Michael Amir

Michael Amir, Manon Flageat, Amanda Prorok

The success of machine learning for real-world robotic systems has created a new form of intellectual property: the trained policy. This raises a critical need for novel methods that verify ownership and detect unauthorized, possibly unsafe misuse. While watermarking is established in other domains, physical policies present a unique challenge: remote detection. Existing methods assume access to the robot's internal state, but auditors are often limited to external observations (e.g., video footage). This ``Physical Observation Gap'' means the watermark must be detected from signals that are noisy, asynchronous, and filtered by unknown system dynamics. We formalize this challenge using the concept of a \textit{glimpse sequence}, and introduce Colored Noise Coherency (CoNoCo), the first watermarking strategy designed for remote detection. CoNoCo embeds a spectral signal into the robot's motions by leveraging the policy's inherent stochasticity. To show it does not degrade performance, we prove CoNoCo preserves the marginal action distribution. Our experiments demonstrate strong, robust detection across various remote modalities, including motion capture and side-way/top-down video footage, in both simulated and real-world robot experiments. This work provides a necessary step toward protecting intellectual property in robotics, offering the first method for validating the provenance of physical policies non-invasively, using purely remote observations.

Rishabh Jain, Keisuke Okumura, Michael Amir et al.

Multi-Agent Path Finding (MAPF) is a representative multi-agent coordination problem, where multiple agents are required to navigate to their respective goals without collisions. Solving MAPF optimally is known to be NP-hard, leading to the adoption of learning-based approaches to alleviate the online computational burden. Prevailing approaches, such as Graph Neural Networks (GNNs), are typically constrained to pairwise message passing between agents. However, this limitation leads to suboptimal behaviours and critical issues, such as attention dilution, particularly in dense environments where group (i.e. beyond just two agents) coordination is most critical. Despite the importance of such higher-order interactions, existing approaches have not been able to fully explore them. To address this representational bottleneck, we introduce HMAGAT (Hypergraph Multi-Agent Attention Network), a novel architecture that leverages attentional mechanisms over directed hypergraphs to explicitly capture group dynamics. Empirically, HMAGAT establishes a new state-of-the-art among learning-based MAPF solvers: e.g., despite having just 1M parameters and being trained on 100$\times$ less data, it outperforms the current SoTA 85M parameter model. Through detailed analysis of HMAGAT's attention values, we demonstrate how hypergraph representations mitigate the attention dilution inherent in GNNs and capture complex interactions where pairwise methods fail. Our results illustrate that appropriate inductive biases are often more critical than the training data size or sheer parameter count for multi-agent problems.

Hao Xiang Li, Michael Amir, Amanda Prorok

The agent-environment co-design paradigm jointly optimises agent policies and environment configurations in search of improved system performance. With application domains ranging from warehouse logistics to windfarm management, co-design promises to fundamentally change how we deploy multi-agent systems. However, current co-design methods struggle to scale. They collapse under high-dimensional environment design spaces and suffer from sample inefficiency when addressing moving targets inherent to joint optimisation. We address these challenges by developing Diffusion Co-Design (DiCoDe), a scalable and sample-efficient co-design framework pushing co-design towards practically relevant settings. DiCoDe incorporates two core innovations. First, we introduce Projected Universal Guidance (PUG), a sampling technique that enables DiCoDe to explore a distribution of reward-maximising environments while satisfying hard constraints such as spatial separation between obstacles. Second, we devise a critic distillation mechanism to share knowledge from the reinforcement learning critic, ensuring that the guided diffusion model adapts to evolving agent policies using a dense and up-to-date learning signal. Together, these improvements lead to superior environment-policy pairs when validated on challenging multi-agent environment co-design benchmarks including warehouse automation, multi-agent pathfinding and wind farm optimisation. Our method consistently exceeds the state-of-the-art, achieving, for example, 39% higher rewards in the warehouse setting with 66% fewer simulation samples. This sets a new standard in agent-environment co-design, and is a stepping stone towards reaping the rewards of co-design in real world domains.

Rishabh Jain, Keisuke Okumura, Michael Amir et al.

