Papers

Imagine that you are in front of a cockpit with several on-off buttons. If you were to thoroughly test it, you would need to try a prohibitive number of configurations. But since most bugs in practice can be isolated to interactions among few components, having tests that cover every possible pairwise configuration is a good start. However, this is a problem that goes from easy to NP-hard as soon as some pairwise configurations are forbidden. In this paper, we revisit unconstrained combinatorial testing with pairwise coverage on binary parameters and contrast it with the constrained case, showing and conjecturing properties that either are upheld or change from one to the other. In particular, we discuss the extent to which it remains a good idea – and sometimes indeed optimal – to have every button almost as many times on as off to minimize testing. We propose the first exact algorithm based on integer programming and a faster heuristic that often produces optimal solutions, both outperforming or competitive with their baselines.

This paper studies transformations that increase efficiency in solving equilibrium systems without information loss. Our approach exploits order-theoretic structure commonly found in economic problems to obtain conditions under which high-dimensional systems can be transformed into low-dimensional systems while preserving exact relationships between their solutions. The transformations can also be used for purposes other than dimensionality reduction, such as simplifying analysis and facilitating stochastic approximation routines. The theoretical ideas are illustrated using applications from economics and finance. In a real option problem, we demonstrate speed gains of up to 70,000 times.

We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of the nominal mixture-support parameters. To address this limitation, we describe the ambiguity set of distributions by developing a novel formulation of a Wasserstein-2 metric that uses the Bures-Wasserstein (BW) metric over probability measures with finite second moments. Unlike FDR, which generally sets finitely many empirical support points a priori, the proposed ambiguity set allows the worst-case distribution to endogenously determine both how many mixture components receive mass and where their means and covariances lie within a continuous support. For the resulting ambiguity set, under mild regularity conditions, we prove strong duality for the inner worst-case chance-constraint problem and derive its semi-infinite reformulation. We then develop an adaptive cutting-surface algorithm, which endogenously determines the locations of mixture components receiving mass, and the mean and covariances of the Gaussian distributions at these locations. The algorithm attains any prescribed optimality gap in finitely many iterations, while a block-alternating local search identifies new components. A case study using the electric-vehicle charging-station energy-allocation problem demonstrates the framework's practical value in achieving any reliability targets. CDR also induces structural changes in energy allocations, unlike FDR, whose allocations remain close to the nominal solution.

We present a trajectory planning method that balances information collection and control effort to improve cislunar spacecraft-to-spacecraft absolute tracking. Expanding use of cislunar space requires alternative navigation and tracking procedures that minimize reliance on ground-based support. Among efforts to address this need, spacecraft-to-spacecraft tracking exploits nonlinear dynamical tracers encoded in a series of relative measurements to infer absolute states of both an observer and a target. The geometry between spacecraft operating under this mode can significantly influence tracking performance. This work considers this geometrical impact by designing observer trajectories that jointly balance control effort and an information-theoretic quantification of the expected spacecraft-to-spacecraft tracking performance. Our methods are designed for multiple low-thrust observation platforms of various sensing modalities and can incorporate multiple space object targets in planning. By leveraging information gain in the optimal control problem, we report almost an order of magnitude improvement in the expected navigation and tracking errors for an optical observer operating in a Distant Retrograde Orbit (DRO). This work demonstrates the feasibility and value of information-optimal low-thrust spacecraft trajectory design for current and upcoming cislunar missions.

This paper presents a safety-critical distributed nonlinear model predictive control (DNMPC) framework for cooperative payload transportation by teams of quadrupedal robots. The proposed approach models the robotic team and the shared payload as a dynamically coupled networked system with rigid holonomic coupling constraints arising from cooperative transportation. To enable distributed real-time optimization, the centralized finite-horizon optimal control problem is decomposed into parallel local NMPC subproblems coordinated through the alternating direction method of multipliers (ADMM). The resulting distributed framework enforces consensus over both payload-state and interaction-wrench trajectories while explicitly incorporating acceleration-level holonomic coupling constraints within the distributed predictive control formulation. Safety-critical obstacle avoidance constraints for both the robotic agents and payload are enforced using higher-order control barrier functions (HOCBFs). The framework is validated through numerical simulations with teams of two, three, and four quadrupedal robots transporting shared payloads in cluttered environments. Real-time experiments on two- and three-robot teams demonstrate safe and robust transportation under payload uncertainty and external disturbances. Compared with centralized NMPC, the proposed framework achieves up to 23% reduction in average NLP solve time while maintaining comparable closed-loop performance. Ablation studies further demonstrate robustness to communication delays and show that explicit payload-state consensus and holonomic constraints substantially improve payload tracking and distributed coordination over existing wrench-only consensus formulations.

