Papers

Full actuation is commonly valued for independent position and attitude tracking. This work establishes a complementary principle: when only a position trajectory is prescribed, minimizing a positively homogeneous allocation cost selects underactuated-like behavior on a fully actuated multirotor. This cost class includes norms and power laws, including standard minimum-norm pseudoinverse allocation. We use fiberwise infimization to transport the actuator-output cost to wrench space, yielding a homogeneous infimal allocation cost. Restriction to unit zero-moment forces defines a directional landscape whose minimizing directions are independent of force magnitude. We show that aligning any fixed minimizing direction with the required world-frame force minimizes instantaneous and integrated zero-moment allocation costs. The resulting body force remains in a fixed one-dimensional subspace without transverse components. We derive an exact optimality-gap decomposition quantifying the additional cost of every other attitude trajectory and characterizing the minimum-cost class. When a disturbance or prescribed-motion change modifies the required-force direction, a fully actuated platform can immediately generate the modified force using transverse authority and reorient toward the new minimum-cost family. A structurally underactuated platform must reorient before generating that force. Thus, homogeneous allocation-cost minimization explains why optimal nominal motion can be underactuated-like, while full actuation remains valuable for disturbance rejection and transient force generation.

We present GPU-accelerated Bregman Douglas–Rachford splitting algorithm (BDRS) for discrete optimal transport problem in three input formats: an explicit cost matrix, a point cloud with a ground cost between them, and a separable cost on a regular grid. For each input format, we propose hardware-aware designs of mathematically equivalent representations for the BDRS iterations to enhance numerical stability and empirical runtime. We benchmark the three proposed implementations against eight GPU baseline solvers from the literature on the same device. We demonstrate that our implementations of BDRS achieve state-of-the-art performance on their respective input formats. To the best of our knowledge, this is the first cross-solver study of GPU DOT solvers with a unified measure of optimality.

Iterative Linear Quadratic Regulator (iLQR) and Differential Dynamic Programming (DDP) are attractive trajectory-optimization methods because their backward recursions provide both nominal trajectories and local time-varying feedback laws. Hard state and input constraints, however, can drive solutions toward constraint boundaries where little corrective authority remains during closed-loop execution. This paper presents Box-iLQR, a log-barrier iLQR method for box-constrained states and controls, with emphasis on the resulting feedback policy. Barrier gradients bias nominal trajectories away from constraint boundaries, while barrier curvature enters the Riccati recursion that determines the feedback gains. We show that control-barrier curvature smoothly attenuates feedback as an actuator approaches saturation, while state-barrier curvature propagates backward through the value function to shape feedback before future state constraints are encountered. This motivates retaining a finite barrier rather than always driving the barrier parameter toward zero, thereby preserving state and actuator margin. Comparisons with CL-DDP and ALTRO are presented on pendulum, cart-pole, Acrobot, and car-parking problems. Monte Carlo experiments demonstrate improved closed-loop behavior with finite barriers, while a six-input MuJoCo fish example demonstrates data-driven Box-iLQR using dynamics Jacobians estimated from simulator rollouts. Box-iLQR achieves convergence comparable to, and in some cases better than, the baseline methods. Moreover, the feedback policy obtained with a finite barrier ensures constraint satisfaction even under execution uncertainty.

This paper refines randomized block coordinate descent by introducing a coordinate-level batch-sampling distribution characterization, yielding a fine-grained randomized batch-sampling coordinate descent framework, which applies to any block coordinate descent method under an arbitrary static stochastic sampling rule for solving large-scale linear least-squares problems. Based on this framework, we derive new linear convergence rate bounds that are invariant to the column scaling of data matrices. Theoretical analysis and numerical experiments validate that the new bounds are significantly sharper than existing results and better aligned with the practical convergence rate. Furthermore, we proposed a learning-based sampling strategy by parameterizing the batch-sampling distribution and optimizing its parameters through gradient-based training. Preliminary numerical results on computed tomography (CT) reconstruction problems demonstrate that the resulting method converges significantly faster than variants using other fixed sampling rules, and outperforms tested adaptive coordinate descent methods and full gradient descent in computational efficiency, confirming that learned sampling distributions can effectively capture problem-specific structure to accelerate convergence within the framework.

