arXiv:2609.12022v1 Announce Type: cross Abstract: We propose to learn the unknown dynamics in the proximity of a small body directly from tracking data, representing them as a feed-forward neural network embedded in the system Hamiltonian. The equations of motion form a Neural Hamiltonian Ordinary Differential Equation, whose variational equations provide exact training gradients: estimation uses position and velocity arcs at realistic noise levels, without acceleration or potential labels, and a continual learning approach warm-starts the network as new data are acquired. The known part of the Hamiltonian carries whatever is available, from the central term and spin state to the constant-density model of the imaged shape. We assess the method against a normalized spherical harmonics expansion estimated from identical arcs through the same machinery, on scenarios built on the shapes of Itokawa, 67P, Bennu and Eros. The network remains usable inside the Brillouin sphere: it plans ballistic descents at Itokawa to \SI{4.6}{m} median touchdown error from tracking alone, against 5.1--\SI{48.9}{m} for harmonics of degree 4--12, and to \SI{0.9}{m} with the imaged shape as prior, a configuration that also recovers localised density anomalies invisible to any harmonics degree. The two representations are complementary, and we discuss their combined use across the phases of a small-body mission.

arXiv:2609.12463v1 Announce Type: cross Abstract: We formulate and analyze the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a given deadline (finite time horizon). The solution for this problem can be seen as a risk-sensitive Schr\"{o}dinger bridge between Gaussian endpoints in the linear quadratic setting. Unlike the risk-neutral case, the LEQG covariance steering controller--still a linear state feedback--can no longer be written in closed form. We show that the optimal controller is parameterized by a symmetric matrix solving an algebraic equation that encodes the implicit dependence on the risk-sensitivity parameter. We explain how the structure of this optimal controller significantly generalizes the existing results for the risk-neutral case. Building on these results, for the matched noise and input channel case, we prove the existence-uniqueness of solution for the LEQG covariance steering problem in the neighborhood of the known risk-neutral optimal solution. We give an illustrative numerical example.

arXiv:2609.12486v1 Announce Type: cross Abstract: We consider an agent acting against a general non-Markovian environment. The agent maintains its agent states, but is free to choose a transition kernel across those states and optimize its state-feedback control policies. We study the bi-level agent design problem that optimizes the transition kernel and the policy it induces, given said kernel with offline data of observations and actions obtained via a behavioral policy. For general environments, we show that a soft $Q$-learning algorithm converges almost surely to the fixed point of a soft Bellman equation defined by the stationary averages that the behavioral policy and the chosen kernel induce, and we delineate what separates the resulting policy from an optimal one. In partially observed Markov decision problems, we analyze convergence properties of parametrized transition kernel design via zero-th order and Bayesian optimization techniques.

arXiv:2609.12505v1 Announce Type: cross Abstract: Vision-based reinforcement learning holds strong potential for decision-making in controlled environment agriculture (CEA). However, its development is hindered by the scarcity of labelled crop images. To address this gap, LettuceVisSim, a lettuce growth simulator that generates labelled time series of crop images, was developed and validated. The simulator contains a process-based model (PBM) for shoot dry weight dynamics, a canopy layout algorithm for deriving canopy layout representations from shoot dry weight, and a Unity rendering engine for image generation. Five findings support the simulator. First, the PBM reproduced shoot dry weight under dynamic plant-density management with $\mathrm{R}^{2}=0.84$. Second, a piecewise cubic regression mapped shoot dry weight to potential projected area with $\mathrm{R}^{2}=0.94$. Third, the canopy layout representation was validated using 12 experimental datasets each having different dynamic environmental and spacing conditions. It reproduced the ground coverage ratio dynamics observed in measured images, achieving $\mathrm{R}^{2}=0.84$ when driven by measured shoot dry weight and $\mathrm{R}^{2}=0.40$ (0.76 excluding one outlier) when driven by PBM-simulated values. Fourth, the Unity rendering engine converted canopy layout representations into RGB and segmentation images at less than 10~ms. Fifth, a demonstration showed that a lighting-control policy can be learned and applied by observing only crop images that were generated with LettuceVisSim, providing a proof of concept of vision-based reinforcement learning in CEA using LettuceVisSim.

