Multiplicative Weights (MW) is a simple yet powerful algorithm for learning linear classifiers, for ensemble learningà la boosting, for approximately solving linear and semidefinite systems, for computing approximate solutions to multicommodity flow problems, and for online convex optimization, among other applications. Recent work in algorithmic game theory, which applies a computational perspective to the design and analysis of systems with mutually competitive actors, has shown that no-regret algorithms like MW naturally drive games toward approximate Coarse Correlated Equilibria (CCEs), and that for certain games, approximate CCEs have bounded cost with respect to the optimal states of such systems. In this paper, we put such results to practice by building distributed systems such as routers and load balancers with performance and convergence guarantees mechanically verified in Coq. The main contributions on which our results rest are (1) the first mechanically verified implementation of Multiplicative Weights (specifically, we show that our MW is no regret) and (2) a language-based formulation, in the form of a DSL, of the class of games satisfying Roughgarden smoothness, a broad characterization of those games whose approximate CCEs have cost bounded with respect to optimal. Composing (1) with (2) within Coq yields a new strategy for building distributed systems with mechanically verified complexity guarantees on the time to convergence to near-optimal system configurations.
e Multiplicative Weights Update method (MWU) is a simple yet powerful algorithm for learning linear classi ers, for ensemble learningà la boosting, for approximately solving linear and semide nite systems, for computing approximate solutions to multicommodity ow problems, and for online convex optimization, among other applications. In this brief announcement, we apply techniques from interactive theorem proving to de ne and prove correct the rst formally veri ed implementation of MWU (speci cally, we show that our MWU is no regret). Our primary application-and one justi cation of the relevance of our work to the PODC community-is to veri ed multi-agent systems, such as distributed multi-agent network ow and load balancing games, for which veri ed MWU provides a convenient method for distributed computation of approximate Coarse Correlated Equilibria. CCS CONCEPTS • eory of computation → Program veri cation; Algorithmic game theory; Convergence and learning in games; Multi-agent learning; Network games; •So ware and its engineering → Distributed systems organizing principles;
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