LiSFC-Search: Lifelong Search for Network SFC Optimization under Non-stationary Drifts

Edge-cloud convergence is reshaping service provisioning across 5G/6G and computing power networks (CPNs). Service function chaining (SFC) requires continuously placing and scheduling virtual network functions (VNFs) chains under compute/bandwidth and end-to-end QoS constraints. Most SFC optimizers assume static or stationary networks, and degrade under long-term topology/resource changes (failures, upgrades, expansions) that induce non-stationary graph drifts. We propose LiSFC, a Lipschitz lifelong planner that transfers MCTS statistics across drifting network configurations using an MDP-distance bound. More precisely, we formulate the problem as a sequence of MDPs indexed by the underlying network graph and constraints, and we define a \emph{graph drift} metric that upper-bounds the LiZero MDP distance. This allows LiSFC to import theoretical guarantees on bias and sample efficiency from the LiZero framework while being tailored to cloud-network convergence. We then design \emph{LiSFC-Search}, an SFC-aware unified MCTS (UMCTS) procedure that uses transferable adaptive UCT (aUCT) bonuses to reuse search statistics from prior CPN configurations. Preliminary results on synthetic CPN topologies and SFC workloads show that LiSFC consistently reduces SFC blocking probability and improves tail delay compared to non-transfer MCTS and purely learning-based baselines, highlighting its potential as an AI/ML building block for cloud-network convergence.