Reverse Ishikawa-Nesterov Learning Scheme for Fractional Mean-Field Games

Reverse Ishikawa-Nesterov's algorithm is one of the speedup techniques for finding best response set in mean-field games. However, the convergence rate was not examined so far. In this work, we evaluate the convergence rate and convergence time of reverse Ishikawa-Nesterov learning scheme for a deterministic fractional mean-field games. The fractional mean-field game problem given by a fractional controlled state dynamics and payoff that measures the gap between a mean-field term and the fractional integral of the state. First, we prove that the problem is well-posed and has a unique best response to mean-field. Second, we derive conditions for convergence of the reverse Ishikawa-based learning scheme and provide the error gap. Finally, we show that the reverse Ishikawa-Nesterov's technique outperforms the standard descent methods.