arXiv:2609.12528v1 Announce Type: cross Abstract: The deployment of a geoengineering program to cool Earth's climate may be imminent. It is crucial that tools be developed to ensure that such a program would achieve its objectives while minimizing disruption. Here we exploit recently developed differentiable atmospheric models to demonstrate a novel geoengineering control strategy. In the differentiable primitive-equation atmospheric model JAX-GCM we impose a uniform $+4$\,K ocean warming and ask what pattern of sea-surface temperature cooling -- in five ocean-masked zonal bands of prescribed SST forcings whose amplitudes are free -- returns land near-surface air temperature closest to the model's own unwarmed climatology. This idealized set-up represents a cooling pattern that could be delivered physically either by marine cloud brightening or stratospheric aerosol injection. Gradients through chaotic dynamics decorrelate from the true sensitivity beyond the Lyapunov horizon, so we optimize greedily over segments of 8 to 14 days, following receding-horizon control. The learned strategy removes $92.3 \pm 0.4\%$ of the realized land warming across a ten-member ensemble of two-year rollouts, and a three-year run sustains it. If we use the spatial pattern of land temperature as the optimization objective, the distributions of precipitation, evaporation, and specific humidity over land are restored as well, even though they are not included in the objective function. The learned strategy from JAX-GCM replayed in the AI emulators LUCIE and NeuralGCM without re-optimization is successful, suggesting robustness. These promising results demonstrate a strategy for designing optimal climate interventions that can be applied broadly for geoengineering scenarios under consideration.

arXiv:2609.12599v1 Announce Type: cross Abstract: Multi-task learning (MTL) requires navigating unavoidable trade-offs among competing objectives. This paradigm is frequently formulated as multi-objective optimization (MOO), where the scalarization is favored to reduce an MOO problem to a single objective. We empirically find that existing merit-function-based scalarization approaches are sensitive to the relative scales of different objectives in practical MTL, where task losses commonly differ by orders of magnitude. The optimization process often favors objectives with larger scales even though the underlying Pareto optimal solutions remains invariant to rescaling (i.e., multiplying an objective by a positive constant). To address this issue, we propose Scale-Invariant Merit-function-based Scalarization (SIMS) for MTL. Specifically, SIMS adopts a transformation-induced merit function to convert the MOO problem of MTL to a single objective that renders optimization invariant to the magnitudes of losses. Theoretically, we prove that the requirement for scale invariance uniquely determines this transformation to be logarithmic. We further show that this general transformation-induced merit function preserves weak Pareto optimality and admits a smooth surrogate with controllable approximation error. Extensive experiments on representative multi-task benchmarks demonstrate that SIMS consistently outperforms existing scalarization methods and achieves state-of-the-art performance.

arXiv:2608.29507v2 Announce Type: replace-cross Abstract: Diffusion models are increasingly used not only for sampling from learned data distributions, but also for generating samples that optimize task-specific objectives. A common approach is to guide the reverse diffusion process using gradients of an external objective. However, when the data distribution is supported on a structured feasible set, such as a manifold or a constraint set, gradient guidance can move samples away from the learned data geometry. In this paper, we study a simple projected-gradient-guided diffusion update based on the observation that the Stein denoising operator can act as an approximate projection onto the data geometry. The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations. We analyze this update as an inexact projected-gradient method for constrained optimization over learned feasible geometries. Our theory covers three settings: linear manifolds, compact convex feasible sets, and compact Riemannian submanifolds. In all these settings, we prove descent and finite-time convergence guarantees. Numerical experiments support the theoretical interpretation and illustrate how the proposed update balances objective descent with preservation of the learned geometry.