This paper addresses the multi-period log-truck routing and scheduling problem ($\mathcal{LTRSP}$), a key operational activity in the forestry industry, where transportation accounts for more than one-third of total operational costs. The Canadian forestry sector faces significant logistical difficulties driven by vast geographic distances, seasonal variability, volatile markets, and environmental considerations. Our research tackles a long-standing open question in the forestry operations literature, namely the absence of an exact and scalable formulation of the forestry vehicle routing problem integrating the full range of operational constraints \cite{ronnqvist2015operations}: How can we model and solve an exact formulation of the forestry VRP problem? In response, we analyze business rules specific to the forestry sector to construct a routing network reflecting real operational practices, and then propose a comprehensive improved mixed-integer linear programming (MILP) formulation incorporating all known forestry operational constraints, with a detailed justification of key modeling choices such as time discretization, along with a decomposition-based solution methodology tailored for large-scale, multi-period industrial instances. To address the inherent combinatorial complexity, we combine state-of-the-art solvers with a metaheuristic decomposition strategy based on Relax&Fix and Fix&Optimize. Computational experiments on historical data from a Canadian forest company demonstrate near-optimal results within practical computation times, with significant financial gains and reduced greenhouse gas emissions.

We consider defining risk probability in stochastic control problems under distribution ambiguity. Current approaches for chance-constrained control typically assume that the true state distribution is known and Gaussian distributed. These assumptions are not amenable to many real-world engineering applications where system dynamics are nonlinear and only approximately modeled. In this work, we define a distribution ambiguity set and, with a variational expression for exponential integrals, bound the expected risk value under an unknown distribution that resides within a relative entropy distance of a nominal Gaussian reference distribution. Our bound recovers the reference risk value in the zero-divergence limit. A method is presented to determine the relative entropy distance defining the ambiguity set that is a function of the reference covariance evolution and second-order dynamical truncation errors. The resulting contributions provide a framework for handling distributional ambiguity in nonlinear covariance steering problems. A stochastic spacecraft guidance example is presented to demonstrate our contributions.

The tuned mass damper inerter (TMDI) is a passive vibration absorber that suppresses structural vibrations by leveraging the inertance property of inerter devices. Previous studies have demonstrated TMDI effectiveness in wind turbines, but relied on simplified structural models. To date, no study has implemented multi-directional TMDIs within aero-hydro-servo-elastic tools such as OpenFAST to enable independent vibration control across multiple turbine components, including the tower, blades, and substructure. This paper addresses this gap by implementing the TMDI in OpenFAST. The governing equations of motion are derived and implemented within the Structural Control (StC) Module, supporting arbitrary TMDI connectivity and independent multi-directional configurations across turbine components. Verification against independent numerical models confirms the implementation's accuracy across all supported configurations. An application study examines the IEA 15MW reference wind turbine equipped with a tower-top TMDI under combined wind-wave loading. Optimal tuning is performed using a simplified two-degree-of-freedom model, with modal properties extracted from an OpenSeesPy finite element model of the IEA 15MW. Results show that TMDIs with secondary mass up to 100 times smaller than a conventional TMD achieve matching or superior vibration suppression in the fore-aft and side-side directions, in terms of peak and standard deviation of tower-top displacement and acceleration. Notably, TMDI stroke is markedly reduced compared to the TMD, better suiting the spatially constrained wind turbine environment. These results support the practical merit of lightweight TMDIs for wind turbine vibration control, with the OpenFAST implementation enabling performance-driven design under realistic loading conditions.