A federated objective is a weighted sum of client risks, and the weights are almost always fixed in advance. We treat them instead as the only instrument of a wisdom-of-crowds mechanism: clients are noisy views of one truth, each seeing it through an independent distortion that is unbiased across the crowd. That the optimal weights are inversely proportional to the clients' error energies is classical; we begin at the question that answer presupposes, which energies belong there and whether a crowd can recover them from itself. Excess risk on the truth is of the exact order of the aggregate bias energy, so no optimizer can repair a bad weight vector; the truth itself is identifiable only up to a linear tilt, so subtracting estimated client biases provably reproduces uniform weighting. The expected per-client second moments, however, are exactly identified from the law of the crowd's disagreement by a well-conditioned linear inversion, a step random-effects meta-analysis cannot take because a source reports once; their realized counterparts are estimable up to an incoherence floor the algorithm can measure. This yields CROWD, which reads the disagreement off the optimization trajectory at no extra cost and matches a Bayesian minimax lower bound in the same constant: per instance as the horizon grows, and unconditionally as the prior becomes diffuse. For arbitrary distortions it stays competitive with the optimal weights, at a ratio governed by a geometric incoherence the algorithm can measure. On real scans split into sites with their own miscalibrated detectors it attains the oracle excess risk; on a companion federation that pulls bias and noise apart, weighting by noise variance is worse than not weighting at all, and CROWD is not.

Actor-critic methods reuse past experience to improve sample efficiency. However, historical data are typically regarded as off-policy samples for the current policy-improvement update. This work introduces Regularized Dual Averaging Actor Critic (RDA2C), which assigns a distinct role to replay. In regularized dual averaging, the subsequent policy is determined by accumulated policy-improvement feedback, so historical advantage estimates contribute directly to the actor objective rather than solely to the most recent update. RDA2C stores state-action samples with critic-estimated advantage labels, fits a dual score model $Z_\theta$ to the aggregated dataset, and derives the current policy from the accumulated score model using the entropy mirror map. In this way, replay defines an empirical dual objective from which the policy is computed. To analyze RDA2C, we establish a finite-time value-gap decomposition, separating the regularized dual-averaging term from errors due to stale-replay supervised fitting, critic bias, finite-buffer variance, and replay coverage, and stating the assumptions under which each error is bounded. RDA2C accepts advantage labels from any critic. With GAE labels, RDA2C outperforms PPO on six of eight MuJoCo tasks and eight of twelve Atari games. RDA2C also outperforms AAPDA, the closest dual-averaging baseline, on six of eight MuJoCo tasks. With twin-$Q$ labels, RDA2C matches SAC at matched batch size and update frequency.

We introduce a tensor envelope (TEE) for composite objectives $\varphi=f+g$, built from a $q$th-order Taylor model of the smooth term $f$ regularized by a $p$th power with $p>q$. To construct it, we first establish a tensor descent lemma and characterize its behavior in the three regimes $q<p<q+1$, $p=q+1$, and $p>q+1$. Under suitable prox-boundedness and parameter conditions, the associated tensor operator (TOP) has nonempty compact values, and TEE is finite-valued and continuous, preserves global minimizers, and inherits the level-boundedness of $\varphi$. We further show that TEE is locally Lipschitz continuous and directionally differentiable, characterize its Fréchet differentiability, and prove that it is $C^1$ whenever TOP is single-valued. As such, TEE preserves the essential optimization landscape properties of $\varphi$ while enjoying a richer analytical structure, which facilitates the design and analysis of tensor-based optimization methods. Finally, TEE serves as a Lyapunov function for the exact tensor iteration: every cluster point is critical, and, for bounded trajectories with $q<p\le q+1$, an $\epsilon$-stationary point is reached within $\mathcal{O}(\epsilon^{-p/(p-1)})$ iterations. To our knowledge, both the tensor descent lemma and this complexity bound are the first of their kind obtained without assuming global Lipschitz or Hölder continuity of the $q$th-order derivative of $f$.

