Exploring Higher-Order Mutation Rates in a Game-Theoretical Setting

In higher-order meta-learning, multiple levels of meta-parameters are used, with each set of (meta)-metaparameters controlling the meta-parameters below. Higher-order mutation rates provide an interesting instance of this paradigm. Under a higher-order mutation scheme, the mutation rate is adaptive in the sense that its own mutation rate is given by a meta-mutation rate, which is then affected by a meta-metamutation rate, and so on, up to some final order n. Such schemes can be conveniently employed with population-based metaheuristics, including genetic algorithms. Recent research has investigated their use in various settings, particularly those characterized by non-stationarity. Building upon such previous work, in this paper we explore the use of higher-order mutation rates within a simple game-theoretical model: the first-price allpay auction. We first analyze the performance of populations of agents with varying meta-mutation orders and rates against a challenging benchmark bidding strategy. Subsequently, we let the meta-learning orders themselves evolve, with a population of agents with time-varying meta-learning orders competing in the auction against each other. Particular emphasis is placed on interpreting the behavior of higher-order mutation rates over time. Our work paves the way for further exploration of meta-mutational mechanisms across a wider range of settings, including reinforcement learning environments.