arXiv:2609.09295v1 Announce Type: cross Abstract: The fixed-charge network flow problem (FCNFP) couples continuous flow allocation with discrete arc-activation decisions, making it a canonical but computationally challenging model for a variety of network design and resource allocation problems. Exact mixed-integer linear programming formulations capture the fixed-charge structure faithfully, but often become difficult to solve on large networks. We propose a scalable continuous-optimization algorithm for large-scale single-commodity FCNFP based on an iteratively reweighted least-squares (IRLS) framework. The method replaces the discontinuous fixed-charge and linear arc cost objective with a smooth nonconvex Lasry--Lions surrogate and solves a sequence of weighted quadratic flow subproblems. Each subproblem is solved by a warm-started dual semismooth Newton method whose Newton systems have weighted graph-Laplacian structure, enabling the use of modern Laplacian solvers. To further improve the discovered arc supports of the challenging underlying combinatorial problem, we also develop an algorithmic variant that incorporates objective-driven perturbation restarts and an anchor-union restricted search that jointly leverages supports discovered by IRLS and by complementary FCNFP heuristics. Computational experiments on 410 benchmark, synthetic, and large-scale instances show that our method obtains the best objective quality among the evaluated scalable FCNFP algorithms, with a mean gap of $1.316\%$ to a time-limited MILP reference and a win-or-tie rate of $90.0\%$ among the non-MILP methods. The results indicate that combining smooth continuous optimization with support-level search is an effective strategy for producing high-quality feasible solutions to large-scale FCNFP.

arXiv:2605.23937v1 Announce Type: new Abstract: Knowledge base (KB) embeddings aim at combining the capability of classical knowledge graph embeddings to generalize the information present in facts, the ABox, with conceptual knowledge represented in an ontology language, the TBox. Several authors have recently explored the idea of mapping concepts to convex regions in a vector space. This is useful to represent hierarchies, typically present in TBoxes, since more general concepts can be mapped to larger regions, containing those regions associated with more specific concepts. However, the power of convexity is rarely leveraged during the actual learning tasks. Here, we introduce BoxLitE, a KB embedding model for DL-Lite$^{\mathcal{H}}$ that allows for convex optimization. We show that for any satisfiable DL-Lite$^{\mathcal{H}}$ KB, there is a BoxLitE embedding that is a weakly faithful model. As a proof of concept, we show how to formulate the KB embedding task as a convex optimization problem and how to obtain embeddings with such desirable faithfulness properties.

arXiv:2605.25095v1 Announce Type: new Abstract: Autonomous driving stacks must pick one trajectory from a multi-modal candidate set; choosing by model confidence ignores safety, traffic-law, and comfort constraints. We present \textsc{RECTOR} (Rule-Enforced Constrained Trajectory Orchestrator), a post-generation reranking layer that scores candidates against a tiered rulebook (Safety~$\succ$~Legal~$\succ$~Road~$\succ$~Comfort) via differentiable proxies and a scene-conditioned applicability mechanism, then selects with a deterministic $\varepsilon$-lexicographic rule that preserves cross-tier priority by construction -- without retraining the predictor. On the Waymo Open Motion Dataset \texttt{validation\_interactive} split (43{,}219 augmented instances, $K{=}6$), under Protocol~B (28-rule proxy catalog, oracle applicability) rule-aware selection cuts Safety+Legal violations from 28.58\% to 20.42\% and Total from 40.32\% to 32.41\% versus confidence-only on the same candidates. A uniform-weight weighted-sum baseline matches binary compliance on this benchmark -- the empirical lift comes from rule-aware ranking, while the lexicographic guarantee is the structural differentiator no weight calibration can replicate. Under adversarial confidence corruption, confidence-only selection fails in 100\% of scenarios while both rule-aware selectors reject the injected mode in $\sim$96\%. All figures are proxy-evaluator results (not a safety certificate), open-loop, 5\,s horizon, U.S.\ rules, validation split.