We study optimal scheduling for remote state estimation over a network with two heterogeneous communication channels: a fast but unreliable channel and a slow but reliable channel. To capture temporal correlations in packet losses, we model the unreliable channel as a Gilbert-Elliott (GE) channel. The remote estimation setup consists of a source, a sensor, and a remote estimator. The source evolves as a discrete-time autoregressive (AR) process, and the sensor decides at each time whether to use the fast unreliable channel or the slow reliable channel. We formulate the scheduling problem faced by the sensor as a Markov decision process (MDP) with a continuous state-space and consider minimizing the infinite horizon average cost criterion, where the cost consists of the squared estimation error and the transmission energy consumed. We establish the existence of an optimal stationary policy. We then characterize the structure of an optimal policy, and show that it has a threshold structure with respect to the estimation error. An optimal policy chooses from amongst the two channels based on whether the error exceeds certain thresholds, where the threshold value depends upon the GE channel state. When the system parameters are unknown, we propose an actor-critic (AC) learning algorithm that exploits the threshold structure of an optimal policy. Numerical results demonstrate that the proposed AC algorithm learns the policy structure effectively and achieves performance close to that of the optimal policy computed using the relative value iteration (RVI).

We consider a novel robust utility maximisation problem under bounded cumulative transition rate uncertainty within the class of non-Markovian marked point processes on a finite state-space. Utility is maximised over the class of admissible controls, while Nature chooses a worst-case biometric scenario from the class of admissible, path-dependent cumulative transition rates restricted by path-dependent upper and lower bounds. We prove a martingale optimality principle and a novel existence and uniqueness result for a non-standard worst-case backwards stochastic differential equation, which allows us to establish existence and uniqueness of worst-case and best-case prospective reserves of life and health insurance contracts with reserve-dependent payments. Finally, we find an explicit solution of a novel robust consumption-insurance problem with power utility preferences.

A truckload carrier must accept or reject each load tender within seconds. The decision depends on fleet state, hours-of-service (HOS) clocks, and appointment windows. We model this as a weakly coupled dynamic program in which the resources relocate and carry clocks: serving a request moves the truck to a new market and depletes its clocks, and whether a truck can serve a request depends on its state. Occupancy-based reusable-resource models do not cover this setting. We build a real-time dual-price policy from the same Lagrangian relaxation that gives the problem's upper bound. Policy and bound come from one object, so every run reports a certified optimality gap. We prove three things. First, the certificate is valid for any duals, any discretization, and any surrogate quality. Second, the policy's same-time spatial-gradient rule is exactly fluid complementary slackness, and the policy is asymptotically optimal in the subcritical fluid regime; the fitted prices are also portable across sample paths, by linear-programming basis stability. Third, certificates have limits: per-resource Lagrangian slack can stay bounded away from zero at every fleet size. We exhibit a three-truck kernel with an exact rational certificate and a replication lemma. On a public closed-loop benchmark with thirty paired seeds, the policy – which needs no rollout labels, only one offline dual solve – beats a rollout-trained surrogate on two of three scenarios (tight: +2.0 pp, 95% CI [+0.5, +3.6], Wilcoxon p = 0.023; mild: +3.5 pp, CI [+2.4, +4.5]) and ties the third. It decides in 0.04-0.09 ms, three orders of magnitude faster than the Monte Carlo rollout teacher. Its certificates are stable across ten bounded instances per scenario, at 57-64% of optimal, within 3-6 points of what the 1000x-slower teacher certifies.

We construct a compact metric space with an atomless probability measure and a bounded Lipschitz cost for which the entropic optimal-transport minimisers have no zero-temperature weak limit. More precisely, $P_\varepsilon$ does not converge as $\varepsilon\downarrow0$. In the example, every unregularised minimiser is singular with respect to $\mu\otimes\mu$, so that the entropy on the optimal face is identically $+\infty$. We describe the cluster set by \[ \operatorname{Clust}(P_\varepsilon)=\{P_w:w\in\mathcal W\}, \] where $P_w$ is the mixture of the two zero-cost graph couplings with weight $w$, and where $\mathcal W\subset[0,1]$ is a non-degenerate compact interval. We then compute two explicit points $w^-<w^+$ in this interval. This shows that compactness, atomlessness, and Lipschitz regularity of the cost do not imply zero-temperature convergence. We also present a compactness theorem for the general problem. If $C\in L^1(\mu\otimes\nu)$ is continuous and bounded from below on Polish spaces, then the zero-temperature cluster set is a nonempty weakly compact connected subset of the optimal face. In the proof, we apply the cluster-point theorem of Bernton, Ghosal, and Nutz and the continuity of $\varepsilon\mapsto\pi_\varepsilon$. Finally, we give local and exterior first-order criteria for full convergence and cluster membership. We show that nonconvergence is possible, but only through a connected continuum of optimal plans.

