Sustainable Multi-Agent Crowdsourcing via Physics-Informed Bandits

Crowdsourcing platforms face a four-way tension between allocation quality, workforce sustainability, operational feasibility, and strategic contractor behaviour--a dilemma we formalise as the Cold-Start, Burnout, Utilisation, and Strategic Agency Dilemma. Existing methods resolve at most two of these tensions simultaneously: greedy heuristics and multi-criteria decision making (MCDM) methods achieve Day-1 quality but cause catastrophic burnout, while bandit algorithms eliminate burnout only through operationally infeasible 100% workforce utilisation.To address this, we introduce FORGE, a physics-grounded $K+1$ multi-agent simulator in which each contractor is a rational agent that declares its own load-acceptance threshold based on its fatigue state, converting the standard passive Restless Multi-Armed Bandit (RMAB) into a genuine Stackelberg game. Operating within FORGE, we propose a Neural-Linear UCB allocator that fuses a Two-Tower embedding network with a Physics-Informed Covariance Prior derived from offline simulator interactions. The prior simultaneously warm-starts skill-cluster geometry and UCB exploration landscape, providing a geometry-aware belief state from episode 1 that measurably reduces cold-start regret.Over $T = 200$ cold-start episodes, the proposed method achieves the highest reward of all non-oracle methods ($\text{LRew} = 0.555 \pm 0.041$) at only 7.6% workforce utilisation--a combination no conventional baseline achieves--while maintaining robustness to workforce turnover up to 50% and observation noise up to $\sigma = 0.20$.