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Distributed Resource Allocation for Human-Autonomy Teaming under Coupled Constraints

Yichen Yao, Ryan Mbagna Nanko, Yue Wang, Xuan Wang

TL;DR

The work tackles distributed resource allocation in a network consisting of autonomous agents and humans under globally coupled constraints, formalized as $A x + B y + c \le 0$ with $y = q(x_N)$. It introduces a graph-based decoupling reformulation that reduces the global coupling to local constraints on the communication graph and couples this with a fully distributed saddle-point algorithm that accounts for human responses through $y_k = q_k(x_{N_k})$, using virtual proxies when $q_k$ is not directly known. Theoretical contributions include a decoupling theorem and convergence proofs (existence of equilibria and asymptotic convergence to a global optimum) alongside a corollary showing robustness to imperfect human models; empirical validation via simulations demonstrates adaptation to varying human risk attitudes. Practically, the approach enables scalable, privacy-preserving resource allocation in manufacturing and other settings where human behavior is uncertain but can be proxied or learned, integrating human preferences into autonomous coordination.

Abstract

This paper studies the optimal resource allocation problem within a multi-agent network composed of both autonomous agents and humans. The main challenge lies in the globally coupled constraints that link the decisions of autonomous agents with those of humans. To address this, we propose a reformulation that transforms these coupled constraints into decoupled local constraints defined over the system's communication graph. Building on this reformulation and incorporating a human response model that captures human-robot interactions while accounting for individual preferences and biases, we develop a fully distributed algorithm. This algorithm guides the states of the autonomous agents to equilibrium points which, when combined with the human responses, yield a globally optimal resource allocation. We provide both theoretical analysis and numerical simulations to validate the effectiveness of the proposed approach.

Distributed Resource Allocation for Human-Autonomy Teaming under Coupled Constraints

TL;DR

The work tackles distributed resource allocation in a network consisting of autonomous agents and humans under globally coupled constraints, formalized as with . It introduces a graph-based decoupling reformulation that reduces the global coupling to local constraints on the communication graph and couples this with a fully distributed saddle-point algorithm that accounts for human responses through , using virtual proxies when is not directly known. Theoretical contributions include a decoupling theorem and convergence proofs (existence of equilibria and asymptotic convergence to a global optimum) alongside a corollary showing robustness to imperfect human models; empirical validation via simulations demonstrates adaptation to varying human risk attitudes. Practically, the approach enables scalable, privacy-preserving resource allocation in manufacturing and other settings where human behavior is uncertain but can be proxied or learned, integrating human preferences into autonomous coordination.

Abstract

This paper studies the optimal resource allocation problem within a multi-agent network composed of both autonomous agents and humans. The main challenge lies in the globally coupled constraints that link the decisions of autonomous agents with those of humans. To address this, we propose a reformulation that transforms these coupled constraints into decoupled local constraints defined over the system's communication graph. Building on this reformulation and incorporating a human response model that captures human-robot interactions while accounting for individual preferences and biases, we develop a fully distributed algorithm. This algorithm guides the states of the autonomous agents to equilibrium points which, when combined with the human responses, yield a globally optimal resource allocation. We provide both theoretical analysis and numerical simulations to validate the effectiveness of the proposed approach.

Paper Structure

This paper contains 14 sections, 3 theorems, 30 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation and Running Example
  3. Human Modeling and Virtual Human Proxy
  4. Main Results
  5. Decoupling the Global Constraint
  6. The Proposed Fully Distributed Algorithm
  7. Analysis
  8. Proof of Theorem \ref{['Thm_0']}
  9. Proof of Theorem \ref{['Thm_1']}
  10. Statement a
  11. Statement b
  12. Proof of Corollary \ref{['col_1']}
  13. Simulated Experiments
  14. Conclusion

Key Result

Theorem 1

(Decoupling the globally coupled constraint over the network) Suppose Assumption Asmp_1-a holds. The coupled constrain in eq_repfb, holds if and only if there exists a vector $\mathbf{z}\in\mathbb{R}^{r(m+h)}$ such that where $\bar{A} = \mathrm{diag}\{A_{i_1},\cdots,A_{i_m}\}$; $\bar{B} = \mathrm{diag}\{B_{k_1},\cdots,B_{k_h}\}$; $\bar{L}= L\otimes I_{r}$ with $L\in\mathbb{R}^{(m+h)\times(m+h)}$

Figures (4)

  • Figure 1: Distributed resource allocation for human-autonomy teaming and the interaction/communication topology.
  • Figure 2: Flowchart of the human modeling process.
  • Figure 3: Convergence indicated by evolution of $W(t)$
  • Figure 4: Proportion of work consumed by humans versus autonomous agents and the system cost.

Theorems & Definitions (5)

  • Remark 1: Human Response Functions
  • Theorem 1
  • Remark 2: Decoupled Constraints over Graph
  • Theorem 2: Effectiveness of the Proposed Algorithm
  • Corollary 1