Epistemic Social Learning: Latent Behavioral Structure under Endogenous Multi-Agent Interaction

In many interactive settings, from social and institutional environments to multi-agent systems, agents must infer latent behavioral structure from limited signals while their own actions shape the data they observe. This endogeneity violates the stationary, exogenous assumptions underlying standard likelihood-based methods, leading to failures in adaptation despite accurate clustering. We propose \emph{Epistemic Social Learning} (ESL), a two-timescale framework that couples belief-based inference with adaptive representation learning under endogenous interaction. At a fast timescale, agents maintain Bayesian beliefs over shared behavioral prototypes. At a slower timescale, prototypes are updated from belief-weighted interaction data via the recursion $\Theta_{m+1} = \Theta_m + \gamma_m \widehat{H}_m$, aligning learned representations with the interaction distributions induced by agent behavior. We formalize ESL as a stochastic approximation process with controlled Markov noise and show that its dynamics track the differential inclusion $\dot{\Theta} \in \mathcal{G}(\Theta)$, whose limit sets correspond to self-consistent interaction regimes. Across repeated games with behavioral shifts, ESL reduces post-switch regret by $26\%$ over strong baselines while improving decision-relevant prediction. These results reveal a fundamental gap between latent identification and adaptive performance under endogenous interaction.