It is well established that formulating an effective constraint model of a problem of interest is crucial to the efficiency with which it can subsequently be solved. Following from the observation that it is difficult, if not impossible, to know a priori which of a set of candidate models will perform best in practice, we envisage a system that explores the space of models through a process of reformulation from an initial model, guided by performance on a set of training instances from the problem class under consideration. We plan to situate this system in a refinement-based approach, where a user writes a constraint specification describing a problem above the level of abstraction at which many modelling decisions are made. In this position paper we set out our plan for an exploratory reformulation system, and discuss progress made so far.

Our focus is on projects, i.e., business processes, which are emerging as the economic drivers of our times. Differently from day-to-day operational processes that do not require detailed planning, a project requires planning and resource-constrained scheduling for coordinating resources across sub- or related projects and organizations. A planner in charge of project planning has to select a set of activities to perform, determine their precedence constraints, and schedule them according to temporal project constraints. We suggest a data-driven project planning approach for classes of projects such as infrastructure building and information systems development projects. A project network is first learned from historical records. The discovered network relaxes temporal constraints embedded in individual projects, thus uncovering where planning and scheduling flexibility can be exploited for greater benefit. Then, the network, which contains multiple project plan variations, from which one has to be selected, is enriched by identifying decision rules and frequent paths. The planner can rely on the project network for: 1) decoding a project variation such that it forms a new project plan, and 2) applying resource-constrained project scheduling procedures to determine the project's schedule and resource allocation. Using two real-world project datasets, we show that the suggested approach may provide the planner with significant flexibility (up to a 26% reduction of the critical path of a real project) to adjust the project plan and schedule. We believe that the proposed approach can play an important part in supporting decision making towards automated data-driven project planning.

We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we consider two problems: recovery of stochastic block models and learning mixtures of spherical Gaussians. For the former, we present the first efficient $(\epsilon, \delta)$-differentially private algorithm for both weak recovery and exact recovery. Previously known algorithms achieving comparable guarantees required quasi-polynomial time. For the latter, we design an $(\epsilon, \delta)$-differentially private algorithm that recovers the centers of the $k$-mixture when the minimum separation is at least $ O(k^{1/t}\sqrt{t})$. For all choices of $t$, this algorithm requires sample complexity $n\geq k^{O(1)}d^{O(t)}$ and time complexity $(nd)^{O(t)}$. Prior work required minimum separation at least $O(\sqrt{k})$ as well as an explicit upper bound on the Euclidean norm of the centers.

In this paper, we present a novel Reduced Robustified NMPC (R$^2$NMPC) algorithm that has the same complexity as an equivalent nominal NMPC while enhancing it with robustified constraints based on the dynamics of ellipsoidal uncertainty sets. This promises both a closed-loop- and constraint satisfaction performance equivalent to common Robustified NMPC approaches, while drastically reducing the computational complexity. The main idea lies in approximating the ellipsoidal uncertainty sets propagation over the prediction horizon with the system dynamics' sensitivities inferred from the last optimal control problem (OCP) solution, and similarly for the gradients to robustify the constraints. Thus, we do not require the decision variables related to the uncertainty propagation within the OCP, rendering it computationally tractable. Next, we illustrate the real-time control capabilities of our algorithm in handling a complex, high-dimensional, and highly nonlinear system, namely the trajectory following of an autonomous passenger vehicle modeled with a dynamic nonlinear single-track model. Our experimental findings, alongside a comparative assessment against other Robust NMPC approaches, affirm the robustness of our method in effectively tracking an optimal racetrack trajectory while satisfying the nonlinear constraints. This performance is achieved while fully utilizing the vehicle's interface limits, even at high speeds of up to 37.5m/s, and successfully managing state estimation disturbances. Remarkably, our approach maintains a mean solving frequency of 144Hz.

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.