We introduce a sampling approach for energy- and score-based generative models that requires no gradient evaluations of the model. Replacing the drift term that would normally contain the score $\nabla_\mathbf{x} \log p_\theta(\bf{x})$ with a high-frequency dithered cosine of the model's value, $\sqrt{\alpha\omega}\,\cos(\omega t + k \log p_\theta(\bf{x}))$, produces, in the high-frequency averaging limit, Langevin Markov chain Monte Carlo for energy-based models and the reverse-time SDE of score-based diffusion. We prove that trajectories of the dithered Itô SDE converge to those of the target SDE, driven by the same Brownian motion, uniformly on compact time intervals in probability, by an averaging argument that extends bounded extremum seeking (ES) to Itô processes, with an explicit $O(\omega^{-1/2})$ mean-square rate under global bounds. The approach is not confined to smooth targets: it extends to $C^{1,1}$ energies with discontinuous curvature (without ellipticity requirement) and to Sobolev energies whose Hessians exist only off measure zero sets; for Lipschitz energies with gradient kinks the averaged limit remains well posed; the Krylov-Röckner integrability class is the boundary of provability. The approach provides a hard a priori bound on the per-step update rate and applies to explicitly time-varying targets on finite horizons. Gradient-free pixel-space sampling is not competitive with well-tuned backpropagation-based samplers at practical evaluation budgets; the regime where the approach offers an advantage is latent-space sampling when the model is a black box and the target drifts in time. We demonstrate latent-space tracking for time-varying images on CelebA-HQ ($256{\times}256$) from limited 1D projection measurements and latent-space EBM sampling on CIFAR-10.

This paper presents a nonlinear extension of Density-Driven Optimal Control (D2OC) for multi-agent spatial coverage with prescribed density distributions. Rather than assigning individual target locations, D2OC drives the collective spatial distribution of agents toward a desired density through a Wasserstein-based objective. We extend this framework to multi-step finite-horizon control for discrete-time control-affine nonlinear systems using sequential convex programming. At each control update, the nonlinear dynamics are locally linearized over the prediction horizon, yielding a strictly convex quadratic program that preserves the Wasserstein barycentric structure while directly incorporating input constraints. We further characterize the effect of constrained control deviations and nonlinear Taylor remainders on the accuracy of the local linear prediction, establishing an explicit finite-horizon error bound and a two-step specialization for receding-horizon implementation. The resulting method retains the decentralized, distribution-driven nature of D2OC while providing a computationally efficient optimization procedure for nonlinear multi-agent systems. Simulations with unicycle and quadrotor teams show coverage performance comparable to nonlinear model predictive control, while substantially reducing computation time. These results demonstrate a tractable and theoretically characterized framework for density-driven spatial coverage under nonlinear dynamics.

We study how the ranks of factors in a positive semidefinite slack factorization constrain its size. We bound the number of low-rank vertex factors in any fixed factorization, and use this to determine the asymptotic order of the minimum factorization size under any fixed bound on vertex-factor ranks: $\Theta(n\log n)$ for permutahedra $\Pi_n$ and $\Theta(\log N)$ for regular $N$-gons. In the rank-one case this gives the order of the minimum dimension of a space of real functions on the vertices in which every facet slack is a sum of squares, with no symmetry or degree restriction. For unrestricted lifts, the bound gives $\mathrm{xc}_{\mathrm{PSD}}(\Pi_n)\ge n+\log_3 n-O(1)$, and shows that a permutahedron factorization of linear size would need vertex factors of rank $\Omega(\log n)$ at all but a vanishing fraction of vertices. We also prove that every polytope of real positive semidefinite rank at most four has at most twelve vertices, and construct explicit size-four lifts for every square-symmetric octagon, so eight is attained. The upper bound combines a count of the polygon corners reached by curves of rank-one factors with incidence constraints on factor ranks. Whether eight is the maximum remains open.

Many decision trees fit the same data almost equally well, yet they can route a query point to different leaves and induce different local empirical distributions. We study decisions that meet prescribed cost, shortage or risk targets despite this predictive multiplicity. We propose the joint Rashomon and robustness optimization framework for optimal decision trees. It jointly selects an operational decision and the largest Rashomon set of trees, so that the targets hold under the local empirical distribution that every tree in this set induces at the query point. We specialize the framework to the regression setting, and we show that a tree affects the decision only through the training observations sharing the query leaf, which we call its query neighborhood. As a result, the robust problem involves only finitely many distinct constraints, which can be examined in order of increasing estimation loss. We develop a constraint generation algorithm that combines query-path pricing with dynamic programming to identify violating neighborhoods without enumerating trees. On synthetic newsvendor instances, the algorithm typically needs few neighborhoods and runs substantially faster than full neighborhood enumeration. On restaurant demand data, the robust orders increase the mean tolerated excess estimation loss by 17.6% and reduce the empirical conditional value-at-risk of the worst 10% of realized costs by 8.3% relative to the sample average approximation orders of the optimal tree, while the mean cost difference is not statistically significant. An interpretability analysis further shows how the retained neighborhoods explain the decision and its robustness limit.

