for reviewer assignment that can optimally solve the reviewer-assignment problem under any given constraints on the probability of assignment for any reviewer-paper pair.

We have included multiple references for knapsack solvers in the paper (including the book above).

Recent advances in 3D Gaussian splatting have significantly improved real-time novel view synthesis, yet insufficient geometric constraints during scene optimization often result in blurred reconstructions of fine-grained details, particularly in regions with high-frequency textures and sharp discontinuities. To address this, we propose a comprehensive optimization framework integrating multisample anti-aliasing (MSAA) with dual geometric constraints. Our system computes pixel colors through adaptive blending of quadruple subsamples, effectively reducing aliasing artifacts in high-frequency components. The framework introduces two constraints: (a) an adaptive weighting strategy that prioritizes under-reconstructed regions through dynamic gradient analysis, and (b) gradient differential constraints enforcing geometric regularization at object boundaries. This targeted optimization enables the model to allocate computational resources preferentially to critical regions requiring refinement while maintaining global consistency. Extensive experimental evaluations across multiple benchmarks demonstrate that our method achieves state-of-the-art performance in detail preservation, particularly in preserving high-frequency textures and sharp discontinuities, while maintaining real-time rendering efficiency. Quantitative metrics and perceptual studies confirm statistically significant improvements over baseline approaches in both structural similarity (SSIM) and perceptual quality (LPIPS).

Internet of Things (IoT) systems increasingly operate in environments where devices must respond in real time while managing fluctuating resource constraints, including energy and bandwidth. Yet, current approaches often fall short in addressing scenarios where operational constraints evolve over time. To address these limitations, we propose a novel Budgeted Multi-Armed Bandit framework tailored for IoT applications with dynamic operational limits. Our model introduces a decaying violation budget, which permits limited constraint violations early in the learning process and gradually enforces stricter compliance over time. We present the Budgeted Upper Confidence Bound (UCB) algorithm, which adaptively balances performance optimization and compliance with time-varying constraints. We provide theoretical guarantees showing that Budgeted UCB achieves sublinear regret and logarithmic constraint violations over the learning horizon. Extensive simulations in a wireless communication setting show that our approach achieves faster adaptation and better constraint satisfaction than standard online learning methods. These results highlight the framework's potential for building adaptive, resource-aware IoT systems.

Despite the popularity of these algorithms, it is well understood that the Sum-of-Squares (SOS) hierarchy based on semidefinite programming (SDP) can provide superior guarantees.

We study convex resource allocation problems with m hard constraints under (\varepsilon,\delta) -joint differential privacy (Joint-DP or JDP) in an offline setting. To approximately solve the problem, we propose a generic algorithm called Noisy Dual Mirror Descent. The algorithm applies noisy Mirror Descent to a dual problem from relaxing the hard constraints for private shadow prices, and then uses the shadow prices to coordinate allocations in the primal problem. When strong duality holds, both preceding results can be improved to \widetilde{\mathcal{O}}(\frac{\sqrt{\ln(1/\delta)}}{\varepsilon}) by better utilizing the geometric structure of the dual space, which is neglected by existing works. To complement our results under strong duality, we derive a minimax lower bound \Omega(\frac{m}{\varepsilon}) for any JDP algorithm outputting feasible allocations.

Humans can observe a single, imperfect demonstration and immediately generalize to very different problem settings. Robots, in contrast, often require hundreds of examples and still struggle to generalize beyond the training conditions. We argue that this limitation arises from the inability to recover the latent explanations that underpin intelligent behavior, and that these explanations can take the form of structured programs consisting of high-level goals, sub-task decomposition, and execution constraints. In this work, we introduce Rational Inverse Reasoning (RIR), a framework for inferring these latent programs through a hierarchical generative model of behavior. RIR frames few-shot imitation as Bayesian program induction: a vision-language model iteratively proposes structured symbolic task hypotheses, while a planner-in-the-loop inference scheme scores each by the likelihood of the observed demonstration under that hypothesis. This loop yields a posterior over concise, executable programs. We evaluate RIR on a suite of continuous manipulation tasks designed to test one-shot and few-shot generalization across variations in object pose, count, geometry, and layout. With as little as one demonstration, RIR infers the intended task structure and generalizes to novel settings, outperforming state-of-the-art vision-language model baselines.