arXiv:2602.19439v1 Announce Type: new Abstract: Problem Definition. Supply chain optimization models frequently become infeasible because of modeling errors. Diagnosis and repair require scarce OR expertise: analysts must interpret solver diagnostics, trace root causes across echelons, and fix formulations without sacrificing operational soundness. Whether AI agents can perform this task remains untested. Methodology/Results. OptiRepair splits this task into a domain-agnostic feasibility phase (iterative IIS-guided repair of any LP) and a domain-specific validation phase (five rationality checks grounded in inventory theory). We test 22 API models from 7 families on 976 multi-echelon supply chain problems and train two 8B-parameter models using self-taught reasoning with solver-verified rewards. The trained models reach 81.7% Rational Recovery Rate (RRR) -- the fraction of problems resolved to both feasibility and operational rationality -- versus 42.2% for the best API model and 21.3% on average. The gap concentrates in Phase 1 repair: API models average 27.6% recovery rate versus 97.2% for trained models. Managerial Implications. Two gaps separate current AI from reliable model repair: solver interaction (API models restore only 27.6% of infeasible formulations) and operational rationale (roughly one in four feasible repairs violate supply chain theory). Each requires a different intervention: solver interaction responds to targeted training; operational rationale requires explicit specification as solver-verifiable checks. For organizations adopting AI in operational planning, formalizing what "rational" means in their context is the higher-return investment.

arXiv:2204.07520v4 Announce Type: replace-cross Abstract: Multi-robot decision-making is the process where multiple robots coordinate actions. In this paper, we aim for efficient and effective multi-robot decision-making despite the robots' limited on-board resources and the often resource-demanding complexity of their tasks. We introduce the first algorithm enabling the robots to choose with which few other robots to coordinate and provably balance the trade-off of centralized vs. decentralized coordination. Particularly, centralization favors globally near-optimal decision-making but at the cost of increased on-board resource requirements; whereas, decentralization favors minimal resource requirements but at a global suboptimality cost. All robots can thus afford our algorithm, irrespective of their resources. We are motivated by the future of autonomy that involves multiple robots coordinating actions to complete resource-demanding tasks, such as target tracking, area coverage, and monitoring. To provide closed-form guarantees, we focus on maximization problems involving monotone and 2nd-order submodular functions. To capture the cost of decentralization, we introduce the notion of Centralization Of Information among non-Neighbors (COIN). We validate our algorithm in simulated scenarios of image covering.

arXiv:2602.13506v1 Announce Type: cross Abstract: Optimizing monotone non-convex functions is a fundamental challenge across machine learning and combinatorial optimization. We introduce and study $\gamma$-weakly $\theta$-up-concavity, a novel first-order condition that characterizes a broad class of such functions. This condition provides a powerful unifying framework, strictly generalizing both DR-submodular functions and One-Sided Smooth (OSS) functions. Our central theoretical contribution demonstrates that $\gamma$-weakly $\theta$-up-concave functions are upper-linearizable: for any feasible point, we can construct a linear surrogate whose gains provably approximate the original non-linear objective. This approximation holds up to a constant factor, namely the approximation coefficient, dependent solely on $\gamma$, $\theta$, and the geometry of the feasible set. This linearizability yields immediate and unified approximation guarantees for a wide range of problems. Specifically, we obtain unified approximation guarantees for offline optimization as well as static and dynamic regret bounds in online settings via standard reductions to linear optimization. Moreover, our framework recovers the optimal approximation coefficient for DR-submodular maximization and significantly improves existing approximation coefficients for OSS optimization, particularly over matroid constraints.

arXiv:2602.14587v1 Announce Type: cross Abstract: Many real-world control problems, ranging from finance to robotics, evolve in continuous time with non-uniform, event-driven decisions. Standard discrete-time reinforcement learning (RL), based on fixed-step Bellman updates, struggles in this setting: as time gaps shrink, the $Q$-function collapses to the value function $V$, eliminating action ranking. Existing continuous-time methods reintroduce action information via an advantage-rate function $q$. However, they enforce optimality through complicated martingale losses or orthogonality constraints, which are sensitive to the choice of test processes. These approaches entangle $V$ and $q$ into a large, complex optimization problem that is difficult to train reliably. To address these limitations, we propose a novel decoupled continuous-time actor-critic algorithm with alternating updates: $q$ is learned from diffusion generators on $V$, and $V$ is updated via a Hamiltonian-based value flow that remains informative under infinitesimal time steps, where standard max/softmax backups fail. Theoretically, we prove rigorous convergence via new probabilistic arguments, sidestepping the challenge that generator-based Hamiltonians lack Bellman-style contraction under the sup-norm. Empirically, our method outperforms prior continuous-time and leading discrete-time baselines across challenging continuous-control benchmarks and a real-world trading task, achieving 21% profit over a single quarter$-$nearly doubling the second-best method.

arXiv:2602.14682v1 Announce Type: cross Abstract: Deep generative models have achieved great success in producing high-quality samples, making them a central tool across machine learning applications. Beyond sample quality, an important yet less systematically studied question is whether trained generative models faithfully capture the diversity of the underlying data distribution. In this work, we address this question by directly comparing the diversity of samples generated by state-of-the-art models with that of test samples drawn from the target data distribution, using recently proposed reference-free entropy-based diversity scores, Vendi and RKE. Across multiple benchmark datasets, we find that test data consistently attains substantially higher Vendi and RKE diversity scores than the generated samples, suggesting a systematic downward diversity bias in modern generative models. To understand the origin of this bias, we analyze the finite-sample behavior of entropy-based diversity scores and show that their expected values increase with sample size, implying that diversity estimated from finite training sets could inherently underestimate the diversity of the true distribution. As a result, optimizing the generators to minimize divergence to empirical data distributions would induce a loss of diversity. Finally, we discuss potential diversity-aware regularization and guidance strategies based on Vendi and RKE as principled directions for mitigating this bias, and provide empirical evidence suggesting their potential to improve the results.