In this paper, we study the optimal control of a phase field tumor growth model of Cahn–Hilliard type with possibly singular potential in which the often assumed parabolic relaxation of the chemical potential is replaced by a hyperbolic one. We investigate the asymptotic behavior of the control problem as the relaxation parameter $\,\alpha\,$ approaches zero. It is shown that the corresponding state and adjoint state variables of the relaxed problem converge in a suitable sense to their counterparts for the unrelaxed regime where $\alpha=0$. Also, weak limits of optimal controls for the relaxed problem can be shown to be optimal controls for the unrelaxed case. Moreover, every fixed optimal control $\,u^*\,$ for the unrelaxed system turns out to be the limit of a family $\{u^*_\alpha\}_{\alpha>0}$ of minimizers of suitable optimal control problems for the relaxed systems, where the original cost functional is replaced by the so-called “adapted” cost functional. It is also shown that the variational inequalities satisfied by $u^*_\alpha$, which constitute the first-order necessary optimality conditions of the relaxed problems with adapted cost functional, converge to the corresponding variational inequality fulfilled by $u^*$ for the unrelaxed problem with the original (nonadapted) cost functional.

Reservoir computing (RC) is a machine learning technique for data-driven modeling of dynamics for forecasting and control, primarily studied in computer science and physics literature with promising applications in neural network learning, physical computing, and neuroscience. Why reservoirs learn and how to choose good reservoir architectures are considered important open questions. We show that the RC problem is mathematically an extension of a classic problem in systems and control theory, the Kazantzis-Kravaris-Luenberger (KKL) observer design problem. As a consequence, many of the questions considered open for RC stand to benefit from a large body of theory in the mature KKL literature, non-exhaustively including on questions of embedding, transverse stability, local and global uniqueness guarantees, and effective data-driven solution constructions. Elaborating on this connection, we show that the surprising forecasting ability of reservoirs is in fact a direct consequence of the well-known observer internal model principle, derive an upper bound on the prediction error over a fixed forecast horizon, and provide a partial explanation for why linear readout training in RC works reasonably well. This work illustrates how classical ideas from systems and control can provide strong theoretical backing and open new questions for modern machine learning methods.

This paper studies intrinsic path following for fully actuated rigid-body attitude dynamics over a broad class of attitude paths, namely arbitrary smooth embedded closed curves on $\mathsf{SO}(3)$. We construct a tangential–transverse state decomposition on a tubular neighborhood using normal and pullback bundle geometry. The resulting second-order dynamics admit a smooth feedback transformation that independently assigns tangential and transverse covariant accelerations. A transverse proportional–derivative law renders the path-following manifold invariant and locally uniformly exponentially stable on an explicit forward-invariant neighborhood, while leaving the tangential dynamics freely assignable. This allows independent regulation of progression along the path, stabilization of a selected attitude on the path, or tracking of a time-varying motion. For a representative fiber path, the tubular coordinates are obtained in closed form up to the natural cut-locus obstruction, and simulations illustrate point stabilization and trajectory tracking.

We develop an amortized, grid-free implementation of continuous Langevin dynamics based policy-value iteration for entropy-regularized, infinite-horizon relaxed stochastic control problems. The improvement rate of the exact iteration is a discounted aggregate of relative Fisher information between the policy and the Gibbs law of its Hamiltonian. The associated score residual is the velocity with which the control's Langevin dynamics transport its law. We project this velocity onto a conditional sampler shared across states, instead of one Langevin dynamics per state, and the value dynamics onto a parametric critic, estimating both projections at sampled states to obtain coupled actor–critic flows. The score loss measures the actor's agreement with the current critic, while the policy-evaluation residual measures the critic's agreement with the actor. We also derive gradient and Hessian residuals, including a Feynman–Kac representation for the gradient equation, to control errors not detected by the projected value iteration. An exact decomposition of the HJB residual combines these errors into a policy-suboptimality bound under verification and logarithmic Sobolev assumptions. In the linear-quadratic class, both projections are exact and recover the pointwise iteration, and we provide numerical experiments on general models to demonstrate the coupled actor–critic learning in high-dimensions.