arXiv:2605.25235v1 Announce Type: cross Abstract: We give an attribution method for neural combinatorial-optimisation (CO) policies that (i) decomposes a decision by constraint families via LP-relaxation duals, (ii) certifies counterfactuals through a combinatorial feasibility model (implemented as a CSP feasibility-decision model), and (iii) bounds the size of a PAC-sufficient explanation with a Bonferroni-corrected Hoeffding sufficient-subset test along a greedy ordering. Across three CO problems and three seeds, our LP-anchored $\Lambda$-attribution matches the CF-derived signal at 96.5% on CVRPTW (n_cert=344) and 77.2% on the Orienteering Problem (n_cert=281) vs 75.0% and 35.2% for proxy gradient (paired diffs +0.215 and +0.420; McNemar exact $p \le 10^{-14}$). In the rank-aligned regime of the Flexible Job-Shop Scheduling Problem, both backends agree on every CSP-certified flip (n_cert=59), confirming the no-gain prediction. Bonferroni-PAC subsets average 5.0 nodes per step ($M=70$, $\varepsilon=\delta=0.2$, $k_{\max}=25$). Reference implementation: https://github.com/sohaibafifi/neuro-co-cax

arXiv:2605.25346v1 Announce Type: cross Abstract: Neural network (NN) dynamics models and control policies achieve strong performance in robotics, but providing sound guarantees under uncertainty remains difficult, especially for closed-loop NN systems. Existing reachability tools provide formal over-approximations, yet are often non-differentiable, overly conservative, or too slow for modern learning and online planning pipelines. To address this, we present a parallelizable, differentiable reachability framework in JAX for continuous- and discrete-time systems with analytical and NN-based dynamics and controllers. Our framework combines Taylor-model flowpipe construction with CROWN-style linear bound propagation through a unified representation that preserves affine dependencies while supporting GPU-batched computation and automatic differentiation. Building on this reachability primitive, we develop (i) a certified training method that encourages reachability-friendly dynamics models and controllers, and (ii) a reachability-aware sampling-based MPC scheme with gradient-based refinement. Experiments on non-prehensile manipulation and quadrotor tasks, including hardware and higher-dimensional evaluations (up to 72D), demonstrate practical online planning while maintaining certified reachable-set over-approximations under bounded uncertainty.

arXiv:2508.12479v2 Announce Type: replace-cross Abstract: Min-max optimization arises in many domains such as game theory, adversarial machine learning, etc. For these problems, gradient-based methods are well understood and enjoy strong guarantees. However, in the absence of convexity or concavity, existing approaches study convergence to an approximate saddle point or first-order stationary points, which may be arbitrarily far from global optima. In this work, we present an algorithmic framework for computing the global minimax value in convex--non-concave and non-convex--concave min-max optimization. For convex--non-concave min-max problems, we use a reformulation that transforms the problem into a non-concave--convex max-min optimization problem with suitably defined feasible sets and objective function. This reformulation can be viewed as an extension of Sion's minimax theorem to the convex--non-concave setting. We then introduce EXOTIC -- an Exact, Optimistic, Tree-based algorithm for solving the reformulated max-min problem. EXOTIC combines an iterative convex optimization solver for the inner minimization with an optimistic hierarchical tree search for the outer maximization, inspired by StroquOOL~\cite{bartlett2019simple}. Unlike StroquOOL, which assumes stochastic zero-mean noisy evaluations, EXOTIC handles deterministic, biased, and budget-dependent evaluation errors arising from finite-time solutions of the inner convex subproblems. We establish an upper bound on its optimality gap. The same framework also applies to non-convex--concave min-max optimization. Empirically, EXOTIC outperforms gradient-based methods on popular benchmarks from the literature. Finally, we demonstrate the utility of EXOTIC by computing security strategies in multi-player games with three or more players -- a computationally challenging task that, to our knowledge, no prior method solves exactly.

