We consider a stochastic multi-arm bandit problem where rewards are subject to adversarial corruption. We propose a novel attack strategy that manipulates a UCB principle into pulling some non-optimal target arm $T - o(T)$ times with a cumulative cost that scales as $\sqrt{\log T}$, where $T$ is the number of rounds. We also prove the first lower bound on the cumulative attack cost. Our lower bound matches our upper bound up to $\log \log T$ factors, showing our attack to be near optimal.

We investigate optimal adversarial attacks against time series forecast made by autoregressive models. In our setting, the environment evolves according to a potentially nonlinear dynamical system. A linear autoregressive model observes the current environment state and predicts its future values. But an adversary can modify the environment state and hence indirectly manipulate the autoregressive model forecasts. The adversary wants to drive the forecasts towards some adversarial targets while minimizing environment modification. We pose this attack problem as optimal control. When the environment dynamics is linear, we provide a closed-form solution to the optimal attack using Linear Quadratic Regulator (LQR). Otherwise, we propose an approximate attack based on Model Predictive Control (MPC) and iterative LQR (iLQR). Our paper thus connects adversarial learning with control theory. We demonstrate the advantage of our methods empirically.