We develop a cutting-plane algorithm for computing pure Nash equilibria in finite integer games with shared constraints, where a deviation may be feasible against one opponent profile and infeasible against another. Conditional equilibrium inequalities capture this dependence through an explicit activation term. We give affine encodings of costs and activation conditions and prove that the resulting inequalities characterize the equilibrium set exactly. Embedded as lazy constraints in branch-and-cut, they yield the Generalized Zero-Regret algorithm for optimizing a linear objective over exact or approximate equilibria; a bisection procedure maintains certified bounds on the smallest achievable approximation factor. We also prove that, when the conditional polytopes have integral vertices, a concave cost is constant on the minimal face containing an equilibrium strategy, so strict concavity forces vertex strategies; for uniform integer-splittable bin packing, a cost-preserving transformation yields vertex equilibria even without strict concavity. We give formulations for bin packing, network formation, and knapsack games with shared capacities and evaluate the algorithm on 3,300 instances, computing a socially optimal equilibrium on all but 43, certifying nonexistence on 16, and certifying approximation factors within a few percent where no exact equilibrium exists.

We consider the ill-posed inverse problem of recovering the drift potential of an overdamped Langevin diffusion from discrete, possibly irregular position observations. Specializing the suboptimality gap for inverse stochastic control to drift-potential recovery, we parametrize the associated value function in a finite basis. Under a basis nondegeneracy condition, the resulting Galerkin estimator is obtained from one positive-definite linear system whose entries are smooth functionals of the empirical time marginals; no transition density is required. The gap equals one half of the squared energy distance to the true potential, yielding a best-approximation identity and energy-seminorm consistency as the basis becomes complete. At a fixed basis, we separate the sample fluctuation from the time-quadrature error, thereby avoiding the Euler–Maruyama $O(\Delta t)$ drift-discretization bias. We also analyze the finite basis as regularization, give a dimension-dependent convergence rate for a concrete basis family, and bound observation-noise bias. One- and two-dimensional experiments verify the predicted sampling-interval behavior. An application to irregular animal telemetry illustrates the method on a single long trajectory.

The Gromov-Wasserstein (GW) problem compares structured distributions without requiring a shared feature space or known correspondences, but its nonconvex objective and coupled marginal constraints make computation challenging. Bregman alternating projected gradient (BAPG) uses inexpensive alternating row and column updates, yet its fixed-penalty relaxation leaves a persistent feasibility gap. We propose Adaptive KL-BAPG (A-KL-BAPG), which combines a finite fixed-penalty burn-in with a guarded increasing-penalty phase. At each tail iteration, the method reuses BAPG's alternating updates and backtracks a delayed-power step until a Sinkhorn-inspired projective-diameter safeguard is satisfied. We prove finite termination of the backtracking at each iteration and show that the feasibility gap vanishes asymptotically. We further establish a best-iterate $O(1/\log N)$ bound for the weighted squared corrected residual and, under a support regularity condition, the existence of a stationary accumulation point for the original GW problem. This distinguishes A-KL-BAPG from fixed-penalty BAPG, whose stationarity guarantees are given for the relaxed problem. Experiments show that A-KL-BAPG achieves a favorable balance of accuracy, objective value, feasibility, and stationarity relative to BAPG variants, projection-based methods, and task-specific baselines. For synthetic and real graph alignment problems, it closely matches the accuracy and objective value of fixed-penalty KL-BAPG while reducing the marginal feasibility gap by 62-99% and the projected stationarity residual by 28-98%. Heterogeneous domain adaptation experiments show a similar pattern: A-KL-BAPG maintains comparable target accuracy and objective values while achieving better feasibility and stationarity than fixed-penalty KL-BAPG.