LLMs have recently made impressive inroads on tasks whose output is structured, such as coding, robotic planning and querying databases. The vision of creating AI-powered personal assistants also involves creating structured outputs, such as a plan for one's day, or for an overseas trip. Here, since the plan is executed by a human, the output doesn't have to satisfy strict syntactic constraints. A useful assistant should also be able to incorporate vague constraints specified by the user in natural language. This makes LLMs an attractive option for planning. We consider the problem of planning one's day. We develop an LLM-based planner (LLMPlan) extended with the ability to self-reflect on its output and a symbolic planner (SymPlan) with the ability to translate text constraints into a symbolic representation. Despite no formal specification of constraints, we find that LLMPlan performs explicit constraint satisfaction akin to the traditional symbolic planners on average (2% performance difference), while retaining the reasoning of implicit requirements. Consequently, LLM-based planners outperform their symbolic counterparts in user satisfaction (70.5% vs. 40.4%) during interactive evaluation with 40 users.

Simulators for mechanical systems are widely used, for example in testing and verification [1, 2], model-based control strategies [3, 4], or learning-based methods [5, 6]. However, many common simulators have numerical difficulties with more complex mechanical systems involving constraints [7]. Such constraints can represent joints connecting rigid bodies, which may form kinematic loops, for example, in exoskeletons. Constraints can also be used to confine the movement of bodies, for example, to model joint limits in robotic arms, or to describe contact with other bodies or the environment in walking and grasping. Exactly enforcing such constraints can cause numerical issues, for example, due to the stiff nature of contact interactions. To alleviate these numerical issues, simulators often allow small constraint violations by representing all constraints as spring-damper elements as in MuJoCo [8] and Brax [9], or by accepting interpenetration of bodies as in Drake [10] and Bullet [11]. Small violations can sometimes be acceptable, for example, contact interpenetration in the order of micrometers for meter-scale walking robots. But millimeter or centimeter violations, for example in MuJoCo, can be considered too large. Employing these methods and accepting larger constraint violations for stable simulations contributes to the sim-to-real gap, a major issue in robotics [12].

Safety-critical control tasks with high levels of uncertainty are becoming increasingly common. Typically, techniques that guarantee safety during learning and control utilize constraint-based safety certificates, which can be leveraged to compute safe control inputs. However, excessive model uncertainty can render robust safety certification methods or infeasible, meaning no control input satisfies the constraints imposed by the safety certificate. This paper considers a learning-based setting with a robust safety certificate based on a control barrier function (CBF) second-order cone program. If the control barrier function certificate is feasible, our approach leverages it to guarantee safety. Otherwise, our method explores the system dynamics to collect data and recover the feasibility of the control barrier function constraint. To this end, we employ a method inspired by well-established tools from Bayesian optimization. We show that if the sampling frequency is high enough, we recover the feasibility of the robust CBF certificate, guaranteeing safety. Our approach requires no prior model and corresponds, to the best of our knowledge, to the first algorithm that guarantees safety in settings with occasionally infeasible safety certificates without requiring a backup non-learning-based controller.

This paper focuses on the distributed online convex optimization problem with time-varying inequality constraints over a network of agents, where each agent collaborates with its neighboring agents to minimize the cumulative network-wide loss over time. To reduce communication overhead between the agents, we propose a distributed event-triggered online primal-dual algorithm over a time-varying directed graph. Dynamic network regret and network cumulative constraint violation are leveraged to measure the performance of the algorithm. Based on the natural decreasing parameter sequences, we establish sublinear dynamic network regret and network cumulative constraint violation bounds. The theoretical results broaden the applicability of event-triggered online convex optimization to the regime with inequality constraints. Finally, a numerical simulation example is provided to verify the theoretical results.

In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality and spatiotemporal correlations, but they are vital to traffic data recovery, especially for high-level missing scenarios. To address this problem, we propose a novel spatiotemporal regularized Tucker decomposition method. First, the traffic matrix is converted into a third-order tensor. Then, based on Tucker decomposition, the tensor is approximated by multiplying non-negative factor matrices with a sparse core tensor. Notably, we do not need to set the tensor rank or determine it through matrix nuclear-norm minimization or tensor rank minimization. The low rankness is characterized by the $l_1$-norm of the core tensor, while the manifold regularization and temporal constraint are employed to capture spatiotemporal correlations and further improve imputation performance. We use an alternating proximal gradient method with guaranteed convergence to address the proposed model. Numerical experiments show that our proposal outperforms matrix-based and tensor-based baselines on real-world spatiotemporal traffic datasets in various missing scenarios.