End-to-end (E2E) network slices (NSs) are provisioned across multiple domains of the 5G network. In hierarchical NS management, a tenant submits a network slice request (NSR), which specifies E2E service level agreement (SLA) requirements. Rather than managing these domains directly, an E2E controller decomposes each NSR into domain-level SLA requirements and delegates resource allocation to domain-specific controllers, which return feasibility and resource-consumption feedback. A poor decomposition policy can therefore cause rejection of the current request by producing infeasible requirements or reduce future admission opportunities by concentrating resource consumption in bottleneck domains. We call this decomposition-policy optimization problem the network slice request decomposition problem (NSR-DP). For practical operation, online approaches to NSR-DP have been proposed. Such approaches must jointly meet two requirements: (R1) control long-term resource budgets and (R2) adapt each decomposition to the performance targets and guarantee levels specified in the arriving NSR's SLA. To meet these requirements, we introduce contextual constrained kernel bandits (CCKB) as an online solution for NSR-DP. To address (R1), CCKB raises penalties for using resources that become tight, thereby discouraging decompositions that consume bottleneck resources. To address (R2), it uses Gaussian processes (GPs) to predict, for the current NSR, the reward and resource usage of candidate decompositions, allowing it to select a decomposition suited to the performance targets and guarantee levels. We establish high-probability guarantees for the resulting formulation and show through extensive 5G simulations across topology, bottleneck, and traffic-mixture settings that CCKB outperforms the baselines in the large majority of conditions.

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