Multi-pass underfill dispensing couples cycle time with process reliability because the sequence determines the inter-pass flow times. This paper formulates a tri-objective multiset-permutation routing model that minimises nominal cycle time and additive duration variance while maximising reliability under hard- and soft-dwell policies; reliability combines pass, schedule-dependent flow and travel terms. Under independent durations and deterministic dwell thresholds, the variance measure equals the cycle-time variance under soft dwell and bounds it from above under hard dwell. A multiset-permutation binary-addition-tree algorithm enumerates the feasible routes without duplication and prunes prefixes by dominance. Six instances, including three BeagleBone Black benchmarks, yield reference Pareto fronts, the largest search space of $1.47 \times 10^{12}$ routes in 38 minutes on 20 CPU cores. Among simulated candidates, the nominally cost-selected routes incur maximum estimated excess costs of USD 0.0014 per board at the modelled duration variability and USD 0.0035 with it doubled. Round-robin dispatch is within 3.7 % of the reference optimum at the tested costs; NSGA-II and simplified swarm optimisation show at most 0.53 % observed cost regret while recovering about 30 % of the largest hard-dwell front. The framework quantifies sequencing trade-offs and heuristic decision regret; physical reliability prediction requires inspection-based calibration.

Modern training on a new task often starts from a previously trained model rather than from scratch, raising the question of how this initialization affects the subsequent training trajectory. Classical implicit-bias results characterize the direction selected by prolonged training, but this direction alone does not provide information regarding the intermediate behavior. We address this question through a geometric approximation of full-batch logistic gradient descent (GD) trajectories on strictly linearly separable data, with large initialization of scale $R$ motivated by prior training. From any limiting normalized initial position, we use minimum-norm projection rules to construct a unique continuous ideal path consisting of finitely many linear segments. The path has two stages: negative-margin correction followed by minimum-margin growth. We prove that, after an explicit two-stage time reparameterization, the fixed-step GD trajectory divided by $R$ converges uniformly to this path on every fixed parameter interval as $R\to\infty$. Further, our quantitative error bounds account for initialization perturbations and the transition between stages. This approximation provides asymptotic formulas for peak evaluation loss and cumulative training loss. In particular, peak evaluation loss can grow linearly in $R$ even when both endpoint losses tend to zero. The cumulative losses in the correction and margin-growth stages, normalized by $R^2$ and $R$, respectively, converge to explicit limits. Experiments on controlled geometries and fixed image features complement our theoretical results.

Mixture-of-experts (MoE) language models send each token to a few experts, so each expert is trained on a different part of the data, and this part changes during training. With a shared learning rate, Muon applies updates of roughly the same size to expert matrices of the same shape, even when an expert's update is poorly aligned with its current gradient. We here propose ExpertMuon-Compass (Compass), which multiplies the Muon step of each expert by two factors. A family factor compares the cosine between the expert's orthogonalized update and its gradient with the same cosine for the other experts in its layer. A scalar radius aggregates the alignment between corresponding rows of the update and gradient into one step-length multiplier. Compass keeps the update direction and the momentum buffer of Muon. In pretraining on FineWeb-Edu, Compass with Nesterov momentum on all matrices performs as well as or better than Muon, NorMuon, and other optimizers, with weight decay matched to NorMuon in the longer runs. Adding its factors to NorMuon gives the same or a lower loss than NorMuon. Compass is the most effective when the data seen by each expert varies during training, for example, as when the languages of a multilingual corpus arrive in separate blocks. With Compass, the expert load stays balanced, and the router assigns tokens to experts more decisively. We also prove a perturbation bound for the two factors.

Policy mirror descent (PMD) has a mature finite-time theory in discounted Markov decision processes (MDPs), but less is known in the average-reward setting, a more natural objective for many control applications. We give a finite-time, finite-sample analysis of PMD in ergodic average-reward MDPs built around a single master recursion that governs convergence for any critic, without external regularization. Its specializations yield linear rates for exact, inexact-tabular, and linear function approximation (LFA) updates, with a superlinear regime for exact PMD. We complement these convergence results with end-to-end sample complexities of order $t_{\mathrm{mix}}^3/\varepsilon^2$ in both tabular ($|S||A|$-dependent) and LFA ($d$-dependent) settings. Our LFA sample complexity sharpens the prior best $t_{\mathrm{mix}}^5$ mixing dependence to $t_{\mathrm{mix}}^3$, and matching information-theoretic lower bounds establish that the critic's $t_{\mathrm{mix}}^3/\varepsilon^2$ sample complexity is unimprovable in both settings.

