Meshal Alharbi

Yubo Cai, Yujun Huang, Meshal Alharbi et al.

Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not by itself reveal which problem classes admit exact and scalable computation. This paper isolates such a class by introducing Linear Design Problems (LDPs): design problems whose feasible functionality--resource relations are polyhedra over Euclidean posets. We show that queries on LDPs reduce exactly to Multi-Objective Linear Programs (MOLPs), thereby connecting monotone co-design semantics with polyhedral multiobjective optimization. We further prove that LDPs are closed under the fundamental co-design interconnections, implying that any interconnection of linear components induces a system-level LDP. To compute the resulting feasible sets, we develop two complementary constructions: a monolithic lifted formulation that preserves block-angular sparsity, and a compositional formulation that incrementally eliminates internal variables through polyhedral projection. Beyond the exact linear setting, we show that convex co-design resource queries admit arbitrarily accurate polyhedral outer approximations, with recession-cone error identically zero for standard nonnegative resource cones. Numerical studies on synthetic series-chain benchmarks, a gripper, and a rover co-design validate the theory.

Johannes Gaber, Meshal Alharbi, Daniele Gammelli et al.

Large robot fleets are now common in warehouses and other logistics settings, where small control gains translate into large operational impacts. In this article, we address task scheduling for lifelong Multi-Agent Pickup-and-Delivery (MAPD) and propose a hybrid method that couples learning-based global guidance with lightweight optimization. A graph neural network policy trained via reinforcement learning outputs a desired distribution of free agents over an aggregated warehouse graph. This signal is converted into region-to-region rebalancing through a minimum-cost flow, and finalized by small, local assignment problems, preserving accuracy while keeping per-step latency within a 1 s compute budget. On congested warehouse benchmarks from the League of Robot Runners (LRR) with up to 500 agents, our approach improves throughput by up to 10% over the 2024 winning scheduler while maintaining real-time execution. The results indicate that coupling graph-structured learned guidance with tractable solvers reduces congestion and yields a practical, scalable blueprint for high-throughput scheduling in large fleets.

Maximilian Stralz, Meshal Alharbi, Yujun Huang et al.

Designing multi-agent robotic systems requires reasoning across tightly coupled decisions spanning heterogeneous domains, including robot design, fleet composition, and planning. Much effort has been devoted to isolated improvements in these domains, whereas system-level co-design considering trade-offs and task requirements remains underexplored. In this work, we present a formal and compositional framework for the task-driven co-design of heterogeneous multi-robot systems. Building on a monotone co-design theory, we introduce general abstractions of robots, fleets, planners, executors, and evaluators as interconnected design problems with well-defined interfaces that are agnostic to both implementations and tasks. This structure enables efficient joint optimization of robot design, fleet composition, and planning under task-specific performance constraints. A series of case studies demonstrates the capabilities of the framework. Various component models can be seamlessly incorporated, including new robot types, task profiles, and probabilistic sensing objectives, while non-obvious design alternatives are systematically uncovered with optimality guarantees. The results highlight the flexibility, scalability, and interpretability of the proposed approach, and illustrate how formal co-design enables principled reasoning about complex heterogeneous multi-robot systems.

Meshal Alharbi, Munther A. Dahleh, Gioele Zardini

Many engineered systems must balance competing objectives, such as performance and safety, cost and reliability, or efficiency and sustainability, and are naturally modeled as compositions of interacting subsystems. We study online multi-objective decision-making in monotone co-design, where functionalities and resources are partially ordered, and the goal is to identify the target-feasible antichain of non-dominated trade-offs using few expensive evaluations. We introduce optimistic evaluators: history-dependent bounds on functionality and resource mappings that enable safe elimination of implementations before full evaluation. Based on these evaluators, we develop an elimination-based rejection-sampling algorithm, prove its soundness, and show that the admissible region shrinks monotonically as information accumulates. We instantiate the framework under monotonicity, Lipschitz continuity, and linear-parametric structure. For compositional co-design problems modeled by multigraphs, we show how local optimistic certificates propagate through the tractable remainder of the graph to yield system-level optimistic feasibility and resource bounds. Experiments on multi-robot fleet design, intermodal mobility systems, and synthetic monotone and Lipschitz benchmarks show substantial sample-efficiency gains over uniform sampling, Bayesian optimization, and multi-objective evolutionary algorithms.

Meshal Alharbi, Mardavij Roozbehani, Munther Dahleh

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 $S_{h+1} = f(S_h, A_h) + W_h$, where $f$ 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 $\tilde{\mathcal{O}}(\text{Poly}(H)\sqrt{T})$ regret under perfect knowledge of $f$, where $T$ is the total number of interactions with the system. This is in contrast to the typical $\tilde{\mathcal{O}}(\text{Poly}(H)\sqrt{SAT})$ regret for existing Q-learning methods. Further, if only a noisy estimate $\hat{f}$ of $f$ 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 $\hat{f}-f$, 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.