We introduce the vehicle routing problem with stochastic demands and outsourcing options (VRP-SDO), in which a logistics service provider partitions customer requests into customers outsourced to a common carrier and customers committed to its fixed fleet. The latter induces a vehicle routing problem with stochastic demands (VRP-SD), solved dynamically. Demands are revealed upon visit; residual demand may be served by other vehicles or after restocking at the depot. Work beyond the regular shift incurs overtime costs, and the unit outsourcing cost decreases with the expected outsourced demand. The objective is to minimize expected travel, overtime, and outsourcing costs. We propose an iterative two-level methodology whose first level partitions customers into committed and outsourced subsets, while the second level estimates the expected VRP-SD routing cost. To avoid solving this problem from scratch at every iteration, we learn an offline routing policy that estimates costs almost instantly for any committed subset. An iterated local search establishes the first-level partitions. We formulate the second level as a Markov decision process and solve it with a deep Q-network whose state is represented by a graph attention network aggregating customer and vehicle information by relevance to the acting vehicle. Trained offline on instances with variable customer cardinality and locations, the policy applies to any daily customer realization; online fine-tuning improves the cost approximation. Experiments show that our policy reduces routing costs by 19.6% relative to a state-of-the-art method and by at least 29.6% over classical heuristics. Our overall algorithm saves 13.7% on average over the version without the attention-based representation and generates high-quality decisions within minutes, whereas benchmarks without an offline-trained estimator require over an hour.

We introduce Treasure Search Optimization (TSO), an interacting particle method for global optimization. Most swarm methods balance exploration and exploitation within a single population, and typically switch between the two by degenerating the noise, annealing a temperature, or tuning a parameter. TSO instead splits these tasks across two kinds of agents. A swarm of explorers stays in exploration mode and a single treasure hunter performs exploitation. The hunter drifts toward an objective-weighted average of the explorers and may teleport to it when the move lowers the objective. The swarm then re-centers around the hunter, creating a feedback loop between search and capture. We model the dynamics as coupled jump-diffusion stochastic differential equations (SDEs). The hunter's jumps are shared by all explorers and act as a common noise. The mean-field limit is therefore a conditional McKean-Vlasov jump-diffusion SDE, whose well-posedness we prove. We also characterize the steady state and prove, via Laplace approximation techniques, that the hunter settles near the global minimum with error of order $1/\alpha$, where $\alpha$ is the weight parameter. Linking the consensus drift to a smoothed free energy, we explain why the swarm ignores spurious local traps and demonstrate how to quantify uncertainty in inverse problems using post-processing Kalman steps after TSO iterations. Numerical experiments on ODE-constrained problems and a low dimensional Bayesian inverse problem demonstrate the effectiveness of the TSO method.

We introduce ideal Gårding polynomials, a convexity-enhanced subclass of Gårding polynomials whose Gårding components are recursively convex under partial differentiation. This class strictly contains real stable polynomials and, after translation and homogenization, lies in the Lorentzian class. Our main result is that ideal Gårding polynomials still admit a robust structure theory despite this additional convexity: they are preserved under polarization, satisfy natural closure properties, and support a linear preserver theory. A key contribution of this paper is a universal model for univariate Gårding polynomials, described by monotone root sequences and equivalently by volume polynomials of Pitman–Stanley polytopes. We establish quotient concavity, and Newton–Maclaurin type inequalities, which leads to the polarization theorem, and suggests further connections with convex geometry and Lorentzian polynomials.

In this paper, we prove that forward ideal sub-Finslerian manifolds support interpolation inequalities for optimal transport, extending the results of Barilari and Rizzi, arXiv:1705.05380, from the sub-Riemannian to the sub-Finslerian setting. A key role is played by the introduction of sub-Finslerian Jacobi fields and the establishment of optimal transport theory on sub-Finslerian manifolds. By combining this transport framework with sub-Finslerian Jacobian estimates, we characterize the generalized distortion coefficients. As an application, we deduce several fundamental geometric inequalities, including the Brunn-Minkowski and Borell-Brascamp-Lieb inequalities. Finally, for the case of the Randers sub-Finslerian Heisenberg group, whose metric is defined by a sub-Riemannian metric perturbed by a drift term, we explicitly show that it satisfies the measure contraction property.

