A Safe Pricing Mechanism for Distributed Resource Allocation with Bandit Feedback

Spencer Hutchinson, Berkay Turan, Mahnoosh Alizadeh

Abstract: Pricing mechanisms are commonly advocated as a main tool to shape customers’ demand in societal scale networked infrastructure such as power or transportation systems. Given that the price response function of each user is generally considered private and unknown, most existing algorithms rely on protocols that explicitly or implicitly solicit this information in order to design prices. However, approaches that rely solely on learning the price response through repeated interactions are more practical and gaining traction. In this paper, we model each customer’s price response by an unknown parameter vector and we design a resource pricing mechanism to manage demand in order to maximize total welfare while ensuring that a set of linear constraints on the consumption are satisfied at all time steps with high probability. We propose an algorithm to address this problem that utilizes the well known principle of optimism in the face of uncertainty (OFU), while simultaneously being pessimistic with respect to constraint violation. Our analysis of this algorithm shows that, with high probability, <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">√</inf> it will not violate the constraints and will achieve $\mathcal{O}(\log (T)\sqrt T )$ regret. Numerical experiments validate these results and demonstrate how our algorithm can be applied to demand response management in power distribution systems.