Robust learning is a critical field that seeks to develop efficient algorithms that can recover an underlying model despite possibly malicious corruptions in the data. In recent decades, being able to deal with corrupted measurements has become of crucial importance.

We show that running SGD on the`1 loss outperforms all current algorithms, theoretically8 and empirically. As pointed out, the dependency onη (or rather η) we obtain23 might notbeoptimal and isstill aninteresting open question. Therefore, in the setting we consider, the rate we34 obtaincannotbeimproved.35 To Reviewer 3. The linear model is one of the simplest model we could have considered and linear regression is36 certainly amongst the oldest and most fundamental statistical methods. AsseeninTheorem 4,thetermsdepending onthevarianceσgoto0asσ 0. Hencetheextreme42 case where there is no'nice' noise is not pathological and the algorithm still performs well.

Ifweassumethereward function is a linear combination of features, it is often the case that the number of featuresk is much lessthanthetotalnumber ofstate-action pairs. When learning a posterior from demonstrations we use Bayesian IRL [4]. Bayesian IRL uses Markov chain Monte Carlo (MCMC) sampling to sample from the posterior P(R|D). The step size was tuned to result in an accept ratio close to0.4. Ifso, then we stop gradient ascent.