Variational Quantum Algorithms (VQAs) are a leading paradigm for near-term quantum computing, yet their training suffers from sensitivity to circuit depth, initialization, and landscape pathologies such as barren plateaus. We study progressive depth training (PDT) – a layerwise curriculum that trains a shallow circuit before appending new layers – and identify a fundamental obstacle: fixed entangling gates (CNOTs) in hardware-efficient ansätze cause initialization shock, an energy spike when new layers are added. We propose identity-paired progressive depth training (IP-PDT), which appends forward/inverse block pairs – each consisting of a standard rotation$+$CNOT block followed by its reverse – that compose to the identity at initialization. Because the adjacent CNOT rings cancel, the effective circuit retains only a single entangling layer surrounded by overparameterized local rotations. We prove a simple Reachable Set Saturation Theorem: under this construction the variational manifold expands exactly once (when post-entangler rotations are first introduced) and then saturates; all subsequent depth increases provide pure overparameterization of single-qubit unitaries. Despite this saturation, progressive addition of rotation parameters can continue to improve optimization outcomes – a phenomenon we term trainability beyond expressibility. We formalize IP-PDT as a continuation method on nested manifolds, prove monotone energy guarantees under an acceptance rule, and connect energy error to ground-state fidelity through spectral-gap inequalities. A detailed resource analysis shows that IP-PDT achieves lower total gate cost than both baselines by eliminating most CNOT gates.

We propose a couple of novel tools for benchmarking optimization algorithms which possibly converge to different solutions on a test set: the quality profiles and the test set profiles. Their aim is to assess and compare algorithms in terms of quality (i.e. value of the objective function) of the obtained solutions, as well as to assess the consistency of the test set. A key distinguishing feature of the quality profiles we propose is its comparative deterministic procedure that emphasizes the accuracy of the solution, rather than the computational burden of solvers. In this regard, several test set–dependent approaches for both comparing and ranking algorithms have already been proposed in the literature, representing widely used benchmarking procedures. We believe that the joint use of such procedures, along with the novel quality profiles detailed here, should enhance the benchmarking process, in all those cases where the comparison encompasses exact methods as well as heuristics. Moreover, the literature on numerical optimization seems to have paid less attention, in the last decade, to determining how appropriate a test set used for benchmarking the selected solvers may be. This motivates the introduction of test set profiles, which assess the appropriateness of a test set and represent the flip side of evaluating the robustness of the solvers on that test set. This paper also includes extensive numerical experiments, showing the usefulness of quality profiles in both smooth and nonsmooth (derivative–free) optimization, along with the reference to a MATLAB code for plotting quality profiles and test set profiles.

We study tight conic relaxations for a quadratically constrained quadratic programming (QCQP) formulation of rank-one doubly nonnegative (DNN) matrix completion. Motivated by sparse QCQPs whose lifted matrix variables include elements not directly specified by the objective or constraints, we interpret tightness as a rank-one completion property for the unspecified elements. For sparsity patterns whose blocks consist of cycles and edges, we prove that the dual formulations associated with the DNN and completely positive (CP) relaxations are equivalent. For cycle-type sparsity patterns, we derive explicit sufficient conditions under which the semidefinite programming (SDP) and DNN relaxations are tight. These sufficient conditions are stated explicitly in terms of local ratio bounds and cumulative-difference conditions on a rank-one optimal solution. We also show that adding suitable edges to the sparsity pattern relaxes the ratio conditions required for tightness. The results provide tractable certificates for when conic relaxations recover a rank-one optimal solution of the underlying QCQP.

We introduce a modified Benamou–Brenier (MBB) formulation of optimal transport that incorporates Euclidean invariance at the dynamical level. We establish existence of minimizers for the resulting variational problem and prove its equivalence to a static formulation defining the Procrustes–Wasserstein distance. In the Gaussian setting, we show that this distance admits a closed-form expression, reducing to the Euclidean distance between the vectors of square roots of the ordered eigenvalues of the covariance matrices. On the computational side, we formulate a primal–dual scheme for the discretized problem. We prove a local conditional subsequential convergence result through an abstract analysis of a class of parameter-dependent saddle-point problems and illustrate the method's performance numerically.