Finding near-optimal solutions for dense multi-agent pathfinding (MAPF) problems in real-time remains challenging even for state-of-the-art planners. To this end, we develop a hybrid framework that integrates a learned heuristic derived from MAGAT, a neural MAPF policy with a graph attention scheme, into a leading search-based algorithm, LaCAM. While prior work has explored learning-guided search in MAPF, such methods have historically underperformed. In contrast, our approach, termed LaGAT, outperforms both purely search-based and purely learning-based methods in dense scenarios. This is achieved through an enhanced MAGAT architecture, a pre-train-then-fine-tune strategy on maps of interest, and a deadlock detection scheme to account for imperfect neural guidance. Our results demonstrate that, when carefully designed, hybrid search offers a powerful solution for tightly coupled, challenging multi-agent coordination problems.

Michael Amir, Guang Yang, Zhan Gao et al.

Constraint-based optimization is a cornerstone of robotics, enabling the design of controllers that reliably encode task and safety requirements such as collision avoidance or formation adherence. However, handcrafted constraints can fail in multi-agent settings that demand complex coordination. We introduce ReCoDe--Reinforcement-based Constraint Design--a decentralized, hybrid framework that merges the reliability of optimization-based controllers with the adaptability of multi-agent reinforcement learning. Rather than discarding expert controllers, ReCoDe improves them by learning additional, dynamic constraints that capture subtler behaviors, for example, by constraining agent movements to prevent congestion in cluttered scenarios. Through local communication, agents collectively constrain their allowed actions to coordinate more effectively under changing conditions. In this work, we focus on applications of ReCoDe to multi-agent navigation tasks requiring intricate, context-based movements and consensus, where we show that it outperforms purely handcrafted controllers, other hybrid approaches, and standard MARL baselines. We give empirical (real robot) and theoretical evidence that retaining a user-defined controller, even when it is imperfect, is more efficient than learning from scratch, especially because ReCoDe can dynamically change the degree to which it relies on this controller.

Michael Amir, Matteo Bettini, Amanda Prorok

The success of teams in robotics, nature, and society often depends on the division of labor among diverse specialists; however, a principled explanation for when such diversity surpasses a homogeneous team is still missing. Focusing on multi-agent task allocation problems, we study this question from the perspective of reward design: what kinds of objectives are best suited for heterogeneous teams? We first consider an instantaneous, non-spatial setting where the global reward is built by two generalized aggregation operators: an inner operator that maps the $N$ agents' effort allocations on individual tasks to a task score, and an outer operator that merges the $M$ task scores into the global team reward. We prove that the curvature of these operators determines whether heterogeneity can increase reward, and that for broad reward families this collapses to a simple convexity test. Next, we ask what incentivizes heterogeneity to emerge when embodied, time-extended agents must learn an effort allocation policy. To study heterogeneity in such settings, we use multi-agent reinforcement learning (MARL) as our computational paradigm, and introduce Heterogeneity Gain Parameter Search (HetGPS), a gradient-based algorithm that optimizes the parameter space of underspecified MARL environments to find scenarios where heterogeneity is advantageous. Across different environments, we show that HetGPS rediscovers the reward regimes predicted by our theory to maximize the advantage of heterogeneity, both validating HetGPS and connecting our theoretical insights to reward design in MARL. Together, these results help us understand when behavioral diversity delivers a measurable benefit.

Michael Amir, Alfred M. Bruckstein

We consider discrete dynamical systems of "ant-like" agents engaged in a sequence of pursuits on a graph environment. The agents emerge one by one at equal time intervals from a source vertex $s$ and pursue each other by greedily attempting to close the distance to their immediate predecessor, the agent that emerged just before them from $s$, until they arrive at the destination point $t$. Such pursuits have been investigated before in the continuous setting and in discrete time when the underlying environment is a regular grid. In both these settings the agents' walks provably converge to a shortest path from $s$ to $t$. Furthermore, assuming a certain natural probability distribution over the move choices of the agents on the grid (in case there are multiple shortest paths between an agent and its predecessor), the walks converge to the uniform distribution over all shortest paths from $s$ to $t$. We study the evolution of agent walks over a general finite graph environment $G$. Our model is a natural generalization of the pursuit rule proposed for the case of the grid. The main results are as follows. We show that "convergence" to the shortest paths in the sense of previous work extends to all pseudo-modular graphs (i.e. graphs in which every three pairwise intersecting disks have a nonempty intersection), and also to environments obtained by taking graph products, generalizing previous results in two different ways. We show that convergence to the shortest paths is also obtained by chordal graphs, and discuss some further positive and negative results for planar graphs. In the most general case, convergence to the shortest paths is not guaranteed, and the agents may get stuck on sets of recurrent, non-optimal walks from $s$ to $t$. However, we show that the limiting distributions of the agents' walks will always be uniform distributions over some set of walks of equal length.