arXiv:2604.03234v1 Announce Type: new Abstract: The Minimum Set Cover Problem (MSCP) is a classical NP-hard combinatorial optimization problem with numerous applications in science and engineering. Although a wide range of exact, approximate, and metaheuristic approaches have been proposed, most methods implicitly treat MSCP instances as monolithic, overlooking potential intrinsic structural properties of the universe. In this work, we investigate the concept of \emph{universe segmentability} in the MSCP and analyze how intrinsic structural decomposition (universe segmentability) can be exploited to enhance heuristic optimization. We propose an efficient preprocessing strategy based on disjoint-set union (union--find) to detect connected components induced by element co-occurrence within subsets, enabling the decomposition of the original instance into independent subproblems. Each subproblem is solved using the GRASP metaheuristic, and partial solutions are combined without compromising feasibility. Extensive experiments on standard benchmark instances and large-scale synthetic datasets show that exploiting natural universe segmentation consistently improves solution quality and scalability, particularly for large and structurally decomposable instances. These gains are supported by a succinct bit-level set representation that enables efficient set operations, making the proposed approach computationally practical at scale.

arXiv:2604.04383v1 Announce Type: new Abstract: Service system performance depends on how participants respond to design choices, but modeling these responses is hard due to the complexity of human behavior. We introduce an LLM-powered multi-agent simulation (LLM-MAS) framework for optimizing service operations. We pose the problem as stochastic optimization with decision-dependent uncertainty: design choices are embedded in prompts and shape the distribution of outcomes from interacting LLM-powered agents. By embedding key numerical information in prompts and extracting it from LLM-generated text, we model this uncertainty as a controlled Markov chain. We develop an on-trajectory learning algorithm that, on a single simulation run, simultaneously constructs zeroth-order gradient estimates and updates design parameters to optimize steady-state performance. We also incorporate variance reduction techniques. In a sustainable supply chain application, our method outperforms benchmarks, including blackbox optimization and using LLMs as numerical solvers or as role-playing system designers. A case study on optimal contest design with real behavioral data shows that LLM-MAS is both as a cost-effective evaluator of known designs and an exploratory tool that can uncover strong designs overlooked by traditional approaches.

arXiv:2604.03278v1 Announce Type: cross Abstract: As power systems advance toward net-zero targets, behind-the-meter renewables are driving rapid growth in distributed energy resources (DERs). Virtual power plants (VPPs) increasingly coordinate these resources to support power distribution network (PDN) operation, with EV charging stations (EVCSs) emerging as a key asset due to their strong impact on local voltages. However, in practice, VPPs must make operational decisions with only partial visibility of PDN states, relying on limited, aggregated information shared by the distribution system operator. This work proposes a safety-enhanced VPP framework for coordinating multiple EVCSs under such realistic information constraints to ensure voltage security while maintaining economic operation. We develop Transformer-assisted Lagrangian Multi-Agent Proximal Policy Optimization (TL-MAPPO), in which EVCS agents learn decentralized charging policies via centralized training with Lagrangian regularization to enforce voltage and demand-satisfaction constraints. A transformer-based embedding layer deployed on each EVCS agent captures temporal correlations among prices, loads, and charging demand to improve decision quality. Experiments on a realistic 33-bus PDN show that the proposed framework reduces voltage violations by approximately 45% and operational costs by approximately 10% compared to representative multi-agent DRL baselines, highlighting its potential for practical VPP deployment.

arXiv:2604.03605v1 Announce Type: cross Abstract: We study online task allocation for multi-robot, multi-queue systems with asymmetric stochastic arrivals and switching delays. We formulate the problem in discrete time: each location can host at most one robot per slot, servicing a task consumes one slot, switching between locations incurs a one-slot travel delay, and arrivals at locations are independent Bernoulli processes with heterogeneous rates. Building on our previous structural result that optimal policies are of exhaustive type, we formulate a discounted-cost Markov decision process and develop an exhaustive-assignment actor-critic policy architecture that enforces exhaustive service by construction and learns only the next-queue allocation for idle robots. Unlike the exhaustive-serve-longest (ESL) queue rule, whose optimality is known only under symmetry, the proposed policy adapts to asymmetry in arrival rates. Across different server-location ratios, loads, and asymmetric arrival profiles, the proposed policy consistently achieves lower discounted holding cost and smaller mean queue length than the ESL baseline, while remaining near-optimal on instances where an optimal benchmark is available. These results show that structure-aware actor-critic methods provide an effective approach for real-time multi-robot scheduling.