We study continuous planar facility location in which a demand point's captured value decays with distance, with the per-point decay scale varying across points. This heterogeneity is ubiquitous yet underexploited, and one nearest-facility objective unifies decay, clustering, and median goals, containing k-means, the Weber/p-median problem, and maximum covering as special cases. We make four contributions. (i) A tractability classification: the discrete objective is always monotone submodular, so the (1-1/e) greedy guarantee holds regardless of decay shape or heterogeneity, and the continuous cooperative objective is concave if and only if the decay is concave in distance; the clip max(0,d) in common coverage specifications is what destroys concavity, and the classification is tight. (ii) An exact discrete method: the candidate-discretized maximum-cover MIP has an empirically tight LP relaxation (~0% gap) and is solved by branch-and-bound in seconds for n <= 500. (iii) A force-as-gradient / large-neighborhood-search heuristic, within 0.5% of the discrete optimum, that outperforms the (1-1/e) greedy, Cooper-style alternating location-allocation, particle swarm optimization, and weighted k-means (30/30 per-instance wins at K=30, p<10^-9) and is competitive with bespoke solvers on k-means, Weber/p-median, and shape-demand instances. (iv) A real-world study: on 592,667 urban-delivery orders, ignoring the calibrated decay variation loses up to 9.7% of captured demand and relocates facilities by up to 37% of the map; a retail dataset calibrates the decay as exponential with scale R ~ 1.4 km.

We introduce the Deep Second-Order Stochastic Residual Method (D2SRM) for high-dimensional, Hessian-dependent fully nonlinear parabolic PDEs. A single scalar space–time network generates derivative-consistent approximations of the solution, gradient, and Hessian, which are trained jointly through second-order Brownian one-step residuals and terminal value and gradient penalties. For globally Lipschitz equations with identity diffusion and sufficiently weak Hessian coupling, we establish well-posedness in a Brownian occupation space and develop a population-level convergence theory. Under additional regularity, an a posteriori estimate bounds the squared full-jet occupation error of any admissible candidate by the time step and its population objective. For approximate population minimizers, the error bound separates time discretization, neural approximation, and population suboptimality; when the latter two terms are $O(h)$, the full-jet occupation norm is $O(h^{1/2})$. Experiments on a 100-dimensional manufactured benchmark compare terminal treatments, probe Hessian couplings inside and outside the proved small-gain range, and show decreasing errors as the time step decreases. The code is available at https://github.com/ZZHPKU/D2SRM.

Non-uniform scaling control enables a multi-agent formation to adjust its shape by compressing or stretching independently along different coordinate axes through inter-agent interactions, offering high flexibility in complex environments. The fundamental idea is encoding the desired formation shape as the kernel of a matrix-valued Laplacian. In open multi-agent systems, however, changes in number of agents, number of edges, and leader selection dynamically alter this Laplacian, destroying the required spectral properties: positive semidefiniteness, correct kernel, and positive definiteness of the follower block (we summarize these properties as the formation spectrum). In this paper, we develop distributed protocols to strategically adjust partial weights of the Laplacian matrix for formation control in arbitrary dimensional space. By implementing the protocols, the desired formation spectrum can be preserved under dynamic topology changes including agent joining, edge addition, agent leaving, and edge removal, while any pair of agents can serve as leaders. Unlike existing Laplacian design methods for affine formation control under topology changes, the proposed approach requires a sparser sensing graph, avoids a predefined parent-child hierarchical structure, and supports leader reassignment. The effectiveness of the proposed protocols is validated through both theoretical analysis and numerical simulations.

We study continuous-time mean-variance portfolio selection with no-shorting constraints and unknown investment opportunity sets from a reinforcement learning (RL) perspective. The problem is a constrained stochastic linear – quadratic control problem for which the entropy-regularized exploratory formulation of Wang et al. (2020) leads to difficulty in theoretical analysis, because enforcing the constraint on the support of randomized policies nullifies the tractable Gaussian exploration. To tackle this challenge, we introduce an auxiliary exploratory problem without entropy in which exploratory policies are still Gaussian whose samples may violate the no-shorting requirement but their means satisfy it. We then prove that, for a suitable choice of exploration variance, the mean of the optimal Gaussian policy of the auxiliary problem coincides with the optimal policy of the original problem. Motivated by this theoretical result, we develop a model-free RL algorithm that learns the optimal policy of the auxiliary (and hence the original) problem directly from trajectory data without estimating the investment opportunity set. A numerical example demonstrates the performance of the proposed algorithm.

