In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
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Question: Understanding the optimization trajectory is critical to understand training of deep neural networks. We show how the hyperparameters of stochastic gradient descent influence the covariance of the gradients (K) and the Hessian of the training loss (H) along this trajectory. Based on a theoretical model, we predict that using a high learning rate or a small batch size in the early phase of training leads SGD to regions of the parameter space with (1) reduced spectral norm of K, and (2) improved conditioning of K and H. We show that the point on the trajectory after which these effects hold, which we refer to as the break-even point, is reached early during training. We demonstrate these effects empirically for a range of deep neural networks applied to multiple different tasks. Finally, we apply our analysis to networks with batch normalization (BN) layers and find that it is necessary to use a high learning rate to achieve loss smoothing effects attributed previously to BN alone.

Answer: In the early phase of training of deep neural networks there exists a "break-even point" which determines properties of the entire optimization trajectory.

Question: A fundamental question in reinforcement learning is whether model-free algorithms are sample efficient. Recently, Jin et al. (2018) proposed a Q-learning algorithm with UCB exploration policy, and proved it has nearly optimal regret bound for finite-horizon episodic MDP. In this paper, we adapt Q-learning with UCB-exploration bonus to infinite-horizon MDP with discounted rewards \emph{without} accessing a generative model. We show that the extit{sample complexity of exploration} of our algorithm is bounded by $ ilde{O}({
rac{SA}{\epsilon^2(1-\gamma)^7}})$. This improves the previously best known result of $ ilde{O}({
rac{SA}{\epsilon^4(1-\gamma)^8}})$ in this setting achieved by delayed Q-learning (Strehlet al., 2006),, and matches the lower bound in terms of $\epsilon$ as well as $S$ and $A$ up to logarithmic factors.

Answer: We adapt Q-learning with UCB-exploration bonus to infinite-horizon MDP with discounted rewards without accessing a generative model, and improves the previously best known result.

Question: Stochastic neural networks with discrete random variables are an important class of models for their expressivity and interpretability. Since direct differentiation and backpropagation is not possible, Monte Carlo gradient estimation techniques have been widely employed for training such models. Efficient stochastic gradient estimators, such Straight-Through and Gumbel-Softmax, work well for shallow models with one or two stochastic layers. Their performance, however, suffers with increasing model complexity.
In this work we focus on stochastic networks with multiple layers of Boolean latent variables. To analyze such such networks, we employ the framework of harmonic analysis for Boolean functions. We use it to derive an analytic formulation for the source of bias in the biased Straight-Through estimator. Based on the analysis we propose \emph{FouST}, a simple gradient estimation algorithm that relies on three simple bias reduction steps. Extensive experiments show that FouST performs favorably compared to state-of-the-art biased estimators, while being much faster than unbiased ones. To the best of our knowledge FouST is the first gradient estimator to train up very deep stochastic neural networks, with up to 80 deterministic and 11 stochastic layers.

Answer:
We present a low-bias estimator for Boolean stochastic variable models with many stochastic layers.