Forl = 2, i. e., for 3 - cycles, thisrelationship is X ikX kj= X ij. Figure 1: Averagematchingerrorunderthe LBCmodel ( left) and LACmodel ( right).

We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations.

The majority of language model training builds on imitation learning.

Tothis end,wepropose adeep latent variable model thatiscapable oflearning rewards from demonstrations of distinct but related tasks in an unsupervised way.

However, the inferred reward function often fails to capture the underlying task objective.

The problem of inverse reinforcement learning (IRL) is relevant to a variety of tasks including valuealignment androbot learning fromdemonstration.

However, since this proof relies on the existence of a convergent subsequence, their proof does not reveal any rate forglobal convergence.

We advance both the theory and practice of robust $\ell_p$-quasinorm regression for $p \in (0,1]$ by using novel variants of iteratively reweighted least-squares (IRLS) to solve the underlying non-smooth problem. In the convex case, $p=1$, we prove that this IRLS variant converges globally at a linear rate under a mild, deterministic condition on the feature matrix called the stable range space property. In the non-convex case, $p\in(0,1)$, we prove that under a similar condition, IRLS converges locally to the global minimizer at a superlinear rate of order $2-p$; the rate becomes quadratic as $p\to 0$. We showcase the proposed methods in three applications: real phase retrieval, regression without correspondences, and robust face restoration. The results show that (1) IRLS can handle a larger number of outliers than other methods, (2) it is faster than competing methods at the same level of accuracy, (3) it restores a sparsely corrupted face image with satisfactory visual quality.