Problem definition: The paper studies an integrated end-to-end planning problem in large-scale paper manufacturing, where production scheduling, trimming decisions, vehicle loading, and multi-period fulfillment of make-to-order and make-to-stock demand must be coordinated over time. In practice, these decisions are often optimized sequentially, leading to material waste, inefficient transportation, and degraded service levels. Solving the fully integrated problem at industrial scale remains computationally challenging due to its combinatorial structure. Methodology/results: A key structural feature of the problem is that downstream fulfillment decisions depend on upstream production and logistics choices only through aggregate supply availability over time. By exploiting this structure, the paper develops an exact mathematical formulation and proposes a two-phase hybrid framework (BDCG-DP) that integrates column generation (CG) using exact dynamic-programming (DP) for supply-side decisions with Benders decomposition (BD) for downstream fulfillment. Computational experiments on proprietary instances from a major North American paper manufacturer show that BDCG-DP lowers total costs by 24.4% compared to a traditional CG-DP on challenging eight-week planning problems. Median runtime for four-week planning problems decreases from over five hours using CG-DP to under one hour using BDCG-DP. Managerial implications: This paper provides the first exact model that integrates production, trimming, load planning, and multi-period fulfillment at an industrial scale. The proposed approach returns integer-feasible plans within 2.3 to 6 hours for the most complex planning problems, enabling planners to access high-quality implementable schedules within hours, a capability that was previously unavailable in practice.

The rapid digitalisation of elite sport has created new opportunities for integrating artificial intelligence (AI), performance analytics, and decision-support systems into athlete development and competition management. However, existing solutions remain fragmented, typically addressing isolated tasks such as performance analysis, athlete monitoring, or referee support. This paper presents \textbf{FST$\cdot$ai~2.5}, an explainable, uncertainty-aware, and secure AI framework for Olympic and Para-Taekwondo. \textbf{FST$\cdot$ai~2.5} introduces a unified digital ecosystem integrating athlete intelligence, competition analytics, federation-scale data management, AI-assisted decision support, athlete and event digital twins, explainable performance indicators, and adaptive training recommendations. The framework supports World Taekwondo (WT), Member National Associations (MNAs), coaches, referees, analysts, and athletes through transparent, secure, and federation-aware governance. By combining multi-source competition data, athlete-performance information, and contextual evidence, \textbf{FST$\cdot$ai~2.5} provides tactical diagnostics, longitudinal athlete monitoring, performance forecasting, personalised development planning, and federation-wide benchmarking using explainable and uncertainty-aware AI. Prototype deployments demonstrate the feasibility of the proposed framework. Although developed for Olympic and Para-Taekwondo, the methodology is broadly applicable to explainable AI, digital twins, and trustworthy decision support in combat sports and other high-performance sporting environments.

