Accurate crop yield forecasting is essential for global food security. However, current AI models systematically underperform when yields deviate from historical trends. We attribute this to the lack of rich, physically grounded datasets directly linking atmospheric states to yields. To address this, we introduce VITA (Variational Inference Transformer for Asymmetric Data), a variational pretraining framework that learns representations from large satellite-based weather datasets and transfers to the ground-based limited measurements available for yield prediction. VITA is trained using detailed meteorological variables as proxy targets during pretraining and learns to predict latent atmospheric states under a seasonality-aware sinusoidal prior. This allows the model to be fine-tuned using limited weather statistics during deployment. Applied to 763 counties in the US Corn Belt, VITA achieves state-of-the-art performance in predicting corn and soybean yields across all evaluation scenarios, particularly during extreme years, with statistically significant improvements (paired t-test, p < 0.0001). Importantly, VITA outperforms prior frameworks like GNN-RNN without soil data, and larger foundational models (e.g., Chronos-Bolt) with less compute, making it practical for real-world use, especially in data-scarce regions. This work highlights how domain-aware AI design can overcome data limitations and support resilient agricultural forecasting in a changing climate.

The problem of sample complexity of online reinforcement learning is often studied in the literature without taking into account any partial knowledge about the system dynamics that could potentially accelerate the learning process. In this paper, we study the sample complexity of online Q-learning methods when some prior knowledge about the dynamics is available or can be learned efficiently. We focus on systems that evolve according to an additive disturbance model of the form S_{h+1} = ƒ(S_h, A_h) + W_h, where ƒ represents the underlying system dynamics, and W_h are unknown disturbances independent of states and actions. In the setting of finite episodic Markov decision processes with S states, A actions, and episode length H, we present an optimistic Q-learning algorithm that achieves Õ(Poly(H)√T) regret under perfect knowledge of ƒ, where T is the total number of interactions with the system. This is in contrast to the typical Õ(Poly(H)√SAT) regret for existing Q-learning methods. Further, if only a noisy estimate ƒ_hat of ƒ is available, our method can learn an approximately optimal policy in a number of samples that is independent of the cardinalities of state and action spaces. The sub-optimality gap depends on the approximation error ƒ_hat − ƒ, as well as the Lipschitz constant of the corresponding optimal value function. Our approach does not require modeling of the transition probabilities and enjoys the same memory complexity as model-free methods.

Model calibration is challenging for large-scale system models with a great number of variables. Existing approaches to partitioning system models and prioritizing data acquisition rely on heuristics rather than formal treatments. The sensor placement problem in physical dynamic systems points to a promising avenue for formalizing data acquisition priorities, which addresses the following question for system models: With the model at hand and pre-existing data availability on a subset of model variables, what are the (next) k model variables that would bring the largest utility to model calibration, once their data are acquired? In this study, we formalize this problem as a combinatorial optimization and adapt two solutions, the information-entropy approach and the miss-probability approach, from physical dynamic systems to system models in management sciences. Next, based on the idea of the data availability partition, we develop a third solution. The new approach can be understood from the entropy perspective and is embedded in the theoretical framework for the evaluation of side information. Our solution applies to system models of all topologies: analytical results of the optimal placement are derived for binary/multinary trees; for general (directed) tree structures, an algorithm to determine the optimal placement is devised, whose complexity is upper-bounded by [Formula: see text] for an n-variable system; for arbitrary model topologies with the presence of loops, sequential-optimal and simulated-annealing schemes are formulated. Three approaches are compared on a validating example; our solution outperforms the two alternatives. Application on a multicompartment system demonstrates the toolkit’s practical use. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0128 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0128 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

