Convergence Conditions for Stochastic Line Search Based Optimization of Over-parametrized Models

In this paper, we deal with algorithms to solve the finite-sum problems related to fitting over-parametrized models, that typically satisfy the interpolation condition. In particular, we focus on approaches based on stochastic line searches and employing general search directions. We define conditions on the sequence of search directions that guarantee finite termination and bounds for the backtracking procedure. Moreover, we shed light on the additional property of directions needed to prove fast (linear) convergence of the general class of algorithms when applied to PL functions in the interpolation regime. From the point of view of algorithms design, the proposed analysis identifies safeguarding conditions that could be employed in relevant algorithmic framework. In particular, it could be of interest to integrate stochastic line searches within momentum, conjugate gradient or adaptive preconditioning methods.

Loss-Optimal Classification Trees: A Generalized Framework and the Logistic Case

The Classification Tree (CT) is one of the most common models in interpretable machine learning. Although such models are usually built with greedy strategies, in recent years, thanks to remarkable advances in Mixer-Integer Programming (MIP) solvers, several exact formulations of the learning problem have been developed. In this paper, we argue that some of the most relevant ones among these training models can be encapsulated within a general framework, whose instances are shaped by the specification of loss functions and regularizers. Next, we introduce a novel realization of this framework: specifically, we consider the logistic loss, handled in the MIP setting by a linear piece-wise approximation, and couple it with $\ell_1$-regularization terms. The resulting Optimal Logistic Tree model numerically proves to be able to induce trees with enhanced interpretability features and competitive generalization capabilities, compared to the state-of-the-art MIP-based approaches.

A Robust Initialization of Residual Blocks for Effective ResNet Training without Batch Normalization

Batch Normalization is an essential component of all state-of-the-art neural networks architectures. However, since it introduces many practical issues, much recent research has been devoted to designing normalization-free architectures. In this paper, we show that weights initialization is key to train ResNet-like normalization-free networks. In particular, we propose a slight modification to the summation operation of a block output to the skip connection branch, so that the whole network is correctly initialized. We show that this modified architecture achieves competitive results on CIFAR-10 without further regularization nor algorithmic modifications.