Optimal Service Caching and Pricing in Edge Computing: a Bayesian Gaussian Process Bandit Approach

Motivated by the emergence of function-as-a-service (FaaS) as a programming abstraction for edge computing, we consider the problem of caching and pricing applications for edge computation offloading in a dynamic environment where Wirelesss Devices (WDs) can be active or inactive at any point in time. We model the problem as a single leader multiple-follower Stackelberg game, where the service operator is the leader and decides what applications to cache and how much to charge for their use, while the WDs are the followers and decide whether or not to offload their computations. We show that the WDs' interaction can be modeled as a player-specific congestion game and show the existence and computability of equilibria. We then show that under perfect and complete information the equilibrium price of the service operator can be computed in polynomial time for any cache placement. For the incomplete information case, we propose a Bayesian Gaussian Process Bandit algorithm for learning an optimal price for a cache placement and provide a bound on its asymptotic regret. We then propose a Gaussian process approximation-based greedy heuristic for computing the cache placement. We use extensive simulations to evaluate the proposed learning scheme, and show that it outperforms state of the art algorithms by up to 50% at little computational overhead.