SAGE: Self-Adaptive Personalized Recommendation with Regret Guarantees from Heterogeneous Experts

Large-scale recommendation systems face fundamental challenges in non-stationary environments where data distributions evolve and user preferences shift over time. Existing methods, particularly collaborative filtering and static fusion approaches, lack adaptive mechanisms to handle temporal drift while maintaining interpretability and stability guarantees. We propose SAGE, an adaptive personalized fusion layer that computes client- and round-specific expert mixtures via convex optimization on the probability simplex, balancing calibrated trust estimates, regime-conditioned uncertainty, and revealed preferences. SAGE yields three theoretical guarantees: (i) existence and uniqueness of a Pareto-optimal solution, (ii) a stability bound quantifying weight perturbation under regime shifts and trust changes, and (iii) monotone ranking consistency. We further introduce SELF, a self-adaptive extension that learns fusion weights online from recommendation feedback, achieving a dynamic-regret bound of $O(T^{2/3} P_T^{1/3})$ against non-stationary expert drift. On FAR-Trans, a real-world financial recommendation benchmark, SAGE achieves nDCG@10 $= 0.317$ (second among 11 baselines). This work contributes new principled approaches to self-evolving recommendation systems in dynamic markets.