Whether exact scalar feedback intrinsically incurs the additional dimension $d$ paid by known zeroth-order methods remains open even for Lipschitz convex optimization. For a universal Lipschitz scale, the value only bound $O(d^2\log(d+1)\log(1/\epsilon))$ and two-point bound $O(d\epsilon^{-2})$ yield the upper bound $\widetilde O\left(d\min\{d,\epsilon^{-2}\}\right)$. By contrast, prior lower bounds for arbitrary randomized algorithms give only $\Omega(\min\{d,\epsilon^{-2}\})$, leaving a factor $d$ unexplained. We close this gap, up to logarithmic factors, for arbitrary adaptive randomized algorithms minimizing a convex objective with a universal Lipschitz scale over the $d$-dimensional Euclidean unit ball, where each query returns only the exact scalar value. Let $T_\epsilon$ denote the minimum number of queries required to return an $\epsilon$-suboptimal point with probability at least $1/2$, uniformly over the function class. We prove that \[T_\epsilon\ge c\,\frac{d\min\{d,\epsilon^{-2}\}}{\log\!\bigl(\min\{d,\epsilon^{-2}\}\bigr)},\] for $d\ge d_0$ and $0<\epsilon\le\epsilon_0$, where $c,\epsilon_0>0$ and $d_0\in\mathbb N$ are universal constants. This gives $\Omega\left(\frac{d}{\epsilon^2\log(1/\epsilon)}\right)$ in the low-accuracy regime $\epsilon\ge d^{-1/2}$ and $\Omega\left(\frac{d^2}{\log d}\right)$ in the high-accuracy regime $\epsilon\le d^{-1/2}$ with the latter independent of $\epsilon$. These bounds match the corresponding upper bound up to logarithmic factors. To our knowledge, this is the first near-optimal lower bound for arbitrary adaptive randomized algorithms throughout both accuracy regimes of exact value Lipschitz convex optimization. The proof uses a random support function hard family and develops a posterior mean energy method for adaptive exact max observations, in place of first-order zero chain constructions and noise based transcript inequalities.

Witsenhausen's counterexample is a canonical problem in decentralized control: a two-stage linear-quadratic-Gaussian team problem in which nonlinear policies strictly outperform every affine one. This paper develops a variational and computational framework for the scalar counterexample based on optimal transport. Building on the transport formulation of Wu and Verdú, we absorb the first controller into a transport map and recast the problem as $J^\star=\inf_Q\{k^2W_2^2(P,Q)+\mathrm{mmse}(Q)\}$, which trades a quadratic Wasserstein transport cost against a minimum mean-square estimation error. The optimal first controller is the monotone rearrangement that pushes the prior $P$ to a minimizer $Q^\star$. We establish the existence and absolute continuity of minimizers, derive an Euler–Lagrange optimality condition, and obtain a semi-closed-form Gaussian benchmark with an explicit second-variation stability threshold. We then show that restricting to finitely supported laws yields an MMSE-regularized optimal quantizer: its optimal values decrease to $J^\star$, its weak limit points are minimizers of the continuous problem, and its stationarity conditions pair centroid levels with power cells, recovering Lloyd–Max quantization as control becomes expensive. This structure leads to an estimation-aware Lloyd algorithm with signalling-based initialization. As $k\to\infty$, the optimal controllers converge to the classical affine pair; as $k\to0$, $J^\star(k)=\sigma^2k^2+o(k^2)$ and the optimal laws collapse onto $\delta_0$, so signalling constellations are a moderate-$k$ phenomenon. Numerical experiments corroborate the theory, and the framework extends to the vector counterexample, where the finite-level program becomes an MMSE-regularized vector quantizer.

In finite horizon dynamic programming with history-dependent preferences, the relevant state may be the entire realized history, even when the physical state is Markov. This paper develops a behavioral state-reduction theory for such Markov decision processes. Under behavioral axioms and a certainty-equivalent richness condition, the full-history problem admits a recursive representation composed of time and risk aggregators. We then derive a canonical preference-augmented (PA) state by quotienting histories that have the same current physical Markov state, are indifferent under every common continuation plan, and remain equivalent after every common one-step extension. This canonical PA state is minimal among reachable recursive factorizations of the underlying preferences. Under Markov feasibility and standard dynamic-programming regularity, a PA Bellman selector induces an optimal full-history policy. With additional rectangularity and exhaustiveness conditions, we reparameterize the preference memory into distinct belief and taste coordinates, and obtain a separated representation and Bellman recursion. We give a taxonomy of examples to illustrate the scope of our framework.

Batteries are becoming a central part of modern energy systems, especially as electricity, transport and heat are decarbonised. In Great Britain, batteries already play an important role by providing flexibility and acting as a buffer for the system, and their importance will continue to grow as the system moves towards net zero by 2050. This perspective reviews how the role of batteries in Great Britain is evolving, their current value, and the growing contribution of batteries in the transport sector.It argues that the full value of electric vehicle batteries will only be realised through coordinated dispatch and better integration into system operation. Evidence from future scenarios developed by the National Energy System Operator (NESO) shows that while electric vehicles could provide most of the storage capacity, unmanaged charging could create challenges for the system rather than benefits. Unlocking this value will require improvements in market design, optimisation, and control strategies.