In cloud-computing systems, network-bandwidth guarantees have been shown to improve predictability of application performance and cost. Most previous work on cloud-bandwidth guarantees has assumed that cloud tenants know what bandwidth guarantees they want. However, application bandwidth demands can be complex and time-varying, and many tenants might lack sufficient information to request a bandwidth guarantee that is well-matched to their needs. A tenant's lack of accurate knowledge about its future bandwidth demands can lead to over-provisioning (and thus reduced cost-efficiency) or under-provisioning (and thus poor user experience in latency-sensitive user-facing applications). We analyze traffic traces gathered over six months from an HP Cloud Services datacenter, finding that application bandwidth consumption is both time-varying and spatially inhomogeneous. This variability makes it hard to predict requirements. To solve this problem, we develop a prediction algorithm usable by a cloud provider to suggest an appropriate bandwidth guarantee to a tenant. The key idea in the prediction algorithm is to treat a set of previously observed traffic matrices as "experts" and learn online the best weighted linear combination of these experts to make its prediction. With tenant VM placement using these predictive guarantees, we find that the inter-rack network utilization in certain datacenter topologies can be more than doubled.