We study evolutionary Nash equilibrium learning in large populations whose payoffs are generated by dynamic mechanisms. Counterclockwise dissipativity (CCW) provides a passivity-like framework for establishing learning/convergence under a broad convex cone of so-called well-behaved learning rules satisfying a natural payoff-alignment condition according to which, away from equilibria, the population's state (strategic profile) moves in a direction positively correlated with the payoffs. The cone is closed under conic combinations and encompasses a broad range of noise-free rules, including discontinuous rules such as best response, imitative rules such as the replicator rule that is not $\delta$-passive, and all noise-free $\delta$-passive rules. Existing CCW results require no knowledge of the particular rule, but establish convergence without providing a Lyapunov function or Lyapunov stability. We develop a methodology that closes this gap by constructing rule-independent Lyapunov functions from CCW storage functions of the payoff mechanism. For a nonlinear class of anticipatory mechanisms, in which agents compare current payoffs with those associated with a smoothed population state, we show that a storage can be derived as a Bregman divergence. The resulting Lyapunov function combines a potential gap with this divergence and establishes global asymptotic stability. A congestion game with a nonlinear congestion-growth toll illustrates the results.

We investigate bi-objective mixed integer programming to which Benders decomposition can be applied, a widely used technique for exploiting problem structures in real-world applications. Our study focuses on a sustainable supply chain network design problem that aims to minimise both economic and environmental objectives. To address the bi-objective nature, we employ the weighted sum method, which requires solving similar problems repeatedly with different weight values. To tackle this, we propose a straightforward acceleration technique that reuses Benders cuts generated in previous iterations of the weighted sum method. This approach enables the Benders decomposition master problem to be initialised with pre-generated cuts. Our computational experiments demonstrate that reusing these cuts significantly reduces computing time.

Neutral atom-based quantum computers have the ability to dynamically reshape the qubit register geometry between experimental runs. This capability enables different types of problems to be mapped directly onto the hardware, significantly enhancing the efficiency of solving, for instance, complex optimization and machine learning use-cases. However, this flexibility requires finding atom positions to implement target pairwise interactions, inducing a difficult nonconvex optimization for setting up the quantum machine. In this work, we introduce a new force-directed method that targets interactions to encode the input problem on the quantum computer. Numerical results show that our new method can improve embedding feasibility and solution quality by orders of magnitude, and remains reliable on the largest instances.

We consider steady-state optimization of nonlinear dynamical systems under time-varying stochastic operating conditions, where the objective is an expected-value function over the current operating-condition distribution, so that changes in the distribution induce a moving stochastic optimum. To address this problem, we propose stochastic sequential feedback optimization (S2FO), which combines projected feedback-gradient updates with sequential sensitivity estimates obtained by linearizing the plant at realized stochastic operating conditions. We analyze the closed-loop performance of S2FO through expected dynamic regret, instantaneous tracking in expectation, and almost-sure convergence under diminishing step sizes. We then apply the method to wind farm power maximization under time-varying stochastic inflow. Simulations on a benchmark layout and on a realistic offshore wind farm show that S2FO improves average power generation when persistent wake interactions are present, and that its advantage decreases as wind-direction variability increases.

We study nonnegative, non-monotone $k$-submodular maximization with $k\ge2$ labels under support constraints, and show how the certified approximation coefficient improves as the support region permits more uniform selection. For a compact convex down-closed support region $P\subseteq[0,1]^n$, the diagonal level $\zeta(P)=\max\{t\in[0,1]:t {\bf 1} \in P\}$ ranges from $\zeta=0$, which carries no geometric promise, to $\zeta=1$, which is unrestricted support. Our main structural result is a comparator-uniform linearization of the multilinear extension, built from an objective-independent action and a comparator-independent update field. For $k\ge3$, its validity reduces, independently of the number of elements, to four polynomial inequalities of degree at most three in one or two variables, only one of which depends on $k$. Explicit parameter choices give a nondecreasing certified profile $\underline{\alpha}_k(\zeta)$, in closed form on all of $[0,1]$ when $k=2$. At $\zeta=0$ we certify $0.4456\ldots$ for $k=2$ and $0.4541\ldots$ for every $k\ge3$, improving the recent $\sqrt2-1$ guarantee for one matroid or one knapsack, as well as the $1/3$-type guarantees for a fixed number of budgets; at $\zeta=1$ we certify $1/2$ for $k=2$, $(\sqrt{17}-3)/2$ for $k=3,4$, and $k/(2k-1)$ for $k\ge5$, whose excess over $1/2$ is of order $1/k$ rather than the previous $1/k^2$. Value-retaining rounding transfers these guarantees to matroid and knapsack constraints, and the same field yields $O(\sqrt T)$ approximate regret online under gradient or post-decision value feedback.

