Data-driven algorithm design is a promising, learning-based approach for beyond worst-case analysis of algorithms with tunable parameters. An important open problem is the design of computationally efficient data-driven algorithms for combinatorial algorithm families with multiple parameters.

Another recent contribution is that of Grave et al. [2019], where a method is proposed to

Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile. In particular, for the special case where the variance profile has a block structure, a series of results identified an effective spectral algorithm for detecting and estimating the signal, identified the threshold signal strength required for that algorithm to succeed, and proved information-theoretic lower bounds that, for some special signal distributions, match the above threshold. We complement these results by studying the computational optimality of this spectral algorithm. Namely, we show that, for a much broader range of signal distributions, whenever the spectral algorithm cannot detect a low-rank signal, then neither can any low-degree polynomial algorithm. This gives the first evidence for a computational hardness conjecture of Guionnet, Ko, Krzakala, and Zdeborová (2023). With similar techniques, we also prove sharp information-theoretic lower bounds for a class of signal distributions not treated by prior work. Unlike all of the above results on inhomogeneous models, our results do not assume that the variance profile has a block structure, and suggest that the same spectral algorithm might remain optimal for quite general profiles. We include a numerical study of this claim for an example of a smoothly-varying rather than piecewise-constant profile. Our proofs involve analyzing the graph sums of a matrix, which also appear in free and traffic probability, but we require new bounds on these quantities that are tighter than existing ones for non-negative matrices, which may be of independent interest.

Insect species subject to infection, predation, and anisotropic environmental conditions may exhibit preferential movement patterns. Given the innate stochasticity of exogenous factors driving these patterns over short timescales, individual insect trajectories typically obey overdamped stochastic dynamics. In practice, data-driven modeling approaches designed to learn the underlying Fokker-Planck equations from observed insect distributions serve as ideal tools for understanding and predicting such behavior. Understanding dispersal dynamics of crop and silvicultural pests can lead to a better forecasting of outbreak intensity and location, which can result in better pest management. In this work, we extend weak-form equation learning techniques, coupled with kernel density estimation, to learn effective models for lepidopteran larval population movement from highly sparse experimental data. Galerkin methods such as the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm have recently proven useful for learning governing equations in several scientific contexts. We demonstrate the utility of the method on a sparse dataset of position measurements of fall armyworms (Spodoptera frugiperda) obtained in simulated agricultural conditions with varied plant resources and infection status.

Coordinating heterogeneous robot teams from free-form natural-language instructions is hard. Language-only planners struggle with long-horizon coordination and hallucination, while purely formal methods require closed-world models. We present FLEET, a hybrid decentralized framework that turns language into optimized multi-robot schedules. An LLM front-end produces (i) a task graph with durations and precedence and (ii) a capability-aware robot--task fitness matrix; a formal back-end solves a makespan-minimization problem while the underlying robots execute their free-form subtasks with agentic closed-loop control. Across multiple free-form language-guided autonomy coordination benchmarks, FLEET improves success over state of the art generative planners on two-agent teams across heterogeneous tasks. Ablations show that mixed integer linear programming (MILP) primarily improves temporal structure, while LLM-derived fitness is decisive for capability-coupled tasks; together they deliver the highest overall performance. We demonstrate the translation to real world challenges with hardware trials using a pair of quadruped robots with disjoint capabilities.

In this paper, we propose a combinatorial framework for the semi-discrete OT, which can be viewed as an extension of the combinatorial framework for the discrete OT but requires several new ideas.

Q-linear convergence of AGN represents a substantial enhancement over the convergence of the existing methods for the overparameterized non-convex LRMS.