Graph Collaborative Filtering (GCF) is widely used in personalized recommendation systems. However, GCF suffers from a fundamental problem where features tend to occupy the embedding space inefficiently (by spanning only a low-dimensional subspace).

In addition, our algorithm also adapts to scenarios where the repulsion is onlyrequired among nearby fewitems intheresult sequence.

Thus training only from high value subset can lead to high bias towards a specific set of elements.

Most existing results only focus on online settings, in which agents can interact with the environment during training.

Many machine learning tasks that involve predicting an output response can be solved by training a weighted regression model.

Theorem D.2.Assumetheconditionsin Lemma D.1 and Assumption 4.1 hold. Proof.DenoterandommatrixXi = (si,ai) (si,ai)> .

Real-world reinforcement learning (RL) applications often come with possibly infinite state and action space, and in such a situation classical RL algorithms developed in the tabular setting are not applicable anymore. A popular approach to overcoming this issue is by applying function approximation techniques to the underlying structures of the Markovdecision processes (MDPs).

We also establish a global superlinear convergence rate ofO((1t)t).

The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner.