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We extend the model of stochastic bandits with adversarial corruption(Lykouriset al., 2018) to the stochastic linear optimization problem (Dani etal., 2008). Our algorithm is agnostic to the amount of corruption chosen by theadaptive adversary. The regret of the algorithm only increases linearly in theamount of corruption. Our algorithm involves using L\"owner-John's ellipsoidfor exploration and dividing time horizon into epochs with exponentiallyincreasing size to limit the influence of corruption.

Stochastic Linear Optimization with Adversarial Corruption