Our algorithm employsonecolumn forsubgradient descent ineach iteration, whereas thedual project subgradient algorithm requires the whole constraint matrix and conducts matrix multiplication in each iteration. In addition, a class of backpressure/max-weight algorithms [25] are developed in the control/queueing literature and the backpressure algorithm can be interpreted from a view of pressuregradient.

In this section we describe in detail the experiment conducted in 4.2. This example is based on theworkbyBlasiusetal.(2020). Inthisdemonstration wecontinuealongthatparadigm whenwe investigate a biological systems in which two species interact, one as a predator and the other as prey.

DCBO is useful in scenarios where all causal effects in a graph are changing over time.

Deep learning algorithms have shown significant development thanks tothelargepre-collected dataset, such as SQuAD [47]innatural language processing (NLP), and ImageNet [4] in computer vision.

However, if error is heavy-tailed, some policies obtain arbitrarily high reward despite achieving no more utility than the base model-a phenomenon we call catastrophic Goodhart. We adapt a discrete optimization method to measure the tails of reward models, finding that they are consistent with light-tailed error.

Onlinedistillation collaboratively trains agroup of peer models, which are treated as students, and all students gain extra knowledge from each other.

Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In this paper, we introduce Star-Shaped DDPM (SS-DDPM).