In addition to its public health crisis, COVID-19 pandemic has led to the shutdown and closure of workplaces with an estimated total cost of more than $16 trillion. Given the long hours an average person spends in buildings and indoor environments, this research article proposes data-driven control strategies to design optimal indoor airflow to minimize the exposure of occupants to viral pathogens in built environments. A general control framework is put forward for designing an optimal velocity field and proximal policy optimization, a reinforcement learning algorithm is employed to solve the control problem in a data-driven fashion. The same framework is used for optimal placement of disinfectants to neutralize the viral pathogens as an alternative to the airflow design when the latter is practically infeasible or hard to implement. We show, via computational simulations, that the control agent learns the optimal policy in both scenarios within a reasonable time. The proposed data-driven control framework in this study will have significant societal and economic benefits by setting the foundation for an improved methodology in designing case-specific infection control guidelines that can be realized by affordable ventilation devices and disinfectants.Note to Practitioners—This paper is motivated by the problem of COVID-19 infection spread in enclosed spaces but it also applies to other airborne pathogens. Airborne disease contagion often takes place in indoor environments; however, ventilation systems are almost never designed to take this into account so as to contain the spread of the pathogens. This is mainly because airflow design requires solving high-dimensional nonlinear partial differential equations known as Navier Stokes equations in fluid dynamics. In this paper, we propose a data-driven approach for solving the control problem of pathogen containment without solving the fluid dynamics equations. To this end, we first mathematically formulate the problem as an optimal control problem and then cast it as a reinforcement learning (RL) task. Reinforcement learning is the data-driven science of sequential decision-making and control in which the controller finds an optimal solution by systematic trial and error and without access to the system dynamics, i.e. fluid and pathogen dynamics in this paper. We employ an state-of-the-art RL algorithm, called PPO, to solve for optimal airflow in a room so as to minimize the exposure risk of occupants. Once it is calculated, the optimal airflow could be realized, via reverse engineering, by proper placement of the ventilation equipment, e.g. inlets, outlets, and fans. As an alternative to the airflow design, we use the same proposed data-driven techniques to find an optimal placement for pathogen disinfectants if there exists one, such as, hydrogen peroxide for COVID-19. Our results show the efficacy of our data-driven approach in designing an steady-state controller with full access to the system states. In future research, we will address the controller design with sparse measurements of the system states.

Matrix completion is the study of recovering an underlying matrix from a sparse subset of noisy observations. Traditionally, it is assumed that the entries of the matrix are “missing completely at random” (MCAR), i.e., each entry is revealed at random, independent of everything else, with uniform probability. This is likely unrealistic due to the presence of “latent confounders”, i.e., unobserved factors that determine both the entries of the underlying matrix and the missingness pattern in the observed matrix. For example, in the context of movie recommender systems—a canonical application for matrix completion—a user who vehemently dislikes horror films is unlikely to ever watch horror films. In general, these confounders yield “missing not at random” (MNAR) data, which can severely impact any inference procedure that does not correct for this bias. We develop a formal causal model for matrix completion through the language of potential outcomes, and provide novel identification arguments for a variety of causal estimands of interest. We design a procedure, which we call “synthetic nearest neighbors” (SNN), to estimate these causal estimands. We prove finite-sample consistency and asymptotic normality of our estimator. Our analysis also leads to new theoretical results for the matrix completion literature. In particular, we establish entry-wise, i.e., max-norm, finite-sample consistency and asymptotic normality results for matrix completion with MNAR data. As a special case, this also provides entry-wise bounds for matrix completion with MCAR data. Across simulated and real data, we demonstrate the efficacy of our proposed estimator.

The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that one can learn the deterministic non-stationary components accurately using multivariate Singular Spectrum Analysis (mSSA) in the absence of a correlated stationary component; meanwhile, in the absence of deterministic non-stationary components, the Autoregressive (AR) stationary component can also be learnt readily, e.g. via Ordinary Least Squares (OLS). However, a theoretical underpinning of multi-stage learning algorithms involving both deterministic and stationary components has been absent in the literature despite its pervasiveness. We resolve this open question by establishing desirable theoretical guarantees for a natural two-stage algorithm, where mSSA is first applied to estimate the non-stationary components despite the presence of a correlated stationary AR component, which is subsequently learned from the residual time series. We provide a finite-sample forecasting consistency bound for the proposed algorithm, SAMoSSA, which is data-driven and thus requires minimal parameter tuning. To establish theoretical guarantees, we overcome three hurdles: (i) we characterize the spectra of Page matrices of stable AR processes, thus extending the analysis of mSSA; (ii) we extend the analysis of AR process identification in the presence of arbitrary bounded perturbations; (iii) we characterize the out-of-sample or forecasting error, as opposed to solely considering model identification. Through representative empirical studies, we validate the superior performance of SAMoSSA compared to existing baselines. Notably, SAMoSSA's ability to account for AR noise structure yields improvements ranging from 5% to 37% across various benchmark datasets.