arXiv:2604.03782v1 Announce Type: cross Abstract: We analyze the last-iterate convergence of the Anchored Gradient Descent Ascent algorithm for smooth convex-concave min-max problems. While previous work established a last-iterate rate of $\mathcal{O}(1/t^{2-2p})$ for the squared gradient norm, where $p \in (1/2, 1)$, it remained an open problem whether the improved exact $\mathcal{O}(1/t)$ rate is achievable. In this work, we resolve this question in the affirmative. This result was discovered autonomously by an AI system capable of writing formal proofs in Lean. The Lean proof can be accessed at https://github.com/google-deepmind/formal-conjectures/pull/3675/commits/a13226b49fd3b897f4c409194f3bcbeb96a08515

arXiv:2604.04891v1 Announce Type: cross Abstract: Gradient normalization is central in deep-learning optimization because it stabilizes training and reduces sensitivity to scale. For deep architectures, parameters are naturally grouped into matrices or blocks, so spectral normalizations are often more faithful than coordinatewise Euclidean ones; Muon is the main motivating example of this paper. More broadly, we study a family of spectral normalization rules, ranging from ordinary gradient descent to Muon and intermediate Schatten-type schemes, in a mean-field regime where parameters are modeled by probability measures. We introduce a family of Spectral Wasserstein distances indexed by a norm gamma on positive semidefinite matrices. The trace norm recovers the classical quadratic Wasserstein distance, the operator norm recovers the Muon geometry, and intermediate Schatten norms interpolate between them. We develop the static Kantorovich formulation, prove comparison bounds with W2, derive a max-min representation, and obtain a conditional Brenier theorem. For Gaussian marginals, the problem reduces to a constrained optimization on covariance matrices, extending the Bures formula and yielding a closed form for commuting covariances in the Schatten family. For monotone norms, including all Schatten cases, we prove the equivalence between the static and dynamic Benamou-Brenier formulations, deduce that the resulting transport cost is a genuine metric equivalent to W2 in fixed dimension, and show that the induced Gaussian covariance cost is also a metric. We then interpret the associated normalized continuity equation as a Spectral Wasserstein gradient flow, identify its exact finite-particle counterpart as a normalized matrix flow, obtain first geodesic-convexity results, and show how positively homogeneous mean-field models induce a spectral unbalanced transport on the sphere.

arXiv:2604.01279v1 Announce Type: cross Abstract: We introduce Sven (Singular Value dEsceNt), a new optimization algorithm for neural networks that exploits the natural decomposition of loss functions into a sum over individual data points, rather than reducing the full loss to a single scalar before computing a parameter update. Sven treats each data point's residual as a separate condition to be satisfied simultaneously, using the Moore-Penrose pseudoinverse of the loss Jacobian to find the minimum-norm parameter update that best satisfies all conditions at once. In practice, this pseudoinverse is approximated via a truncated singular value decomposition, retaining only the $k$ most significant directions and incurring a computational overhead of only a factor of $k$ relative to stochastic gradient descent. This is in comparison to traditional natural gradient methods, which scale as the square of the number of parameters. We show that Sven can be understood as a natural gradient method generalized to the over-parametrized regime, recovering natural gradient descent in the under-parametrized limit. On regression tasks, Sven significantly outperforms standard first-order methods including Adam, converging faster and to a lower final loss, while remaining competitive with LBFGS at a fraction of the wall-time cost. We discuss the primary challenge to scaling, namely memory overhead, and propose mitigation strategies. Beyond standard machine learning benchmarks, we anticipate that Sven will find natural application in scientific computing settings where custom loss functions decompose into several conditions.