arXiv:2602.14872v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RL for transformers on compositional reasoning tasks. Our theory characterizes how the effectiveness of RLVR is governed by the smoothness of the difficulty spectrum. When data contains abrupt discontinuities in difficulty, learning undergoes grokking-type phase transitions, producing prolonged plateaus before progress recurs. In contrast, a smooth difficulty spectrum leads to a relay effect: persistent gradient signals on easier problems elevate the model's capabilities to the point where harder ones become tractable, resulting in steady and continuous improvement. Our theory explains how RLVR can improve performance at the edge of competence, and suggests that appropriately designed data mixtures can yield scalable gains. As a technical contribution, our analysis develops and adapts tools from Fourier analysis on finite groups to our setting. We validate the predicted mechanisms empirically via synthetic experiments.

arXiv:2602.14881v1 Announce Type: cross Abstract: We introduce a novel numerical framework for the exploration of Blaschke--Santal\'o diagrams, which are efficient tools characterizing the possible inequalities relating some given shape functionals. We introduce a parametrization of convex bodies in arbitrary dimensions using a specific invertible neural network architecture based on gauge functions, allowing an intrinsic conservation of the convexity of the sets during the shape optimization process. To achieve a uniform sampling inside the diagram, and thus a satisfying description of it, we introduce an interacting particle system that minimizes a Riesz energy functional via automatic differentiation in PyTorch. The effectiveness of the method is demonstrated on several diagrams involving both geometric and PDE-type functionals for convex bodies of $\mathbb{R}^2$ and $\mathbb{R}^3$, namely, the volume, the perimeter, the moment of inertia, the torsional rigidity, the Willmore energy, and the first two Neumann eigenvalues of the Laplacian.

arXiv:2405.14273v5 Announce Type: replace-cross Abstract: A data-driven inverse optimization problem (DDIOP) seeks to estimate an objective function (i.e., weights) that is consistent with observed optimal-solution data, and is important in many applications, including those involving mixed integer linear programs (MILPs). In the DDIOP for MILPs, the prediction loss on features (PLF), defined as the discrepancy between observed and predicted feature values, becomes discontinuous with respect to the weights, which makes it difficult to apply gradient-based optimization. To address this issue, we focus on a Lipschitz continuous and convex suboptimality loss. By exploiting its convex and piecewise-linear structure and the interiority of the minimum set, we show that a broad class of gradient-based optimization methods, including projected subgradient descent (PSGD), reaches the minimum suboptimality loss value in a finite number of iterations, thereby exactly solving the DDIOP for MILPs. Furthermore, as a corollary, we show that PSGD attains the minimum PLF in finitely many iterations. We also derive an upper bound on the number of iterations required for PSGD to reach finite convergence, and confirm the finite-step behavior through numerical experiments.

arXiv:2509.13550v2 Announce Type: replace-cross Abstract: We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. Progress is measured by the Pareto stationarity gap $\mathcal{G}(x)$, the norm of the best convex combination of objective gradients. Our analysis relies on a non-degenerate lifting that embeds hard single-objective instances into MOO instances with distinct objectives and non-singleton Pareto fronts while preserving lower bounds on $\mathcal{G}$. We establish: (i) in the $\mu$-strongly convex case, any span first-order method has worst-case linear convergence no faster than $\exp(-\Theta(T/\sqrt{\kappa}))$ after $T$ oracle calls, yielding $\Theta(\sqrt{\kappa}\log(1/\varepsilon))$ iterations and matching accelerated upper bounds; (ii) in the convex case, an $\Omega(1/T)$ min-iterate lower bound for oblivious one-step methods and a universal last-iterate lower bound $\Omega(1/T^2)$ for oblivious span methods via polynomial-degree arguments, and we further show this latter bound is loose (for general adaptive methods) by importing geometric lower bounds to obtain an $\Omega(1/T)$ min-iterate lower bound for general adaptive first-order methods; (iii) in the nonconvex case with $L$-Lipschitz gradients, an $\Omega(\sqrt{L}/(T+1))$-type lower bound on $\mathcal{G}$ (tight in order), implying $\Omega(1/\varepsilon^2)$ iterations to reach $\mathcal{G}(x)\le\varepsilon$ up to natural scaling.

arXiv:2510.04455v2 Announce Type: replace-cross Abstract: Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety of domains, including power systems and scheduling. However, to the best of our knowledge, existing data-driven inverse optimization methods primarily focus on learning objective functions under known constraints, and learning both objective functions and constraints from data remains largely unexplored. In this paper, we propose a two-stage approach for a class of inverse optimization problems in which the objective is a linear combination of given feature functions and the constraints are parameterized by unknown functions and thresholds. Our method first learns the constraints and then, conditioned on the learned constraints, estimates the objective-function weights. On the theoretical side, we provide finite-sample guarantees for solving the proposed inverse optimization problem. To this end, we develop statistical learning tools for pseudo-metric spaces under sub-Gaussian assumptions and use them to derive a learning-theoretic framework for inverse optimization with both unknown objectives and constraints. On the experimental side, we demonstrate that our method successfully solves inverse optimization problems on scheduling instances formulated as ILPs with up to 100 decision variables.