The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning method to identify meaningful low-dimensional state and action representations from empirical trajectories. The method exploits the MDP's tensor structure by kernelization, importance sampling and low-Tucker-rank approximation. This method can be further used to cluster states and actions respectively and find the best discrete MDP abstraction. We provide sharp statistical error bounds for tensor concentration and the preservation of diffusion distance after embedding. We further prove that the learned state/action abstractions provide accurate approximations to latent block structures if they exist, enabling function approximation in downstream tasks such as policy evaluation.

A large class of sequential decision-making problems under uncertainty, with broad applications from preventive maintenance to event-triggered control can be modeled in the framework of semi-Markov decision processes (SMDPs). Unlike Markov decision processes (MDPs), SMDPs are underexplored in the online and reinforcement learning (RL) settings. In this paper, we extend the well-known deterministic policy gradient (DPG) theorem in MDPs to SMDPs under average-reward criterion. The existing stochastic policy gradient methods not only require, in general, a large number of samples for training, but they also suffer from high variance in the gradient estimation when applied to problems with deterministic optimal policy. Our DPG method can potentially remedy these issues. On the basis of this method and depending on the choice of a critic, different actor–critic algorithms can easily be developed in the RL setup. We present two example actor–critic algorithms. Both algorithms employ our developed policy gradient theorem for their actors, but use two different critics; one uses a simple SARSA update while the other one uses the same on-policy update but with compatible function approximators. We demonstrate the efficacy of our method both mathematically and via simulations.

We address the problem of learning the parameters of a stable linear time invariant (LTI) system with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus on learning the best lower order approximation allowed by finite data. Motivated by subspace algorithms in systems theory, where the doubly infinite system Hankel matrix captures both order and good lower order approximations, we construct a Hankel-like matrix from noisy finite data using ordinary least squares. This circumvents the non-convexities that arise in system identification, and allows accurate estimation of the underlying LTI system. Our results rely on careful analysis of self-normalized martingale difference terms that helps bound identification error up to logarithmic factors of the lower bound. We provide a data-dependent scheme for order selection and find an accurate realization of system parameters, corresponding to that order, by an approach that is closely related to the Ho-Kalman subspace algorithm. We demonstrate that the proposed model order selection procedure is not overly conservative, i.e., for the given data length it is not possible to estimate higher order models or find higher order approximations with reasonable accuracy.

The ability to move fast and accurately track moving objects is fundamentally constrained by the biophysics of neurons and dynamics of the muscles involved. Yet the corresponding trade-offs between these factors and tracking motor commands have not been rigorously quantified. We use feedback control principles to quantify performance limitations of the sensorimotor control system (SCS) to track fast periodic movements. We show that (1) linear models of the SCS fail to predict known undesirable phenomena, including skipped cycles, overshoot and undershoot, produced when tracking signals in the "fast regime," while nonlinear pulsatile control models can predict such undesirable phenomena, and (2) tools from nonlinear control theory allow us to characterize fundamental limitations in this fast regime. Using a validated and tractable nonlinear model of the SCS, we derive an analytical upper bound on frequencies that the SCS model can reliably track before producing such undesirable phenomena as a function of the neurons' biophysical constraints and muscle dynamics. The performance limitations derived here have important implications in sensorimotor control. For example, if the primary motor cortex is compromised due to disease or damage, the theory suggests ways to manipulate muscle dynamics by adding the necessary compensatory forces using an assistive neuroprosthetic device to restore motor performance and, more important, fast and agile movements. Just how one should compensate can be informed by our SCS model and the theory developed here.

We introduce a new class of (dynamical) systems that inherently capture cascading effects (viewed as consequential effects) and are naturally amenable to combinations. We develop an axiomatic general theory around those systems, and guide the endeavor towards an understanding of cascading failure. The theory evolves as an interplay of lattices and fixed points, and its results may be instantiated to commonly studied models of cascade effects. We characterize the systems through their fixed points, and equip them with two operators. We uncover properties of the operators, and express global systems through combinations of local systems. We enhance the theory with a notion of failure, and understand the class of shocks inducing a system to failure. We develop a notion of mu-rank to capture the energy of a system, and understand the minimal amount of effort required to fail a system, termed resilience. We deduce a dual notion of fragility and show that the combination of systems sets a limit on the amount of fragility inherited.