We give approximation algorithms for $\max\{F(x):x\in\K\}$, where $\K$ is a nonempty compact down-closed convex subset of the unit cube and $F$ is a nonnegative diminishing-returns (DR) submodular polynomial: every entry of its Hessian is nonpositive on the cube. Starting from quadratic or cubic coefficients, we decompose the objective exactly into nonnegative rooted atoms and affine terms. Concave upper bounds for these components give a tractable roof. We then decrease the coordinates of a roof optimizer using maps that work for all components at once, recovering a fraction of the roof value while preserving feasibility. For quadratics, we also retain the concave diagonal residual exactly. Under the stated assumptions on optimization access, these constructions give deterministic polynomial-time factors of $1/2$ for quadratics and $8/17$ for cubics, up to any prescribed additive error. The cubic result includes positive cubic coefficients and repeated variables. The factor $8/17$ also holds for two larger classes: supplied compatible rooted certificates of literal degree at most twelve, and sums of nonnegative submodular local functions of arity at most four. At arbitrary finite literal degree, a common scalar map attains the optimal single-map factor $2\sqrt3-3$. Global monotonicity and concave-cardinality structure give stronger guarantees for multilinear local-function sums, with no recovery beyond the identity map. Standard matroid rounding transfers the multilinear guarantees without loss. We also prove online preservation for directed-hypergraph cuts and, separately, a Unique-Games inapproximability bound of approximately $0.82843$ for explicit quadratic input under a cardinality upper bound.

Analog quantum computing with neutral atom computers is rapidly evolving into a promising way to perform combinatorial optimization tasks at scale. As technology matures, exploring real use cases leveraging such unique information processors becomes warranted; one example is logistics management where vehicles are assigned routes to perform a given task. Autonomous aerial vehicles (drones) are increasingly used for surveillance over a given territory. In this paper, we propose an innovative framework integrating classical machine learning forecasts and quantum annealing to find the best combination of tours for a given surveillance criterion. The risk maps produced by machine learning are used to find possible surveillance tours, while a quantum-assisted heuristic chooses the best combination, producing a full surveillance plan. By modelling our decision problem for drone paths as a Team Orienteering Problem (TOP) with additional constraints, we construct a new heuristic using quantum annealing to find good solutions. We apply this framework to wildfire prevention, where finding tours most likely to detect a starting fire has clear benefits. We study the effect of larger quantum resources on heuristic performance and compare those results to the use of classical resources.

We study decentralized minimization of sums of smooth strongly convex functions, one per agent, with communication restricted to neighbors in a graph. Existing decentralized algorithms typically emulate a centralized method; the network serves only to exchange information, from which agents approximate the global quantities that the method needs. This paper breaks with this paradigm. We introduce a graph decomposition framework that uses the network to design the method, not merely execute it. It jointly determines how agreement is imposed, which variables are optimized jointly (blocks), and which connected subgraphs host the agents solving each block. The convergence analysis quantifies the trade-offs among these choices. GATE (Graph-Tearing message passing) instantiates the framework by assigning one dual variable per edge and partitioning the edges into trees. Agents interleave edge updates with local message passing recursions that summarize optimization within each tree (block). Its surrogate variant, GATE-S, uses tractable local models and compact messages to reduce computation and communication. We establish linear convergence and show that the topology-aware design acts as a preconditioner: the rate depends jointly on topology and function geometry through the coupling between subproblems defined on the selected subgraphs, whereas consensus-based optimization methods pay the worst case of each separately, the centralized condition number times the inverse spectral gap. On tree-dominant graphs, convergence is provably faster: the rate scales with the tree diameter, linearly in the number of agents on rings and barbells against quadratically for non-accelerated consensus-optimization methods. Experiments support the predicted scaling and savings in iterations and communication.