Byzantine Fault-Tolerant Min-Max Optimization

In this report, we consider a min-max optimization problem under adversarial manipulation, where there are $n$ cost functions $Q_i(x)$'s, up to $f$ of which may be replaced by arbitrary faulty functions by an adversary. The goal is to minimize the maximum cost over $x$ among the $n$ functions in spite of the faulty functions. The problem formulation naturally extends to Byzantine fault-tolerant distributed min-max optimization. We present a simple algorithm for fault-tolerant min-max optimization, and provide some bounds on the output of the algorithm. We also present an approximate algorithm for this problem. To the best of our knowledge, we are the first to consider this problem.

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