A network of nodes communicate via point-to-point memoryless independent noisy channels. Each node has some real-valued initial measurement or message. The goal of each of the nodes is to acquire an estimate of a given function of all the initial measurements in the network. As the main contribution of this paper, a lower bound on computation time is derived. This bound must be satisfied by any algorithm used by the nodes to communicate and compute, so that the mean-square error in the nodes' estimate is within a given interval around zero. The derivation utilizes information theoretic inequalities reminiscent of those used in rate distortion theory along with a novel “perturbation” technique so as to be broadly applicable. To understand the tightness of the bound, a specific scenario is considered. Nodes are required to learn a linear combination of the initial values in the network while communicating over erasure channels. A distributed quantized algorithm is developed, and it is shown that the computation time essentially scales as is implied by the lower bound. In particular, the computation time depends reciprocally on “conductance”, which is a property of the network that captures the information-flow bottleneck. As a by-product, this leads to a quantized algorithm, for computing separable functions in a network, with minimal computation time.

Bayesian network structure learning is a useful tool for elucidation of regulatory structures of biomolecular pathways. The approach however is limited by its acyclicity constraint, a problematic one in the cycle-containing biological domain. Here, we introduce a novel method for modeling cyclic pathways in biology, by employing our newly introduced Generalized Bayesian Networks (GBNs) and proposing a structure learning algorithm suitable for the biological domain. This algorithm relies on data and perturbations which are feasible for collection in an experimental setting, such as perturbations affecting either the abundance or activity of a molecule. We present theoretical arguments as well as structure learning results from simulated data. We also present results from a small real world dataset, involving genes from the galactose system in S. cerevisiae.

We consider a network of nodes, each having an initial value or measurement, and seeking to acquire an estimate of a given function of all the nodespsila values in the network. Each node may exchange with its neighbors a finite number of bits every time communication is initiated. In this paper, we present an algorithm for computation of separable functions, under the constraint that communicated messages are quantized, so that with some specified probability, all nodes have an estimate of the function value within a desired interval of accuracy. We derive an upper bound on the computation time needed to achieve this goal, and show that the dependence of the computation time on the network topology, via the ldquoconductancerdquo of the graph representing this topology, matches a lower bound derived from Information Theoretic analysis. Hence, the algorithmpsilas running time is optimal with respect to dependence on the graph structure.

The goal of n nodes, each measuring a component of a source and communicating via broadcast compressed messages, is to ultimately achieve consensus, with high reliability, on the modulo-q sum of the measured data. We provide an example (specifically, a joint probability mass function for the source) for which we characterize the "K-rate region" the rates necessary and sufficient for consensus. For our example, when there are two nodes in the network, the K-rate region coincides with the Slepian-Wolf rate region. However, for more than 2 nodes, compressing for consensus can result in lower rates than compressing, as in the Slepian-Wolf formulation, for the entire data sequences in the network. We quantify the savings in rate that are obtained, when compressing for K in comparison to the Slepian-Wolf rates, as the number of nodes in the network grows.

In this paper, we introduce an approach for the efficient solution of motion-planning problems for time-invariant dynamical control systems with symmetries, such as mobile robots and autonomous vehicles, under a variety of differential and algebraic constraints on the state and on the control inputs. Motion plans are described as the concatenation of a number of well-defined motion primitives, selected from a finite library. Rules for the concatenation of primitives are given in the form of a regular language, defined through a finite-state machine called a Maneuver Automaton. We analyze the reachability properties of the language, and present algorithms for the solution of a class of motion-planning problems. In particular, it is shown that the solution of steering problems for nonlinear dynamical systems with symmetries and invariant constraints can be reduced to the solution of a sequence of kinematic inversion problems. A detailed example of the application of the proposed approach to motion planning for a small aerobatic helicopter is presented.

In the thresholding method of denoising the optimum threshold is obtained as a function of additive noise variance. In practical problems, where the variance of the noise is unknown, the first step is to estimate the noise variance. The estimated noise variance is then implemented in calculation of the optimum threshold. The current available methods of variance estimation are heuristic. Here, we provide a new method for estimation of the additive noise variance. The method is derived from a new denoising method which is proposed in Beheshti et al. (2002). Unlike thresholding approaches the denoising method in Beheshti is based on comparison of subspaces of the basis. It compares a defined description length (DL) of the noisy data in the subspaces. We show how the estimation of the noise variance and the denoising process can be done simultaneously.